How to draw A ⊕ B ⊕ C as a Venn diagram?
up vote
16
down vote
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2
You see my code and please answer my two questions:
documentclass{article}
usepackage{amsmath,amssymb,mathptmx}
usepackage{pstricks}
usepackage{pst-node}
usepackage{auto-pst-pdf}
begin{document}
begin{pspicture}[showgrid](-3,-3)(8,8)%[linestyle=none]
psclip{%
pscircle(0,0){3}
pscircle(4,0){3} }
pscircle[fillcolor=blue,fillstyle=solid](2,3){3}
endpsclip
pscircle(0,0){3}
pscircle(4,0){3}
pscircle(2,3){3}
end{pspicture}
end{document}
The output picture:
Picture 1:
Its code (use TikZ):
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
fill[blue,even odd rule] (0,0) circle (3) (4,0) circle (3) (2,3) circle (3);
end{tikzpicture}
My questions:
How to make my picture like Picture 1? Truly I don't know how to fill color to it.
(After completing the previous question) Do you see the TikZ code of Picture 1? Look at the important option
even odd rule. Do PStricks have the equivalent command, macro,.. as TikZ?
Notice: I prefer PStricks to TikZ but sometimes I recognize the TikZ code is better.
Sorry if I make you being uncomfortable.
color pstricks
edited Nov 30 at 9:15
Community♦
1
asked Nov 30 at 6:08
chishimotoji
365212
This question has an open bounty worth +500
reputation from Artificial Stupidity ending in 6 days.
One or more of the answers is exemplary and worthy of an additional bounty.
a bounty to compensate space, time and energy sacrificed by @jfbu
add a comment |
up vote
16
down vote
favorite
2
You see my code and please answer my two questions:
documentclass{article}
usepackage{amsmath,amssymb,mathptmx}
usepackage{pstricks}
usepackage{pst-node}
usepackage{auto-pst-pdf}
begin{document}
begin{pspicture}[showgrid](-3,-3)(8,8)%[linestyle=none]
psclip{%
pscircle(0,0){3}
pscircle(4,0){3} }
pscircle[fillcolor=blue,fillstyle=solid](2,3){3}
endpsclip
pscircle(0,0){3}
pscircle(4,0){3}
pscircle(2,3){3}
end{pspicture}
end{document}
The output picture:
Picture 1:
Its code (use TikZ):
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
fill[blue,even odd rule] (0,0) circle (3) (4,0) circle (3) (2,3) circle (3);
end{tikzpicture}
My questions:
How to make my picture like Picture 1? Truly I don't know how to fill color to it.
(After completing the previous question) Do you see the TikZ code of Picture 1? Look at the important option
even odd rule. Do PStricks have the equivalent command, macro,.. as TikZ?
Notice: I prefer PStricks to TikZ but sometimes I recognize the TikZ code is better.
Sorry if I make you being uncomfortable.
color pstricks
edited Nov 30 at 9:15
Community♦
1
asked Nov 30 at 6:08
chishimotoji
365212
This question has an open bounty worth +500
reputation from Artificial Stupidity ending in 6 days.
One or more of the answers is exemplary and worthy of an additional bounty.
a bounty to compensate space, time and energy sacrificed by @jfbu
@ Dũng Vũ Thank you.
– chishimotoji
Nov 30 at 6:39
add a comment |
up vote
16
down vote
favorite
2
up vote
16
down vote
favorite
2
2
You see my code and please answer my two questions:
documentclass{article}
usepackage{amsmath,amssymb,mathptmx}
usepackage{pstricks}
usepackage{pst-node}
usepackage{auto-pst-pdf}
begin{document}
begin{pspicture}[showgrid](-3,-3)(8,8)%[linestyle=none]
psclip{%
pscircle(0,0){3}
pscircle(4,0){3} }
pscircle[fillcolor=blue,fillstyle=solid](2,3){3}
endpsclip
pscircle(0,0){3}
pscircle(4,0){3}
pscircle(2,3){3}
end{pspicture}
end{document}
The output picture:
Picture 1:
Its code (use TikZ):
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
fill[blue,even odd rule] (0,0) circle (3) (4,0) circle (3) (2,3) circle (3);
end{tikzpicture}
My questions:
How to make my picture like Picture 1? Truly I don't know how to fill color to it.
(After completing the previous question) Do you see the TikZ code of Picture 1? Look at the important option
even odd rule. Do PStricks have the equivalent command, macro,.. as TikZ?
Notice: I prefer PStricks to TikZ but sometimes I recognize the TikZ code is better.
Sorry if I make you being uncomfortable.
color pstricks
edited Nov 30 at 9:15
Community♦
1
asked Nov 30 at 6:08
chishimotoji
365212
You see my code and please answer my two questions:
documentclass{article}
usepackage{amsmath,amssymb,mathptmx}
usepackage{pstricks}
usepackage{pst-node}
usepackage{auto-pst-pdf}
begin{document}
begin{pspicture}[showgrid](-3,-3)(8,8)%[linestyle=none]
psclip{%
pscircle(0,0){3}
pscircle(4,0){3} }
pscircle[fillcolor=blue,fillstyle=solid](2,3){3}
endpsclip
pscircle(0,0){3}
pscircle(4,0){3}
pscircle(2,3){3}
end{pspicture}
end{document}
The output picture:
Picture 1:
Its code (use TikZ):
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
fill[blue,even odd rule] (0,0) circle (3) (4,0) circle (3) (2,3) circle (3);
end{tikzpicture}
My questions:
How to make my picture like Picture 1? Truly I don't know how to fill color to it.
(After completing the previous question) Do you see the TikZ code of Picture 1? Look at the important option
even odd rule. Do PStricks have the equivalent command, macro,.. as TikZ?
Notice: I prefer PStricks to TikZ but sometimes I recognize the TikZ code is better.
Sorry if I make you being uncomfortable.
color pstricks
color pstricks
edited Nov 30 at 9:15
Community♦
1
asked Nov 30 at 6:08
chishimotoji
365212
edited Nov 30 at 9:15
Community♦
1
asked Nov 30 at 6:08
chishimotoji
365212
edited Nov 30 at 9:15
Community♦
1
edited Nov 30 at 9:15
Community♦
1
edited Nov 30 at 9:15
Community♦
1
1
asked Nov 30 at 6:08
chishimotoji
365212
asked Nov 30 at 6:08
chishimotoji
365212
asked Nov 30 at 6:08
chishimotoji
365212
365212
This question has an open bounty worth +500
reputation from Artificial Stupidity ending in 6 days.
One or more of the answers is exemplary and worthy of an additional bounty.
a bounty to compensate space, time and energy sacrificed by @jfbu
This question has an open bounty worth +500
reputation from Artificial Stupidity ending in 6 days.
One or more of the answers is exemplary and worthy of an additional bounty.
a bounty to compensate space, time and energy sacrificed by @jfbu
@ Dũng Vũ Thank you.
– chishimotoji
Nov 30 at 6:39
add a comment |
@ Dũng Vũ Thank you.
– chishimotoji
Nov 30 at 6:39
@ Dũng Vũ Thank you.
– chishimotoji
Nov 30 at 6:39
@ Dũng Vũ Thank you.
– chishimotoji
Nov 30 at 6:39
add a comment |
5 Answers
5
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up vote
18
down vote
accepted
A PSTricks solution just for fun!
Answer 1
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}
The stroke color is left black just for a trivial reason.
Cartesian coordinates are used in response to the request.
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(0,1.5){3}
pscircle(1.29,-0.75){3}
pscircle(-1.29,-0.75){3}
}
end{pspicture}
end{document}
Answer 2
Non-zero winding rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}
Non-zero winding rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
psarcn(0,0){1}{360}{0}
pscircle{2}
}
end{pspicture}
end{document}
Even-odd rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=eofill,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}
answered Nov 30 at 7:59
Artificial Stupidity
4,32611037
As your code, the important option is " fillstyle=eofill " . I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:42
add a comment |
up vote
13
down vote
Here is an answer based on the one by @Thomas. Differences
the "elementary" regions I, II, ..., VIII are not numbered the same. My numbering is that "N" is the Roman number of "n+1" where "n" in binary is "abc", and the region is intersection of A or not A with B or not B with C or not C according to a, b, c = 0 or 1. (Boolean logic)
the macro needs only one input: a TeX formula for the set. Please enrich the syntax by adding suitable definitions converting TeX math macros into Boolean logic notation, as understood by
xintexprI have dropped all fancy customization of colors, but xparse virtuosos will add the fancy optional arguments to re-install it if needed.
Thus, the big point here is that xintexpr computes automatically from the TeX typesetting formula which regions are to be filled in diagram.
attention to
setminusit must be used either with parenthesessetminus (...)or without but then with only one lettersetminus A
ok,setminus Acap Bnot ok, because the translation here to xintexpr
boolean will do naively something equivalent toand not(A) and B, not the expectedand not(A and B). In short, you must treatsetminusas having maximally tying precedence.
documentclass[pstricks, border=10pt]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
%ExplSyntaxOn
% We could use some automated macro creation but well
% 000
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}%
% 001
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
% 010
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
% 011
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisB*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
% 100
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
% 101
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
% 110
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
EreignisB*[#1][#2]%
endpsclip
}
% 111
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisB
EreignisC
}%
}%
EreignisA*[#1][#2]%
EreignisB*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
%ExplSyntaxOff
%xintverbosetrue
makeatletter
newcommandVennFromTeX[1]{%
VennFromTeX@main #1%
}%
defVennFromTeX@main$#1${%
begingroup
xintglobaldefstrue
defoverline##1{!(##1)}% or not(##1)
defcap{&&}% or 'and'
defcup{||}% or 'or'
defoplus{ 'xor' }%
defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
letbiglempty
letbigrempty
% ....
% (add above all needed extra definitions: letBiglempty etc...)
xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
endgroup
% we could make a loop here (using @Roman), but let's stay simple
% I trust xparse experts can wrap this up in macros allowing to customize
% the colors
% ATTENTION THAT THESE arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
xintifboolexpr{MyBool(0, 0, 0)}{arealI[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 0, 1)}{arealII[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 1, 0)}{arealIII[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 1, 1)}{arealIV[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 0, 0)}{arealV[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 0, 1)}{arealVI[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 1, 0)}{arealVII[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 1, 1)}{arealVIII[cyan][0.8]}{}%
EndeEllipsen{$#1$}%
}%
makeatother
begin{document}
%testing if I, II, ..., VIII are as expected
% makeatletter
% xintFor*#1in{xintSeq{0}{7}}do{%
% begin{pspicture}(0,-1)(5,4)
% rput(2,0){thenumexpr1+#1}
% @nameuse{areal@Roman{numexpr1+#1}}[cyan][0.8]
% EndeEllipsen{}
% end{pspicture}
% }%
% end{document}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Acap Bcap C$}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Aoplus Boplus C$}
end{pspicture}
end{document}
Produces
Here is code to generate all 256 Venn diagrams. Just insert it in body of above document and don't forget to add usepackage{xintbinhex} to preamble.
% generating all graphics
% 0<= n <= 255 has eight binary digits
% abcdefgh
% a=1 -> region VIII is included (A cap B cap C)
% b=1 -> region VII is included
% ...
% h=1 -> region I is included (overline{A}cap overline{B} cap overline{C})
% We want also to describe the region as a formula...
% We could use 8 xintFor loops #1, ..., #8, but then
% we still need to convert #1*7 to binary, #2*6, #3*5 etc...
% I thus use xintbinhex per convenience but ifodd would be enough
% As I use xintbinhex, I also use a single xintFor* loop
%defgobbleone#1{}%
defgobbletwo#1#2{}%
xintFor* #1 in {xintSeq{0}{255}}:
{%
xintDigitsOfxintDecToBin{thenumexpr256+#1relax}toRegions
% due to leading 1 there will be a shift of indexing in Regions
edefx{xintifboolexpr{Regions{thenumexpr9-0}}% 000
{unexpanded{allowbreakcup
overline{A}capoverline{B}capoverline{C}}}%
{}%
xintifboolexpr{Regions{9-1}}% 001
{unexpanded{allowbreakcup overline{A}capoverline{B}cap C}}%
{}%
xintifboolexpr{Regions{9-2}}% 010
{unexpanded{allowbreakcup overline{A}cap B capoverline{C}}}%
{}%
xintifboolexpr{Regions{9-3}}% 011
{unexpanded{allowbreakcup overline{A} cap B cap C}}%
{}%
xintifboolexpr{Regions{9-4}}% 100
{unexpanded{allowbreakcup Acap overline{B}cap overline{C}}}%
{}%
xintifboolexpr{Regions{9-5}}% 101
{unexpanded{allowbreakcup Acap overline{B}cap C}}%
{}%
xintifboolexpr{Regions{9-6}}% 110
{unexpanded{allowbreakcup Acap Bcap overline{C}}}%
{}%
xintifboolexpr{Regions{9-7}}% 111
{unexpanded{allowbreakcup Acap B cap C}}%
{}%
}%
xintifForFirst{defx{emptyset}}
{oodefx{expandaftergobbletwox}}%
begin{pspicture}(0,-2)(5,4)
% I will leave here each Region as individual call, so a color can
% be added by modifying this code
xintifboolexpr{Regions{9-0}}{arealI[cyan][0.8]}{}%
xintifboolexpr{Regions{9-1}}{arealII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-2}}{arealIII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-3}}{arealIV[cyan][0.8]}{}%
xintifboolexpr{Regions{9-4}}{arealV[cyan][0.8]}{}%
xintifboolexpr{Regions{9-5}}{arealVI[cyan][0.8]}{}%
xintifboolexpr{Regions{9-6}}{arealVII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-7}}{arealVIII[cyan][0.8]}{}%
EndeEllipsen{parbox{4cm}{centering$x$}}%
end{pspicture}%
}%
Defect: the description of the set is as a disjoint union of atomic events. There might be some canonical shorter description but I never really thought about it. For example one of those diagram will represent $Omegasetminus A$ but this not the way it will be legended.
Here is how this example comes out (on page 16 of document with nothing else, i.e. it corresponds to #1 = 15 in the loop, 15=1111 means to keep atomic events 0=000, 1=001, 2=010, 3=011, which is complement of A in Omega.
Here is now with 4 sets.
This time, with TikZ code (I know neither PSTricks nor TikZ and can only survive from copying pre-existing drawing instructions; in this case I started from https://tex.stackexchange.com/a/100091/4686 by @JohnHammersley in 2013).
First I include an image of all atomic events, which are the regions to which the Atomic... macros in code next refer. (this was done for checking while preparing answer)
Here is the code for VennFromTeX, use it as VennFromTeX{$ set formula with A, B, C, D $}. Same instructions as above for three sets.
(one may wish to enlarge the syntax for example by allowing use of U or Omega and defining it in xintexpr to be simply 1, and similarly emptyset could be defined to be 0).
documentclass[12pt, tikz, border=10pt]{standalone}
usepackage{tikz}
usetikzlibrary{positioning,shapes.geometric}
usepackage{xintexpr}% for VennFromTeX
% For drawing
deffirstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
defsecondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
defthirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
deffourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
defbounding{(-5,-3) rectangle (5,4)}
% Elementary sets
% ABCD
% abcd a, b, c, d in {0, 1}
defAtomic{% 0000
begin{scope}[even odd rule]% exterior
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] bounding;
end{scope}
}%
defAtomici{% 0001
begin{scope}[even odd rule]% fourth ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
fill[yellow] fourthellip;
end{scope}
}%
defAtomicii{% 0010
begin{scope}[even odd rule]% third ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] thirdellip;
end{scope}
}%
defAtomiciii{% 0011
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] thirdellip;
end{scope}
}%
defAtomiciv{% 0100
begin{scope}[even odd rule]% second ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] secondellip;
end{scope}
}%
defAtomicv{% 0101
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] secondellip;
end{scope}
}%
defAtomicvi{% 0110
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] secondellip;
end{scope}
}%
defAtomicvii{% 0111
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip;
fill[yellow] secondellip;
end{scope}
}%
defAtomicviii{% 1000
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicix{% 1001
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicx{% 1010
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxi{% 1011
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicxii{% 1100
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxiii{% 1101
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicxiv{% 1110
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxv{% 1111
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip;
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
makeatletter
newcommandVennFromTeX[1]{VennFromTeX@main #1}%
defVennFromTeX@main$#1${%
begingroup
xintglobaldefstrue
defoverline##1{!(##1)}% or not(##1)
defcap{&&}% or 'and'
defcup{||}% or 'or'
defoplus{ 'xor' }%
defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
letbiglempty
letbigrempty
% ....
% (add above all needed extra definitions: letBiglempty etc...)
xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
endgroup
begin{tikzpicture}
xintFor* ##1 in {01}:
{%
xintFor* ##2 in {01}:
{%
xintFor* ##3 in {01}:
{%
xintFor* ##4 in {01}:
{%
xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
{csname
Atomicromannumeralnumexpr##1*8+##2*4+##3*2+##4endcsname}%
{}%
}%
}%
}%
}%
draw bounding;
% fill[white] firstellip;
% fill[white] secondellip;
% fill[white] thirdellip;
% fill[white] fourthellip;
draw firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
draw secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
draw thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
draw fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};
draw bounding node [label=below left:$U$] {};
draw (0, 0) node [yshift=+4.4cm] {$#1$};
end{tikzpicture}
}%
makeatother
begin{document}
% xintverbosetrue
VennFromTeX{$Acap Bcap Ccap D$}
VennFromTeX{$(Acap B)cup (Ccap D)$}
VennFromTeX{$(overline{A}cupoverline{B})cap(overline{C}cupoverline{D})$}
% attention to use parentheses for disambiguating setminus
VennFromTeX{$(Acup B cup C) setminus(Bcup Ccup D)$}
VennFromTeX{$(Acup B cup C) cap (Bcup Ccup D)$}
VennFromTeX{$((Asetminus (Bcup Ccup D)) cup Bcap Ccap
D)setminus (Acap Bcap Ccap D)$}
end{document}
Be careful to read the caveat top regarding usage of setminus in input.
and finally
answered yesterday
jfbu
44.9k65145
(+1) Thank you for your answer!
– chishimotoji
yesterday
(+1) Wow, fantastic!
– Thomas
yesterday
Encyclopedic answer
– Diaa
yesterday
careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check theparboxin second part how to work around that, and I also increased the vertical dimension.
– jfbu
yesterday
1
@ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
– jfbu
yesterday
|
show 12 more comments
up vote
12
down vote
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{%
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}
Some other simple example:
documentclass[pstricks]{standalone}
usepackage{pstricks}
begin{document}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(-1,0.5){1.5}% these object(s) will clip
pscircle(1,0.5){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
endpsclip
pscircle(-1,0.5){1.5}% to get the clipped circle lines
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(-1,0.5){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle(-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(0,-1){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle(-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(0,-1){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
end{document}
answered Nov 30 at 8:09
Herbert
266k23405716
1
I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:38
1
tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
– Herbert
Nov 30 at 11:20
I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
– chishimotoji
yesterday
2
clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake.psclip{the way of the knife} ... the cake .. endpsclip
– Herbert
yesterday
add a comment |
up vote
8
down vote
A TikZ solution for comparison purposes.
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
draw[even odd rule,fill=blue](0,0)circle(3)(4,0)circle(3)(2,3)circle(3);
end{tikzpicture}
end{document}
Update: To answer @ArtificialStupidity's comment
Here is a solution with different coordinate points from those of the question asked by the OP. The centres of the circles form an equilateral triangle here.
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
draw[even odd rule,fill=blue](0,0)circle(3)(3,0)circle(3)(60:3)circle(3);
end{tikzpicture}
end{document}
answered Nov 30 at 11:05
AndréC
6,62711140
@ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
– AndréC
Nov 30 at 12:05
+1 for the equilateral triangle Δ
– stendarr
Nov 30 at 14:03
add a comment |
up vote
8
down vote
With this definitions every surface can be colored.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
defKOEA{2.5,2}
defFOEA{radiusK,radiusK}
defKOEB{2,1}
defFOEB{radiusK,radiusK}
defKOEC{3,1}
defFOEC{radiusK,radiusK}
defKOEO{2.5,1.375}
defFOEO{2.5,2.5}
%uncomment the following lines to have ellipses
%defKOEA{1.9,2.2}
%defFOEA{1.4,1}
%
%defKOEB{3.3,2.2}
%defFOEB{1.2,1}
%
%defKOEC{2.75,1.4}
%defFOEC{1.4,1}
%
%defKOEO{2.5,2}
%defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
begin{document}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EndeEllipsen*{$Asetminus C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVI
EndeEllipsen*{$Acap Bcap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
arealVI
EndeEllipsen*{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EreignisC*%
EndeEllipsen*{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
arealIV
arealVIII
EndeEllipsen*{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVIII
EndeEllipsen*{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealII
arealV
arealVI
arealVII
EndeEllipsen*{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
EndeEllipsen*{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
Perhaps you want to check out this.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
%defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
%
%defKOEA{2.5,2}
%defFOEA{radiusK,radiusK}
%
%defKOEB{2,1}
%defFOEB{radiusK,radiusK}
%
%defKOEC{3,1}
%defFOEC{radiusK,radiusK}
%
%defKOEO{2.5,1.375}
%defFOEO{2.5,2.5}
%uncomment the following lines to have ellipses
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
begin{document}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EndeEllipsen{$Asetminus C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVI
EndeEllipsen{$Acap Bcap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
arealVI
EndeEllipsen{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EreignisC*%
EndeEllipsen{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
arealIV
arealVIII
EndeEllipsen{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVIII
EndeEllipsen{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealII
arealV
arealVI
arealVII
EndeEllipsen{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
EndeEllipsen{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
With the help of xint-package using xintFor and xintForpair you can write
VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
so every surface becomes an own color, or you write
VennIII[blue](0.5){2,4,6,8}{Text}%
and all becomes color blue with opacity 0.5.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
%ExplSyntaxOn
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{!O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}%
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
%ExplSyntaxOff
NewDocumentCommand{VIIIarea}{O{cyan}O{0.8}m}{%
xintifboolexpr{#3=1}{arealI[#1][#2]}{}%
xintifboolexpr{#3=2}{arealII[#1][#2]}{}%
xintifboolexpr{#3=3}{arealIII[#1][#2]}{}%
xintifboolexpr{#3=4}{arealIV[#1][#2]}{}%
xintifboolexpr{#3=5}{arealV[#1][#2]}{}%
xintifboolexpr{#3=6}{arealVI[#1][#2]}{}%
xintifboolexpr{#3=7}{arealVII[#1][#2]}{}%
xintifboolexpr{#3=8}{arealVIII[#1][#2]}{}%
}
NewDocumentCommand{VennIII}{oD(){0.8}m!g}{%
IfValueTF{#1}%
{%
xintFor ##1 in {#3}do {VIIIarea[#1][#2]{##1}}%
}%
{%
xintForpair ##1##2 in {#3}do {VIIIarea[##2][#2]{##1}}%
}%
EndeEllipsen{IfValueT{#4}{#4}}%
}
begin{document}
begin{pspicture}(0,-1)(5,4)
VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[orange]{6}{$Acap Bcap C$}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{3,5,6}{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[magenta](0.5){1,5,6,7}{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[green](0.2){1,4,8}{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{8}{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{3,5}{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
answered 2 days ago
Thomas
654212
Hey bro, is there a shorter way? Your code seem being enormously complex.
– chishimotoji
2 days ago
This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
– Thomas
2 days ago
A answer sentence is very good.
– chishimotoji
2 days ago
add a comment |
5 Answers
5
active
oldest
votes
5 Answers
5
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
18
down vote
accepted
A PSTricks solution just for fun!
Answer 1
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}
The stroke color is left black just for a trivial reason.
Cartesian coordinates are used in response to the request.
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(0,1.5){3}
pscircle(1.29,-0.75){3}
pscircle(-1.29,-0.75){3}
}
end{pspicture}
end{document}
Answer 2
Non-zero winding rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}
Non-zero winding rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
psarcn(0,0){1}{360}{0}
pscircle{2}
}
end{pspicture}
end{document}
Even-odd rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=eofill,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}
answered Nov 30 at 7:59
Artificial Stupidity
4,32611037
As your code, the important option is " fillstyle=eofill " . I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:42
add a comment |
up vote
18
down vote
accepted
A PSTricks solution just for fun!
Answer 1
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}
The stroke color is left black just for a trivial reason.
Cartesian coordinates are used in response to the request.
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(0,1.5){3}
pscircle(1.29,-0.75){3}
pscircle(-1.29,-0.75){3}
}
end{pspicture}
end{document}
Answer 2
Non-zero winding rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}
Non-zero winding rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
psarcn(0,0){1}{360}{0}
pscircle{2}
}
end{pspicture}
end{document}
Even-odd rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=eofill,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}
answered Nov 30 at 7:59
Artificial Stupidity
4,32611037
As your code, the important option is " fillstyle=eofill " . I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:42
add a comment |
up vote
18
down vote
accepted
up vote
18
down vote
accepted
A PSTricks solution just for fun!
Answer 1
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}
The stroke color is left black just for a trivial reason.
Cartesian coordinates are used in response to the request.
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(0,1.5){3}
pscircle(1.29,-0.75){3}
pscircle(-1.29,-0.75){3}
}
end{pspicture}
end{document}
Answer 2
Non-zero winding rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}
Non-zero winding rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
psarcn(0,0){1}{360}{0}
pscircle{2}
}
end{pspicture}
end{document}
Even-odd rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=eofill,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}
answered Nov 30 at 7:59
Artificial Stupidity
4,32611037
A PSTricks solution just for fun!
Answer 1
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}
The stroke color is left black just for a trivial reason.
Cartesian coordinates are used in response to the request.
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(0,1.5){3}
pscircle(1.29,-0.75){3}
pscircle(-1.29,-0.75){3}
}
end{pspicture}
end{document}
Answer 2
Non-zero winding rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}
Non-zero winding rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
psarcn(0,0){1}{360}{0}
pscircle{2}
}
end{pspicture}
end{document}
Even-odd rule:
documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=eofill,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}
answered Nov 30 at 7:59
Artificial Stupidity
4,32611037
edited Nov 30 at 9:06
answered Nov 30 at 7:59
Artificial Stupidity
4,32611037
answered Nov 30 at 7:59
Artificial Stupidity
4,32611037
answered Nov 30 at 7:59
Artificial Stupidity
4,32611037
4,32611037
As your code, the important option is " fillstyle=eofill " . I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:42
add a comment |
As your code, the important option is " fillstyle=eofill " . I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:42
As your code, the important option is " fillstyle=eofill " . I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:42
As your code, the important option is " fillstyle=eofill " . I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:42
add a comment |
up vote
13
down vote
Here is an answer based on the one by @Thomas. Differences
the "elementary" regions I, II, ..., VIII are not numbered the same. My numbering is that "N" is the Roman number of "n+1" where "n" in binary is "abc", and the region is intersection of A or not A with B or not B with C or not C according to a, b, c = 0 or 1. (Boolean logic)
the macro needs only one input: a TeX formula for the set. Please enrich the syntax by adding suitable definitions converting TeX math macros into Boolean logic notation, as understood by
xintexprI have dropped all fancy customization of colors, but xparse virtuosos will add the fancy optional arguments to re-install it if needed.
Thus, the big point here is that xintexpr computes automatically from the TeX typesetting formula which regions are to be filled in diagram.
attention to
setminusit must be used either with parenthesessetminus (...)or without but then with only one lettersetminus A
ok,setminus Acap Bnot ok, because the translation here to xintexpr
boolean will do naively something equivalent toand not(A) and B, not the expectedand not(A and B). In short, you must treatsetminusas having maximally tying precedence.
documentclass[pstricks, border=10pt]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
%ExplSyntaxOn
% We could use some automated macro creation but well
% 000
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}%
% 001
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
% 010
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
% 011
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisB*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
% 100
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
% 101
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
% 110
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
EreignisB*[#1][#2]%
endpsclip
}
% 111
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisB
EreignisC
}%
}%
EreignisA*[#1][#2]%
EreignisB*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
%ExplSyntaxOff
%xintverbosetrue
makeatletter
newcommandVennFromTeX[1]{%
VennFromTeX@main #1%
}%
defVennFromTeX@main$#1${%
begingroup
xintglobaldefstrue
defoverline##1{!(##1)}% or not(##1)
defcap{&&}% or 'and'
defcup{||}% or 'or'
defoplus{ 'xor' }%
defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
letbiglempty
letbigrempty
% ....
% (add above all needed extra definitions: letBiglempty etc...)
xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
endgroup
% we could make a loop here (using @Roman), but let's stay simple
% I trust xparse experts can wrap this up in macros allowing to customize
% the colors
% ATTENTION THAT THESE arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
xintifboolexpr{MyBool(0, 0, 0)}{arealI[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 0, 1)}{arealII[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 1, 0)}{arealIII[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 1, 1)}{arealIV[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 0, 0)}{arealV[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 0, 1)}{arealVI[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 1, 0)}{arealVII[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 1, 1)}{arealVIII[cyan][0.8]}{}%
EndeEllipsen{$#1$}%
}%
makeatother
begin{document}
%testing if I, II, ..., VIII are as expected
% makeatletter
% xintFor*#1in{xintSeq{0}{7}}do{%
% begin{pspicture}(0,-1)(5,4)
% rput(2,0){thenumexpr1+#1}
% @nameuse{areal@Roman{numexpr1+#1}}[cyan][0.8]
% EndeEllipsen{}
% end{pspicture}
% }%
% end{document}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Acap Bcap C$}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Aoplus Boplus C$}
end{pspicture}
end{document}
Produces
Here is code to generate all 256 Venn diagrams. Just insert it in body of above document and don't forget to add usepackage{xintbinhex} to preamble.
% generating all graphics
% 0<= n <= 255 has eight binary digits
% abcdefgh
% a=1 -> region VIII is included (A cap B cap C)
% b=1 -> region VII is included
% ...
% h=1 -> region I is included (overline{A}cap overline{B} cap overline{C})
% We want also to describe the region as a formula...
% We could use 8 xintFor loops #1, ..., #8, but then
% we still need to convert #1*7 to binary, #2*6, #3*5 etc...
% I thus use xintbinhex per convenience but ifodd would be enough
% As I use xintbinhex, I also use a single xintFor* loop
%defgobbleone#1{}%
defgobbletwo#1#2{}%
xintFor* #1 in {xintSeq{0}{255}}:
{%
xintDigitsOfxintDecToBin{thenumexpr256+#1relax}toRegions
% due to leading 1 there will be a shift of indexing in Regions
edefx{xintifboolexpr{Regions{thenumexpr9-0}}% 000
{unexpanded{allowbreakcup
overline{A}capoverline{B}capoverline{C}}}%
{}%
xintifboolexpr{Regions{9-1}}% 001
{unexpanded{allowbreakcup overline{A}capoverline{B}cap C}}%
{}%
xintifboolexpr{Regions{9-2}}% 010
{unexpanded{allowbreakcup overline{A}cap B capoverline{C}}}%
{}%
xintifboolexpr{Regions{9-3}}% 011
{unexpanded{allowbreakcup overline{A} cap B cap C}}%
{}%
xintifboolexpr{Regions{9-4}}% 100
{unexpanded{allowbreakcup Acap overline{B}cap overline{C}}}%
{}%
xintifboolexpr{Regions{9-5}}% 101
{unexpanded{allowbreakcup Acap overline{B}cap C}}%
{}%
xintifboolexpr{Regions{9-6}}% 110
{unexpanded{allowbreakcup Acap Bcap overline{C}}}%
{}%
xintifboolexpr{Regions{9-7}}% 111
{unexpanded{allowbreakcup Acap B cap C}}%
{}%
}%
xintifForFirst{defx{emptyset}}
{oodefx{expandaftergobbletwox}}%
begin{pspicture}(0,-2)(5,4)
% I will leave here each Region as individual call, so a color can
% be added by modifying this code
xintifboolexpr{Regions{9-0}}{arealI[cyan][0.8]}{}%
xintifboolexpr{Regions{9-1}}{arealII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-2}}{arealIII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-3}}{arealIV[cyan][0.8]}{}%
xintifboolexpr{Regions{9-4}}{arealV[cyan][0.8]}{}%
xintifboolexpr{Regions{9-5}}{arealVI[cyan][0.8]}{}%
xintifboolexpr{Regions{9-6}}{arealVII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-7}}{arealVIII[cyan][0.8]}{}%
EndeEllipsen{parbox{4cm}{centering$x$}}%
end{pspicture}%
}%
Defect: the description of the set is as a disjoint union of atomic events. There might be some canonical shorter description but I never really thought about it. For example one of those diagram will represent $Omegasetminus A$ but this not the way it will be legended.
Here is how this example comes out (on page 16 of document with nothing else, i.e. it corresponds to #1 = 15 in the loop, 15=1111 means to keep atomic events 0=000, 1=001, 2=010, 3=011, which is complement of A in Omega.
Here is now with 4 sets.
This time, with TikZ code (I know neither PSTricks nor TikZ and can only survive from copying pre-existing drawing instructions; in this case I started from https://tex.stackexchange.com/a/100091/4686 by @JohnHammersley in 2013).
First I include an image of all atomic events, which are the regions to which the Atomic... macros in code next refer. (this was done for checking while preparing answer)
Here is the code for VennFromTeX, use it as VennFromTeX{$ set formula with A, B, C, D $}. Same instructions as above for three sets.
(one may wish to enlarge the syntax for example by allowing use of U or Omega and defining it in xintexpr to be simply 1, and similarly emptyset could be defined to be 0).
documentclass[12pt, tikz, border=10pt]{standalone}
usepackage{tikz}
usetikzlibrary{positioning,shapes.geometric}
usepackage{xintexpr}% for VennFromTeX
% For drawing
deffirstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
defsecondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
defthirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
deffourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
defbounding{(-5,-3) rectangle (5,4)}
% Elementary sets
% ABCD
% abcd a, b, c, d in {0, 1}
defAtomic{% 0000
begin{scope}[even odd rule]% exterior
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] bounding;
end{scope}
}%
defAtomici{% 0001
begin{scope}[even odd rule]% fourth ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
fill[yellow] fourthellip;
end{scope}
}%
defAtomicii{% 0010
begin{scope}[even odd rule]% third ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] thirdellip;
end{scope}
}%
defAtomiciii{% 0011
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] thirdellip;
end{scope}
}%
defAtomiciv{% 0100
begin{scope}[even odd rule]% second ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] secondellip;
end{scope}
}%
defAtomicv{% 0101
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] secondellip;
end{scope}
}%
defAtomicvi{% 0110
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] secondellip;
end{scope}
}%
defAtomicvii{% 0111
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip;
fill[yellow] secondellip;
end{scope}
}%
defAtomicviii{% 1000
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicix{% 1001
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicx{% 1010
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxi{% 1011
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicxii{% 1100
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxiii{% 1101
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicxiv{% 1110
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxv{% 1111
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip;
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
makeatletter
newcommandVennFromTeX[1]{VennFromTeX@main #1}%
defVennFromTeX@main$#1${%
begingroup
xintglobaldefstrue
defoverline##1{!(##1)}% or not(##1)
defcap{&&}% or 'and'
defcup{||}% or 'or'
defoplus{ 'xor' }%
defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
letbiglempty
letbigrempty
% ....
% (add above all needed extra definitions: letBiglempty etc...)
xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
endgroup
begin{tikzpicture}
xintFor* ##1 in {01}:
{%
xintFor* ##2 in {01}:
{%
xintFor* ##3 in {01}:
{%
xintFor* ##4 in {01}:
{%
xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
{csname
Atomicromannumeralnumexpr##1*8+##2*4+##3*2+##4endcsname}%
{}%
}%
}%
}%
}%
draw bounding;
% fill[white] firstellip;
% fill[white] secondellip;
% fill[white] thirdellip;
% fill[white] fourthellip;
draw firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
draw secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
draw thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
draw fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};
draw bounding node [label=below left:$U$] {};
draw (0, 0) node [yshift=+4.4cm] {$#1$};
end{tikzpicture}
}%
makeatother
begin{document}
% xintverbosetrue
VennFromTeX{$Acap Bcap Ccap D$}
VennFromTeX{$(Acap B)cup (Ccap D)$}
VennFromTeX{$(overline{A}cupoverline{B})cap(overline{C}cupoverline{D})$}
% attention to use parentheses for disambiguating setminus
VennFromTeX{$(Acup B cup C) setminus(Bcup Ccup D)$}
VennFromTeX{$(Acup B cup C) cap (Bcup Ccup D)$}
VennFromTeX{$((Asetminus (Bcup Ccup D)) cup Bcap Ccap
D)setminus (Acap Bcap Ccap D)$}
end{document}
Be careful to read the caveat top regarding usage of setminus in input.
and finally
answered yesterday
jfbu
44.9k65145
(+1) Thank you for your answer!
– chishimotoji
yesterday
(+1) Wow, fantastic!
– Thomas
yesterday
Encyclopedic answer
– Diaa
yesterday
careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check theparboxin second part how to work around that, and I also increased the vertical dimension.
– jfbu
yesterday
1
@ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
– jfbu
yesterday
|
show 12 more comments
up vote
13
down vote
Here is an answer based on the one by @Thomas. Differences
the "elementary" regions I, II, ..., VIII are not numbered the same. My numbering is that "N" is the Roman number of "n+1" where "n" in binary is "abc", and the region is intersection of A or not A with B or not B with C or not C according to a, b, c = 0 or 1. (Boolean logic)
the macro needs only one input: a TeX formula for the set. Please enrich the syntax by adding suitable definitions converting TeX math macros into Boolean logic notation, as understood by
xintexprI have dropped all fancy customization of colors, but xparse virtuosos will add the fancy optional arguments to re-install it if needed.
Thus, the big point here is that xintexpr computes automatically from the TeX typesetting formula which regions are to be filled in diagram.
attention to
setminusit must be used either with parenthesessetminus (...)or without but then with only one lettersetminus A
ok,setminus Acap Bnot ok, because the translation here to xintexpr
boolean will do naively something equivalent toand not(A) and B, not the expectedand not(A and B). In short, you must treatsetminusas having maximally tying precedence.
documentclass[pstricks, border=10pt]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
%ExplSyntaxOn
% We could use some automated macro creation but well
% 000
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}%
% 001
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
% 010
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
% 011
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisB*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
% 100
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
% 101
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
% 110
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
EreignisB*[#1][#2]%
endpsclip
}
% 111
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisB
EreignisC
}%
}%
EreignisA*[#1][#2]%
EreignisB*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
%ExplSyntaxOff
%xintverbosetrue
makeatletter
newcommandVennFromTeX[1]{%
VennFromTeX@main #1%
}%
defVennFromTeX@main$#1${%
begingroup
xintglobaldefstrue
defoverline##1{!(##1)}% or not(##1)
defcap{&&}% or 'and'
defcup{||}% or 'or'
defoplus{ 'xor' }%
defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
letbiglempty
letbigrempty
% ....
% (add above all needed extra definitions: letBiglempty etc...)
xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
endgroup
% we could make a loop here (using @Roman), but let's stay simple
% I trust xparse experts can wrap this up in macros allowing to customize
% the colors
% ATTENTION THAT THESE arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
xintifboolexpr{MyBool(0, 0, 0)}{arealI[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 0, 1)}{arealII[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 1, 0)}{arealIII[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 1, 1)}{arealIV[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 0, 0)}{arealV[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 0, 1)}{arealVI[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 1, 0)}{arealVII[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 1, 1)}{arealVIII[cyan][0.8]}{}%
EndeEllipsen{$#1$}%
}%
makeatother
begin{document}
%testing if I, II, ..., VIII are as expected
% makeatletter
% xintFor*#1in{xintSeq{0}{7}}do{%
% begin{pspicture}(0,-1)(5,4)
% rput(2,0){thenumexpr1+#1}
% @nameuse{areal@Roman{numexpr1+#1}}[cyan][0.8]
% EndeEllipsen{}
% end{pspicture}
% }%
% end{document}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Acap Bcap C$}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Aoplus Boplus C$}
end{pspicture}
end{document}
Produces
Here is code to generate all 256 Venn diagrams. Just insert it in body of above document and don't forget to add usepackage{xintbinhex} to preamble.
% generating all graphics
% 0<= n <= 255 has eight binary digits
% abcdefgh
% a=1 -> region VIII is included (A cap B cap C)
% b=1 -> region VII is included
% ...
% h=1 -> region I is included (overline{A}cap overline{B} cap overline{C})
% We want also to describe the region as a formula...
% We could use 8 xintFor loops #1, ..., #8, but then
% we still need to convert #1*7 to binary, #2*6, #3*5 etc...
% I thus use xintbinhex per convenience but ifodd would be enough
% As I use xintbinhex, I also use a single xintFor* loop
%defgobbleone#1{}%
defgobbletwo#1#2{}%
xintFor* #1 in {xintSeq{0}{255}}:
{%
xintDigitsOfxintDecToBin{thenumexpr256+#1relax}toRegions
% due to leading 1 there will be a shift of indexing in Regions
edefx{xintifboolexpr{Regions{thenumexpr9-0}}% 000
{unexpanded{allowbreakcup
overline{A}capoverline{B}capoverline{C}}}%
{}%
xintifboolexpr{Regions{9-1}}% 001
{unexpanded{allowbreakcup overline{A}capoverline{B}cap C}}%
{}%
xintifboolexpr{Regions{9-2}}% 010
{unexpanded{allowbreakcup overline{A}cap B capoverline{C}}}%
{}%
xintifboolexpr{Regions{9-3}}% 011
{unexpanded{allowbreakcup overline{A} cap B cap C}}%
{}%
xintifboolexpr{Regions{9-4}}% 100
{unexpanded{allowbreakcup Acap overline{B}cap overline{C}}}%
{}%
xintifboolexpr{Regions{9-5}}% 101
{unexpanded{allowbreakcup Acap overline{B}cap C}}%
{}%
xintifboolexpr{Regions{9-6}}% 110
{unexpanded{allowbreakcup Acap Bcap overline{C}}}%
{}%
xintifboolexpr{Regions{9-7}}% 111
{unexpanded{allowbreakcup Acap B cap C}}%
{}%
}%
xintifForFirst{defx{emptyset}}
{oodefx{expandaftergobbletwox}}%
begin{pspicture}(0,-2)(5,4)
% I will leave here each Region as individual call, so a color can
% be added by modifying this code
xintifboolexpr{Regions{9-0}}{arealI[cyan][0.8]}{}%
xintifboolexpr{Regions{9-1}}{arealII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-2}}{arealIII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-3}}{arealIV[cyan][0.8]}{}%
xintifboolexpr{Regions{9-4}}{arealV[cyan][0.8]}{}%
xintifboolexpr{Regions{9-5}}{arealVI[cyan][0.8]}{}%
xintifboolexpr{Regions{9-6}}{arealVII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-7}}{arealVIII[cyan][0.8]}{}%
EndeEllipsen{parbox{4cm}{centering$x$}}%
end{pspicture}%
}%
Defect: the description of the set is as a disjoint union of atomic events. There might be some canonical shorter description but I never really thought about it. For example one of those diagram will represent $Omegasetminus A$ but this not the way it will be legended.
Here is how this example comes out (on page 16 of document with nothing else, i.e. it corresponds to #1 = 15 in the loop, 15=1111 means to keep atomic events 0=000, 1=001, 2=010, 3=011, which is complement of A in Omega.
Here is now with 4 sets.
This time, with TikZ code (I know neither PSTricks nor TikZ and can only survive from copying pre-existing drawing instructions; in this case I started from https://tex.stackexchange.com/a/100091/4686 by @JohnHammersley in 2013).
First I include an image of all atomic events, which are the regions to which the Atomic... macros in code next refer. (this was done for checking while preparing answer)
Here is the code for VennFromTeX, use it as VennFromTeX{$ set formula with A, B, C, D $}. Same instructions as above for three sets.
(one may wish to enlarge the syntax for example by allowing use of U or Omega and defining it in xintexpr to be simply 1, and similarly emptyset could be defined to be 0).
documentclass[12pt, tikz, border=10pt]{standalone}
usepackage{tikz}
usetikzlibrary{positioning,shapes.geometric}
usepackage{xintexpr}% for VennFromTeX
% For drawing
deffirstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
defsecondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
defthirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
deffourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
defbounding{(-5,-3) rectangle (5,4)}
% Elementary sets
% ABCD
% abcd a, b, c, d in {0, 1}
defAtomic{% 0000
begin{scope}[even odd rule]% exterior
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] bounding;
end{scope}
}%
defAtomici{% 0001
begin{scope}[even odd rule]% fourth ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
fill[yellow] fourthellip;
end{scope}
}%
defAtomicii{% 0010
begin{scope}[even odd rule]% third ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] thirdellip;
end{scope}
}%
defAtomiciii{% 0011
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] thirdellip;
end{scope}
}%
defAtomiciv{% 0100
begin{scope}[even odd rule]% second ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] secondellip;
end{scope}
}%
defAtomicv{% 0101
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] secondellip;
end{scope}
}%
defAtomicvi{% 0110
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] secondellip;
end{scope}
}%
defAtomicvii{% 0111
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip;
fill[yellow] secondellip;
end{scope}
}%
defAtomicviii{% 1000
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicix{% 1001
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicx{% 1010
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxi{% 1011
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicxii{% 1100
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxiii{% 1101
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicxiv{% 1110
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxv{% 1111
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip;
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
makeatletter
newcommandVennFromTeX[1]{VennFromTeX@main #1}%
defVennFromTeX@main$#1${%
begingroup
xintglobaldefstrue
defoverline##1{!(##1)}% or not(##1)
defcap{&&}% or 'and'
defcup{||}% or 'or'
defoplus{ 'xor' }%
defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
letbiglempty
letbigrempty
% ....
% (add above all needed extra definitions: letBiglempty etc...)
xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
endgroup
begin{tikzpicture}
xintFor* ##1 in {01}:
{%
xintFor* ##2 in {01}:
{%
xintFor* ##3 in {01}:
{%
xintFor* ##4 in {01}:
{%
xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
{csname
Atomicromannumeralnumexpr##1*8+##2*4+##3*2+##4endcsname}%
{}%
}%
}%
}%
}%
draw bounding;
% fill[white] firstellip;
% fill[white] secondellip;
% fill[white] thirdellip;
% fill[white] fourthellip;
draw firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
draw secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
draw thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
draw fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};
draw bounding node [label=below left:$U$] {};
draw (0, 0) node [yshift=+4.4cm] {$#1$};
end{tikzpicture}
}%
makeatother
begin{document}
% xintverbosetrue
VennFromTeX{$Acap Bcap Ccap D$}
VennFromTeX{$(Acap B)cup (Ccap D)$}
VennFromTeX{$(overline{A}cupoverline{B})cap(overline{C}cupoverline{D})$}
% attention to use parentheses for disambiguating setminus
VennFromTeX{$(Acup B cup C) setminus(Bcup Ccup D)$}
VennFromTeX{$(Acup B cup C) cap (Bcup Ccup D)$}
VennFromTeX{$((Asetminus (Bcup Ccup D)) cup Bcap Ccap
D)setminus (Acap Bcap Ccap D)$}
end{document}
Be careful to read the caveat top regarding usage of setminus in input.
and finally
answered yesterday
jfbu
44.9k65145
(+1) Thank you for your answer!
– chishimotoji
yesterday
(+1) Wow, fantastic!
– Thomas
yesterday
Encyclopedic answer
– Diaa
yesterday
careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check theparboxin second part how to work around that, and I also increased the vertical dimension.
– jfbu
yesterday
1
@ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
– jfbu
yesterday
|
show 12 more comments
up vote
13
down vote
up vote
13
down vote
Here is an answer based on the one by @Thomas. Differences
the "elementary" regions I, II, ..., VIII are not numbered the same. My numbering is that "N" is the Roman number of "n+1" where "n" in binary is "abc", and the region is intersection of A or not A with B or not B with C or not C according to a, b, c = 0 or 1. (Boolean logic)
the macro needs only one input: a TeX formula for the set. Please enrich the syntax by adding suitable definitions converting TeX math macros into Boolean logic notation, as understood by
xintexprI have dropped all fancy customization of colors, but xparse virtuosos will add the fancy optional arguments to re-install it if needed.
Thus, the big point here is that xintexpr computes automatically from the TeX typesetting formula which regions are to be filled in diagram.
attention to
setminusit must be used either with parenthesessetminus (...)or without but then with only one lettersetminus A
ok,setminus Acap Bnot ok, because the translation here to xintexpr
boolean will do naively something equivalent toand not(A) and B, not the expectedand not(A and B). In short, you must treatsetminusas having maximally tying precedence.
documentclass[pstricks, border=10pt]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
%ExplSyntaxOn
% We could use some automated macro creation but well
% 000
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}%
% 001
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
% 010
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
% 011
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisB*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
% 100
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
% 101
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
% 110
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
EreignisB*[#1][#2]%
endpsclip
}
% 111
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisB
EreignisC
}%
}%
EreignisA*[#1][#2]%
EreignisB*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
%ExplSyntaxOff
%xintverbosetrue
makeatletter
newcommandVennFromTeX[1]{%
VennFromTeX@main #1%
}%
defVennFromTeX@main$#1${%
begingroup
xintglobaldefstrue
defoverline##1{!(##1)}% or not(##1)
defcap{&&}% or 'and'
defcup{||}% or 'or'
defoplus{ 'xor' }%
defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
letbiglempty
letbigrempty
% ....
% (add above all needed extra definitions: letBiglempty etc...)
xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
endgroup
% we could make a loop here (using @Roman), but let's stay simple
% I trust xparse experts can wrap this up in macros allowing to customize
% the colors
% ATTENTION THAT THESE arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
xintifboolexpr{MyBool(0, 0, 0)}{arealI[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 0, 1)}{arealII[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 1, 0)}{arealIII[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 1, 1)}{arealIV[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 0, 0)}{arealV[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 0, 1)}{arealVI[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 1, 0)}{arealVII[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 1, 1)}{arealVIII[cyan][0.8]}{}%
EndeEllipsen{$#1$}%
}%
makeatother
begin{document}
%testing if I, II, ..., VIII are as expected
% makeatletter
% xintFor*#1in{xintSeq{0}{7}}do{%
% begin{pspicture}(0,-1)(5,4)
% rput(2,0){thenumexpr1+#1}
% @nameuse{areal@Roman{numexpr1+#1}}[cyan][0.8]
% EndeEllipsen{}
% end{pspicture}
% }%
% end{document}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Acap Bcap C$}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Aoplus Boplus C$}
end{pspicture}
end{document}
Produces
Here is code to generate all 256 Venn diagrams. Just insert it in body of above document and don't forget to add usepackage{xintbinhex} to preamble.
% generating all graphics
% 0<= n <= 255 has eight binary digits
% abcdefgh
% a=1 -> region VIII is included (A cap B cap C)
% b=1 -> region VII is included
% ...
% h=1 -> region I is included (overline{A}cap overline{B} cap overline{C})
% We want also to describe the region as a formula...
% We could use 8 xintFor loops #1, ..., #8, but then
% we still need to convert #1*7 to binary, #2*6, #3*5 etc...
% I thus use xintbinhex per convenience but ifodd would be enough
% As I use xintbinhex, I also use a single xintFor* loop
%defgobbleone#1{}%
defgobbletwo#1#2{}%
xintFor* #1 in {xintSeq{0}{255}}:
{%
xintDigitsOfxintDecToBin{thenumexpr256+#1relax}toRegions
% due to leading 1 there will be a shift of indexing in Regions
edefx{xintifboolexpr{Regions{thenumexpr9-0}}% 000
{unexpanded{allowbreakcup
overline{A}capoverline{B}capoverline{C}}}%
{}%
xintifboolexpr{Regions{9-1}}% 001
{unexpanded{allowbreakcup overline{A}capoverline{B}cap C}}%
{}%
xintifboolexpr{Regions{9-2}}% 010
{unexpanded{allowbreakcup overline{A}cap B capoverline{C}}}%
{}%
xintifboolexpr{Regions{9-3}}% 011
{unexpanded{allowbreakcup overline{A} cap B cap C}}%
{}%
xintifboolexpr{Regions{9-4}}% 100
{unexpanded{allowbreakcup Acap overline{B}cap overline{C}}}%
{}%
xintifboolexpr{Regions{9-5}}% 101
{unexpanded{allowbreakcup Acap overline{B}cap C}}%
{}%
xintifboolexpr{Regions{9-6}}% 110
{unexpanded{allowbreakcup Acap Bcap overline{C}}}%
{}%
xintifboolexpr{Regions{9-7}}% 111
{unexpanded{allowbreakcup Acap B cap C}}%
{}%
}%
xintifForFirst{defx{emptyset}}
{oodefx{expandaftergobbletwox}}%
begin{pspicture}(0,-2)(5,4)
% I will leave here each Region as individual call, so a color can
% be added by modifying this code
xintifboolexpr{Regions{9-0}}{arealI[cyan][0.8]}{}%
xintifboolexpr{Regions{9-1}}{arealII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-2}}{arealIII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-3}}{arealIV[cyan][0.8]}{}%
xintifboolexpr{Regions{9-4}}{arealV[cyan][0.8]}{}%
xintifboolexpr{Regions{9-5}}{arealVI[cyan][0.8]}{}%
xintifboolexpr{Regions{9-6}}{arealVII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-7}}{arealVIII[cyan][0.8]}{}%
EndeEllipsen{parbox{4cm}{centering$x$}}%
end{pspicture}%
}%
Defect: the description of the set is as a disjoint union of atomic events. There might be some canonical shorter description but I never really thought about it. For example one of those diagram will represent $Omegasetminus A$ but this not the way it will be legended.
Here is how this example comes out (on page 16 of document with nothing else, i.e. it corresponds to #1 = 15 in the loop, 15=1111 means to keep atomic events 0=000, 1=001, 2=010, 3=011, which is complement of A in Omega.
Here is now with 4 sets.
This time, with TikZ code (I know neither PSTricks nor TikZ and can only survive from copying pre-existing drawing instructions; in this case I started from https://tex.stackexchange.com/a/100091/4686 by @JohnHammersley in 2013).
First I include an image of all atomic events, which are the regions to which the Atomic... macros in code next refer. (this was done for checking while preparing answer)
Here is the code for VennFromTeX, use it as VennFromTeX{$ set formula with A, B, C, D $}. Same instructions as above for three sets.
(one may wish to enlarge the syntax for example by allowing use of U or Omega and defining it in xintexpr to be simply 1, and similarly emptyset could be defined to be 0).
documentclass[12pt, tikz, border=10pt]{standalone}
usepackage{tikz}
usetikzlibrary{positioning,shapes.geometric}
usepackage{xintexpr}% for VennFromTeX
% For drawing
deffirstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
defsecondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
defthirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
deffourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
defbounding{(-5,-3) rectangle (5,4)}
% Elementary sets
% ABCD
% abcd a, b, c, d in {0, 1}
defAtomic{% 0000
begin{scope}[even odd rule]% exterior
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] bounding;
end{scope}
}%
defAtomici{% 0001
begin{scope}[even odd rule]% fourth ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
fill[yellow] fourthellip;
end{scope}
}%
defAtomicii{% 0010
begin{scope}[even odd rule]% third ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] thirdellip;
end{scope}
}%
defAtomiciii{% 0011
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] thirdellip;
end{scope}
}%
defAtomiciv{% 0100
begin{scope}[even odd rule]% second ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] secondellip;
end{scope}
}%
defAtomicv{% 0101
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] secondellip;
end{scope}
}%
defAtomicvi{% 0110
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] secondellip;
end{scope}
}%
defAtomicvii{% 0111
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip;
fill[yellow] secondellip;
end{scope}
}%
defAtomicviii{% 1000
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicix{% 1001
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicx{% 1010
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxi{% 1011
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicxii{% 1100
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxiii{% 1101
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicxiv{% 1110
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxv{% 1111
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip;
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
makeatletter
newcommandVennFromTeX[1]{VennFromTeX@main #1}%
defVennFromTeX@main$#1${%
begingroup
xintglobaldefstrue
defoverline##1{!(##1)}% or not(##1)
defcap{&&}% or 'and'
defcup{||}% or 'or'
defoplus{ 'xor' }%
defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
letbiglempty
letbigrempty
% ....
% (add above all needed extra definitions: letBiglempty etc...)
xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
endgroup
begin{tikzpicture}
xintFor* ##1 in {01}:
{%
xintFor* ##2 in {01}:
{%
xintFor* ##3 in {01}:
{%
xintFor* ##4 in {01}:
{%
xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
{csname
Atomicromannumeralnumexpr##1*8+##2*4+##3*2+##4endcsname}%
{}%
}%
}%
}%
}%
draw bounding;
% fill[white] firstellip;
% fill[white] secondellip;
% fill[white] thirdellip;
% fill[white] fourthellip;
draw firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
draw secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
draw thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
draw fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};
draw bounding node [label=below left:$U$] {};
draw (0, 0) node [yshift=+4.4cm] {$#1$};
end{tikzpicture}
}%
makeatother
begin{document}
% xintverbosetrue
VennFromTeX{$Acap Bcap Ccap D$}
VennFromTeX{$(Acap B)cup (Ccap D)$}
VennFromTeX{$(overline{A}cupoverline{B})cap(overline{C}cupoverline{D})$}
% attention to use parentheses for disambiguating setminus
VennFromTeX{$(Acup B cup C) setminus(Bcup Ccup D)$}
VennFromTeX{$(Acup B cup C) cap (Bcup Ccup D)$}
VennFromTeX{$((Asetminus (Bcup Ccup D)) cup Bcap Ccap
D)setminus (Acap Bcap Ccap D)$}
end{document}
Be careful to read the caveat top regarding usage of setminus in input.
and finally
answered yesterday
jfbu
44.9k65145
Here is an answer based on the one by @Thomas. Differences
the "elementary" regions I, II, ..., VIII are not numbered the same. My numbering is that "N" is the Roman number of "n+1" where "n" in binary is "abc", and the region is intersection of A or not A with B or not B with C or not C according to a, b, c = 0 or 1. (Boolean logic)
the macro needs only one input: a TeX formula for the set. Please enrich the syntax by adding suitable definitions converting TeX math macros into Boolean logic notation, as understood by
xintexprI have dropped all fancy customization of colors, but xparse virtuosos will add the fancy optional arguments to re-install it if needed.
Thus, the big point here is that xintexpr computes automatically from the TeX typesetting formula which regions are to be filled in diagram.
attention to
setminusit must be used either with parenthesessetminus (...)or without but then with only one lettersetminus A
ok,setminus Acap Bnot ok, because the translation here to xintexpr
boolean will do naively something equivalent toand not(A) and B, not the expectedand not(A and B). In short, you must treatsetminusas having maximally tying precedence.
documentclass[pstricks, border=10pt]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
%ExplSyntaxOn
% We could use some automated macro creation but well
% 000
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}%
% 001
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
% 010
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
% 011
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisB*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
% 100
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
% 101
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
% 110
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
EreignisB*[#1][#2]%
endpsclip
}
% 111
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisB
EreignisC
}%
}%
EreignisA*[#1][#2]%
EreignisB*[#1][#2]%
EreignisC*[#1][#2]%
endpsclip
}
%ExplSyntaxOff
%xintverbosetrue
makeatletter
newcommandVennFromTeX[1]{%
VennFromTeX@main #1%
}%
defVennFromTeX@main$#1${%
begingroup
xintglobaldefstrue
defoverline##1{!(##1)}% or not(##1)
defcap{&&}% or 'and'
defcup{||}% or 'or'
defoplus{ 'xor' }%
defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
letbiglempty
letbigrempty
% ....
% (add above all needed extra definitions: letBiglempty etc...)
xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
endgroup
% we could make a loop here (using @Roman), but let's stay simple
% I trust xparse experts can wrap this up in macros allowing to customize
% the colors
% ATTENTION THAT THESE arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
xintifboolexpr{MyBool(0, 0, 0)}{arealI[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 0, 1)}{arealII[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 1, 0)}{arealIII[cyan][0.8]}{}%
xintifboolexpr{MyBool(0, 1, 1)}{arealIV[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 0, 0)}{arealV[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 0, 1)}{arealVI[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 1, 0)}{arealVII[cyan][0.8]}{}%
xintifboolexpr{MyBool(1, 1, 1)}{arealVIII[cyan][0.8]}{}%
EndeEllipsen{$#1$}%
}%
makeatother
begin{document}
%testing if I, II, ..., VIII are as expected
% makeatletter
% xintFor*#1in{xintSeq{0}{7}}do{%
% begin{pspicture}(0,-1)(5,4)
% rput(2,0){thenumexpr1+#1}
% @nameuse{areal@Roman{numexpr1+#1}}[cyan][0.8]
% EndeEllipsen{}
% end{pspicture}
% }%
% end{document}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Acap Bcap C$}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennFromTeX{$Aoplus Boplus C$}
end{pspicture}
end{document}
Produces
Here is code to generate all 256 Venn diagrams. Just insert it in body of above document and don't forget to add usepackage{xintbinhex} to preamble.
% generating all graphics
% 0<= n <= 255 has eight binary digits
% abcdefgh
% a=1 -> region VIII is included (A cap B cap C)
% b=1 -> region VII is included
% ...
% h=1 -> region I is included (overline{A}cap overline{B} cap overline{C})
% We want also to describe the region as a formula...
% We could use 8 xintFor loops #1, ..., #8, but then
% we still need to convert #1*7 to binary, #2*6, #3*5 etc...
% I thus use xintbinhex per convenience but ifodd would be enough
% As I use xintbinhex, I also use a single xintFor* loop
%defgobbleone#1{}%
defgobbletwo#1#2{}%
xintFor* #1 in {xintSeq{0}{255}}:
{%
xintDigitsOfxintDecToBin{thenumexpr256+#1relax}toRegions
% due to leading 1 there will be a shift of indexing in Regions
edefx{xintifboolexpr{Regions{thenumexpr9-0}}% 000
{unexpanded{allowbreakcup
overline{A}capoverline{B}capoverline{C}}}%
{}%
xintifboolexpr{Regions{9-1}}% 001
{unexpanded{allowbreakcup overline{A}capoverline{B}cap C}}%
{}%
xintifboolexpr{Regions{9-2}}% 010
{unexpanded{allowbreakcup overline{A}cap B capoverline{C}}}%
{}%
xintifboolexpr{Regions{9-3}}% 011
{unexpanded{allowbreakcup overline{A} cap B cap C}}%
{}%
xintifboolexpr{Regions{9-4}}% 100
{unexpanded{allowbreakcup Acap overline{B}cap overline{C}}}%
{}%
xintifboolexpr{Regions{9-5}}% 101
{unexpanded{allowbreakcup Acap overline{B}cap C}}%
{}%
xintifboolexpr{Regions{9-6}}% 110
{unexpanded{allowbreakcup Acap Bcap overline{C}}}%
{}%
xintifboolexpr{Regions{9-7}}% 111
{unexpanded{allowbreakcup Acap B cap C}}%
{}%
}%
xintifForFirst{defx{emptyset}}
{oodefx{expandaftergobbletwox}}%
begin{pspicture}(0,-2)(5,4)
% I will leave here each Region as individual call, so a color can
% be added by modifying this code
xintifboolexpr{Regions{9-0}}{arealI[cyan][0.8]}{}%
xintifboolexpr{Regions{9-1}}{arealII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-2}}{arealIII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-3}}{arealIV[cyan][0.8]}{}%
xintifboolexpr{Regions{9-4}}{arealV[cyan][0.8]}{}%
xintifboolexpr{Regions{9-5}}{arealVI[cyan][0.8]}{}%
xintifboolexpr{Regions{9-6}}{arealVII[cyan][0.8]}{}%
xintifboolexpr{Regions{9-7}}{arealVIII[cyan][0.8]}{}%
EndeEllipsen{parbox{4cm}{centering$x$}}%
end{pspicture}%
}%
Defect: the description of the set is as a disjoint union of atomic events. There might be some canonical shorter description but I never really thought about it. For example one of those diagram will represent $Omegasetminus A$ but this not the way it will be legended.
Here is how this example comes out (on page 16 of document with nothing else, i.e. it corresponds to #1 = 15 in the loop, 15=1111 means to keep atomic events 0=000, 1=001, 2=010, 3=011, which is complement of A in Omega.
Here is now with 4 sets.
This time, with TikZ code (I know neither PSTricks nor TikZ and can only survive from copying pre-existing drawing instructions; in this case I started from https://tex.stackexchange.com/a/100091/4686 by @JohnHammersley in 2013).
First I include an image of all atomic events, which are the regions to which the Atomic... macros in code next refer. (this was done for checking while preparing answer)
Here is the code for VennFromTeX, use it as VennFromTeX{$ set formula with A, B, C, D $}. Same instructions as above for three sets.
(one may wish to enlarge the syntax for example by allowing use of U or Omega and defining it in xintexpr to be simply 1, and similarly emptyset could be defined to be 0).
documentclass[12pt, tikz, border=10pt]{standalone}
usepackage{tikz}
usetikzlibrary{positioning,shapes.geometric}
usepackage{xintexpr}% for VennFromTeX
% For drawing
deffirstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
defsecondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
defthirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
deffourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
defbounding{(-5,-3) rectangle (5,4)}
% Elementary sets
% ABCD
% abcd a, b, c, d in {0, 1}
defAtomic{% 0000
begin{scope}[even odd rule]% exterior
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] bounding;
end{scope}
}%
defAtomici{% 0001
begin{scope}[even odd rule]% fourth ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
fill[yellow] fourthellip;
end{scope}
}%
defAtomicii{% 0010
begin{scope}[even odd rule]% third ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] thirdellip;
end{scope}
}%
defAtomiciii{% 0011
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip secondellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] thirdellip;
end{scope}
}%
defAtomiciv{% 0100
begin{scope}[even odd rule]% second ellipse corner
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] secondellip;
end{scope}
}%
defAtomicv{% 0101
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] secondellip;
end{scope}
}%
defAtomicvi{% 0110
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] secondellip;
end{scope}
}%
defAtomicvii{% 0111
begin{scope}[even odd rule]%
clip firstellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip;
fill[yellow] secondellip;
end{scope}
}%
defAtomicviii{% 1000
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicix{% 1001
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicx{% 1010
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxi{% 1011
begin{scope}[even odd rule]%
clip secondellip (-5,-5) rectangle (5,5);
clip thirdellip;
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicxii{% 1100
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxiii{% 1101
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip (-5,-5) rectangle (5,5);
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
defAtomicxiv{% 1110
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip;
clip fourthellip (-5,-5) rectangle (5,5);
fill[yellow] firstellip;
end{scope}
}%
defAtomicxv{% 1111
begin{scope}[even odd rule]%
clip secondellip;
clip thirdellip;
clip fourthellip;
fill[yellow] firstellip;
end{scope}
}%
makeatletter
newcommandVennFromTeX[1]{VennFromTeX@main #1}%
defVennFromTeX@main$#1${%
begingroup
xintglobaldefstrue
defoverline##1{!(##1)}% or not(##1)
defcap{&&}% or 'and'
defcup{||}% or 'or'
defoplus{ 'xor' }%
defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
letbiglempty
letbigrempty
% ....
% (add above all needed extra definitions: letBiglempty etc...)
xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
endgroup
begin{tikzpicture}
xintFor* ##1 in {01}:
{%
xintFor* ##2 in {01}:
{%
xintFor* ##3 in {01}:
{%
xintFor* ##4 in {01}:
{%
xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
{csname
Atomicromannumeralnumexpr##1*8+##2*4+##3*2+##4endcsname}%
{}%
}%
}%
}%
}%
draw bounding;
% fill[white] firstellip;
% fill[white] secondellip;
% fill[white] thirdellip;
% fill[white] fourthellip;
draw firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
draw secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
draw thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
draw fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};
draw bounding node [label=below left:$U$] {};
draw (0, 0) node [yshift=+4.4cm] {$#1$};
end{tikzpicture}
}%
makeatother
begin{document}
% xintverbosetrue
VennFromTeX{$Acap Bcap Ccap D$}
VennFromTeX{$(Acap B)cup (Ccap D)$}
VennFromTeX{$(overline{A}cupoverline{B})cap(overline{C}cupoverline{D})$}
% attention to use parentheses for disambiguating setminus
VennFromTeX{$(Acup B cup C) setminus(Bcup Ccup D)$}
VennFromTeX{$(Acup B cup C) cap (Bcup Ccup D)$}
VennFromTeX{$((Asetminus (Bcup Ccup D)) cup Bcap Ccap
D)setminus (Acap Bcap Ccap D)$}
end{document}
Be careful to read the caveat top regarding usage of setminus in input.
and finally
answered yesterday
jfbu
44.9k65145
edited yesterday
answered yesterday
jfbu
44.9k65145
answered yesterday
jfbu
44.9k65145
answered yesterday
jfbu
44.9k65145
44.9k65145
(+1) Thank you for your answer!
– chishimotoji
yesterday
(+1) Wow, fantastic!
– Thomas
yesterday
Encyclopedic answer
– Diaa
yesterday
careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check theparboxin second part how to work around that, and I also increased the vertical dimension.
– jfbu
yesterday
1
@ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
– jfbu
yesterday
|
show 12 more comments
(+1) Thank you for your answer!
– chishimotoji
yesterday
(+1) Wow, fantastic!
– Thomas
yesterday
Encyclopedic answer
– Diaa
yesterday
careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check theparboxin second part how to work around that, and I also increased the vertical dimension.
– jfbu
yesterday
1
@ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
– jfbu
yesterday
(+1) Thank you for your answer!
– chishimotoji
yesterday
(+1) Thank you for your answer!
– chishimotoji
yesterday
(+1) Wow, fantastic!
– Thomas
yesterday
(+1) Wow, fantastic!
– Thomas
yesterday
Encyclopedic answer
– Diaa
yesterday
Encyclopedic answer
– Diaa
yesterday
careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check the
parbox in second part how to work around that, and I also increased the vertical dimension.– jfbu
yesterday
careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check the
parbox in second part how to work around that, and I also increased the vertical dimension.– jfbu
yesterday
1
1
@ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
– jfbu
yesterday
@ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
– jfbu
yesterday
|
show 12 more comments
up vote
12
down vote
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{%
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}
Some other simple example:
documentclass[pstricks]{standalone}
usepackage{pstricks}
begin{document}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(-1,0.5){1.5}% these object(s) will clip
pscircle(1,0.5){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
endpsclip
pscircle(-1,0.5){1.5}% to get the clipped circle lines
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(-1,0.5){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle(-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(0,-1){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle(-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(0,-1){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
end{document}
answered Nov 30 at 8:09
Herbert
266k23405716
1
I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:38
1
tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
– Herbert
Nov 30 at 11:20
I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
– chishimotoji
yesterday
2
clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake.psclip{the way of the knife} ... the cake .. endpsclip
– Herbert
yesterday
add a comment |
up vote
12
down vote
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{%
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}
Some other simple example:
documentclass[pstricks]{standalone}
usepackage{pstricks}
begin{document}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(-1,0.5){1.5}% these object(s) will clip
pscircle(1,0.5){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
endpsclip
pscircle(-1,0.5){1.5}% to get the clipped circle lines
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(-1,0.5){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle(-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(0,-1){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle(-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(0,-1){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
end{document}
answered Nov 30 at 8:09
Herbert
266k23405716
1
I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:38
1
tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
– Herbert
Nov 30 at 11:20
I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
– chishimotoji
yesterday
2
clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake.psclip{the way of the knife} ... the cake .. endpsclip
– Herbert
yesterday
add a comment |
up vote
12
down vote
up vote
12
down vote
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{%
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}
Some other simple example:
documentclass[pstricks]{standalone}
usepackage{pstricks}
begin{document}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(-1,0.5){1.5}% these object(s) will clip
pscircle(1,0.5){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
endpsclip
pscircle(-1,0.5){1.5}% to get the clipped circle lines
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(-1,0.5){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle(-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(0,-1){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle(-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(0,-1){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
end{document}
answered Nov 30 at 8:09
Herbert
266k23405716
documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{%
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}
Some other simple example:
documentclass[pstricks]{standalone}
usepackage{pstricks}
begin{document}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(-1,0.5){1.5}% these object(s) will clip
pscircle(1,0.5){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
endpsclip
pscircle(-1,0.5){1.5}% to get the clipped circle lines
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(-1,0.5){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle(-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(0,-1){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle(-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
begin{pspicture}(-3.2,-3.2)(3.2,3.2)
pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
psclip{pscircle(0,-1){1.5}}
pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
endpsclip
pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
pscircle(0,-1){1.5}
pscircle(1,0.5){1.5}
end{pspicture}
end{document}
answered Nov 30 at 8:09
Herbert
266k23405716
edited yesterday
answered Nov 30 at 8:09
Herbert
266k23405716
answered Nov 30 at 8:09
Herbert
266k23405716
answered Nov 30 at 8:09
Herbert
266k23405716
266k23405716
1
I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:38
1
tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
– Herbert
Nov 30 at 11:20
I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
– chishimotoji
yesterday
2
clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake.psclip{the way of the knife} ... the cake .. endpsclip
– Herbert
yesterday
add a comment |
1
I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:38
1
tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
– Herbert
Nov 30 at 11:20
I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
– chishimotoji
yesterday
2
clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake.psclip{the way of the knife} ... the cake .. endpsclip
– Herbert
yesterday
1
1
I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:38
I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
– chishimotoji
Nov 30 at 8:38
1
1
tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
– Herbert
Nov 30 at 11:20
tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
– Herbert
Nov 30 at 11:20
I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
– chishimotoji
yesterday
I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
– chishimotoji
yesterday
2
2
clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake.
psclip{the way of the knife} ... the cake .. endpsclip– Herbert
yesterday
clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake.
psclip{the way of the knife} ... the cake .. endpsclip– Herbert
yesterday
add a comment |
up vote
8
down vote
A TikZ solution for comparison purposes.
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
draw[even odd rule,fill=blue](0,0)circle(3)(4,0)circle(3)(2,3)circle(3);
end{tikzpicture}
end{document}
Update: To answer @ArtificialStupidity's comment
Here is a solution with different coordinate points from those of the question asked by the OP. The centres of the circles form an equilateral triangle here.
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
draw[even odd rule,fill=blue](0,0)circle(3)(3,0)circle(3)(60:3)circle(3);
end{tikzpicture}
end{document}
answered Nov 30 at 11:05
AndréC
6,62711140
@ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
– AndréC
Nov 30 at 12:05
+1 for the equilateral triangle Δ
– stendarr
Nov 30 at 14:03
add a comment |
up vote
8
down vote
A TikZ solution for comparison purposes.
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
draw[even odd rule,fill=blue](0,0)circle(3)(4,0)circle(3)(2,3)circle(3);
end{tikzpicture}
end{document}
Update: To answer @ArtificialStupidity's comment
Here is a solution with different coordinate points from those of the question asked by the OP. The centres of the circles form an equilateral triangle here.
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
draw[even odd rule,fill=blue](0,0)circle(3)(3,0)circle(3)(60:3)circle(3);
end{tikzpicture}
end{document}
answered Nov 30 at 11:05
AndréC
6,62711140
@ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
– AndréC
Nov 30 at 12:05
+1 for the equilateral triangle Δ
– stendarr
Nov 30 at 14:03
add a comment |
up vote
8
down vote
up vote
8
down vote
A TikZ solution for comparison purposes.
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
draw[even odd rule,fill=blue](0,0)circle(3)(4,0)circle(3)(2,3)circle(3);
end{tikzpicture}
end{document}
Update: To answer @ArtificialStupidity's comment
Here is a solution with different coordinate points from those of the question asked by the OP. The centres of the circles form an equilateral triangle here.
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
draw[even odd rule,fill=blue](0,0)circle(3)(3,0)circle(3)(60:3)circle(3);
end{tikzpicture}
end{document}
answered Nov 30 at 11:05
AndréC
6,62711140
A TikZ solution for comparison purposes.
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
draw[even odd rule,fill=blue](0,0)circle(3)(4,0)circle(3)(2,3)circle(3);
end{tikzpicture}
end{document}
Update: To answer @ArtificialStupidity's comment
Here is a solution with different coordinate points from those of the question asked by the OP. The centres of the circles form an equilateral triangle here.
documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
draw[even odd rule,fill=blue](0,0)circle(3)(3,0)circle(3)(60:3)circle(3);
end{tikzpicture}
end{document}
answered Nov 30 at 11:05
AndréC
6,62711140
edited Nov 30 at 12:11
answered Nov 30 at 11:05
AndréC
6,62711140
answered Nov 30 at 11:05
AndréC
6,62711140
answered Nov 30 at 11:05
AndréC
6,62711140
6,62711140
@ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
– AndréC
Nov 30 at 12:05
+1 for the equilateral triangle Δ
– stendarr
Nov 30 at 14:03
add a comment |
@ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
– AndréC
Nov 30 at 12:05
+1 for the equilateral triangle Δ
– stendarr
Nov 30 at 14:03
@ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
– AndréC
Nov 30 at 12:05
@ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
– AndréC
Nov 30 at 12:05
+1 for the equilateral triangle Δ
– stendarr
Nov 30 at 14:03
+1 for the equilateral triangle Δ
– stendarr
Nov 30 at 14:03
add a comment |
up vote
8
down vote
With this definitions every surface can be colored.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
defKOEA{2.5,2}
defFOEA{radiusK,radiusK}
defKOEB{2,1}
defFOEB{radiusK,radiusK}
defKOEC{3,1}
defFOEC{radiusK,radiusK}
defKOEO{2.5,1.375}
defFOEO{2.5,2.5}
%uncomment the following lines to have ellipses
%defKOEA{1.9,2.2}
%defFOEA{1.4,1}
%
%defKOEB{3.3,2.2}
%defFOEB{1.2,1}
%
%defKOEC{2.75,1.4}
%defFOEC{1.4,1}
%
%defKOEO{2.5,2}
%defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
begin{document}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EndeEllipsen*{$Asetminus C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVI
EndeEllipsen*{$Acap Bcap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
arealVI
EndeEllipsen*{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EreignisC*%
EndeEllipsen*{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
arealIV
arealVIII
EndeEllipsen*{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVIII
EndeEllipsen*{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealII
arealV
arealVI
arealVII
EndeEllipsen*{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
EndeEllipsen*{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
Perhaps you want to check out this.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
%defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
%
%defKOEA{2.5,2}
%defFOEA{radiusK,radiusK}
%
%defKOEB{2,1}
%defFOEB{radiusK,radiusK}
%
%defKOEC{3,1}
%defFOEC{radiusK,radiusK}
%
%defKOEO{2.5,1.375}
%defFOEO{2.5,2.5}
%uncomment the following lines to have ellipses
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
begin{document}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EndeEllipsen{$Asetminus C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVI
EndeEllipsen{$Acap Bcap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
arealVI
EndeEllipsen{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EreignisC*%
EndeEllipsen{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
arealIV
arealVIII
EndeEllipsen{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVIII
EndeEllipsen{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealII
arealV
arealVI
arealVII
EndeEllipsen{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
EndeEllipsen{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
With the help of xint-package using xintFor and xintForpair you can write
VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
so every surface becomes an own color, or you write
VennIII[blue](0.5){2,4,6,8}{Text}%
and all becomes color blue with opacity 0.5.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
%ExplSyntaxOn
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{!O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}%
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
%ExplSyntaxOff
NewDocumentCommand{VIIIarea}{O{cyan}O{0.8}m}{%
xintifboolexpr{#3=1}{arealI[#1][#2]}{}%
xintifboolexpr{#3=2}{arealII[#1][#2]}{}%
xintifboolexpr{#3=3}{arealIII[#1][#2]}{}%
xintifboolexpr{#3=4}{arealIV[#1][#2]}{}%
xintifboolexpr{#3=5}{arealV[#1][#2]}{}%
xintifboolexpr{#3=6}{arealVI[#1][#2]}{}%
xintifboolexpr{#3=7}{arealVII[#1][#2]}{}%
xintifboolexpr{#3=8}{arealVIII[#1][#2]}{}%
}
NewDocumentCommand{VennIII}{oD(){0.8}m!g}{%
IfValueTF{#1}%
{%
xintFor ##1 in {#3}do {VIIIarea[#1][#2]{##1}}%
}%
{%
xintForpair ##1##2 in {#3}do {VIIIarea[##2][#2]{##1}}%
}%
EndeEllipsen{IfValueT{#4}{#4}}%
}
begin{document}
begin{pspicture}(0,-1)(5,4)
VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[orange]{6}{$Acap Bcap C$}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{3,5,6}{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[magenta](0.5){1,5,6,7}{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[green](0.2){1,4,8}{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{8}{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{3,5}{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
answered 2 days ago
Thomas
654212
Hey bro, is there a shorter way? Your code seem being enormously complex.
– chishimotoji
2 days ago
This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
– Thomas
2 days ago
A answer sentence is very good.
– chishimotoji
2 days ago
add a comment |
up vote
8
down vote
With this definitions every surface can be colored.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
defKOEA{2.5,2}
defFOEA{radiusK,radiusK}
defKOEB{2,1}
defFOEB{radiusK,radiusK}
defKOEC{3,1}
defFOEC{radiusK,radiusK}
defKOEO{2.5,1.375}
defFOEO{2.5,2.5}
%uncomment the following lines to have ellipses
%defKOEA{1.9,2.2}
%defFOEA{1.4,1}
%
%defKOEB{3.3,2.2}
%defFOEB{1.2,1}
%
%defKOEC{2.75,1.4}
%defFOEC{1.4,1}
%
%defKOEO{2.5,2}
%defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
begin{document}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EndeEllipsen*{$Asetminus C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVI
EndeEllipsen*{$Acap Bcap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
arealVI
EndeEllipsen*{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EreignisC*%
EndeEllipsen*{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
arealIV
arealVIII
EndeEllipsen*{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVIII
EndeEllipsen*{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealII
arealV
arealVI
arealVII
EndeEllipsen*{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
EndeEllipsen*{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
Perhaps you want to check out this.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
%defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
%
%defKOEA{2.5,2}
%defFOEA{radiusK,radiusK}
%
%defKOEB{2,1}
%defFOEB{radiusK,radiusK}
%
%defKOEC{3,1}
%defFOEC{radiusK,radiusK}
%
%defKOEO{2.5,1.375}
%defFOEO{2.5,2.5}
%uncomment the following lines to have ellipses
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
begin{document}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EndeEllipsen{$Asetminus C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVI
EndeEllipsen{$Acap Bcap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
arealVI
EndeEllipsen{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EreignisC*%
EndeEllipsen{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
arealIV
arealVIII
EndeEllipsen{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVIII
EndeEllipsen{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealII
arealV
arealVI
arealVII
EndeEllipsen{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
EndeEllipsen{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
With the help of xint-package using xintFor and xintForpair you can write
VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
so every surface becomes an own color, or you write
VennIII[blue](0.5){2,4,6,8}{Text}%
and all becomes color blue with opacity 0.5.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
%ExplSyntaxOn
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{!O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}%
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
%ExplSyntaxOff
NewDocumentCommand{VIIIarea}{O{cyan}O{0.8}m}{%
xintifboolexpr{#3=1}{arealI[#1][#2]}{}%
xintifboolexpr{#3=2}{arealII[#1][#2]}{}%
xintifboolexpr{#3=3}{arealIII[#1][#2]}{}%
xintifboolexpr{#3=4}{arealIV[#1][#2]}{}%
xintifboolexpr{#3=5}{arealV[#1][#2]}{}%
xintifboolexpr{#3=6}{arealVI[#1][#2]}{}%
xintifboolexpr{#3=7}{arealVII[#1][#2]}{}%
xintifboolexpr{#3=8}{arealVIII[#1][#2]}{}%
}
NewDocumentCommand{VennIII}{oD(){0.8}m!g}{%
IfValueTF{#1}%
{%
xintFor ##1 in {#3}do {VIIIarea[#1][#2]{##1}}%
}%
{%
xintForpair ##1##2 in {#3}do {VIIIarea[##2][#2]{##1}}%
}%
EndeEllipsen{IfValueT{#4}{#4}}%
}
begin{document}
begin{pspicture}(0,-1)(5,4)
VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[orange]{6}{$Acap Bcap C$}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{3,5,6}{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[magenta](0.5){1,5,6,7}{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[green](0.2){1,4,8}{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{8}{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{3,5}{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
answered 2 days ago
Thomas
654212
Hey bro, is there a shorter way? Your code seem being enormously complex.
– chishimotoji
2 days ago
This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
– Thomas
2 days ago
A answer sentence is very good.
– chishimotoji
2 days ago
add a comment |
up vote
8
down vote
up vote
8
down vote
With this definitions every surface can be colored.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
defKOEA{2.5,2}
defFOEA{radiusK,radiusK}
defKOEB{2,1}
defFOEB{radiusK,radiusK}
defKOEC{3,1}
defFOEC{radiusK,radiusK}
defKOEO{2.5,1.375}
defFOEO{2.5,2.5}
%uncomment the following lines to have ellipses
%defKOEA{1.9,2.2}
%defFOEA{1.4,1}
%
%defKOEB{3.3,2.2}
%defFOEB{1.2,1}
%
%defKOEC{2.75,1.4}
%defFOEC{1.4,1}
%
%defKOEO{2.5,2}
%defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
begin{document}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EndeEllipsen*{$Asetminus C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVI
EndeEllipsen*{$Acap Bcap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
arealVI
EndeEllipsen*{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EreignisC*%
EndeEllipsen*{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
arealIV
arealVIII
EndeEllipsen*{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVIII
EndeEllipsen*{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealII
arealV
arealVI
arealVII
EndeEllipsen*{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
EndeEllipsen*{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
Perhaps you want to check out this.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
%defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
%
%defKOEA{2.5,2}
%defFOEA{radiusK,radiusK}
%
%defKOEB{2,1}
%defFOEB{radiusK,radiusK}
%
%defKOEC{3,1}
%defFOEC{radiusK,radiusK}
%
%defKOEO{2.5,1.375}
%defFOEO{2.5,2.5}
%uncomment the following lines to have ellipses
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
begin{document}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EndeEllipsen{$Asetminus C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVI
EndeEllipsen{$Acap Bcap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
arealVI
EndeEllipsen{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EreignisC*%
EndeEllipsen{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
arealIV
arealVIII
EndeEllipsen{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVIII
EndeEllipsen{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealII
arealV
arealVI
arealVII
EndeEllipsen{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
EndeEllipsen{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
With the help of xint-package using xintFor and xintForpair you can write
VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
so every surface becomes an own color, or you write
VennIII[blue](0.5){2,4,6,8}{Text}%
and all becomes color blue with opacity 0.5.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
%ExplSyntaxOn
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{!O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}%
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
%ExplSyntaxOff
NewDocumentCommand{VIIIarea}{O{cyan}O{0.8}m}{%
xintifboolexpr{#3=1}{arealI[#1][#2]}{}%
xintifboolexpr{#3=2}{arealII[#1][#2]}{}%
xintifboolexpr{#3=3}{arealIII[#1][#2]}{}%
xintifboolexpr{#3=4}{arealIV[#1][#2]}{}%
xintifboolexpr{#3=5}{arealV[#1][#2]}{}%
xintifboolexpr{#3=6}{arealVI[#1][#2]}{}%
xintifboolexpr{#3=7}{arealVII[#1][#2]}{}%
xintifboolexpr{#3=8}{arealVIII[#1][#2]}{}%
}
NewDocumentCommand{VennIII}{oD(){0.8}m!g}{%
IfValueTF{#1}%
{%
xintFor ##1 in {#3}do {VIIIarea[#1][#2]{##1}}%
}%
{%
xintForpair ##1##2 in {#3}do {VIIIarea[##2][#2]{##1}}%
}%
EndeEllipsen{IfValueT{#4}{#4}}%
}
begin{document}
begin{pspicture}(0,-1)(5,4)
VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[orange]{6}{$Acap Bcap C$}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{3,5,6}{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[magenta](0.5){1,5,6,7}{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[green](0.2){1,4,8}{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{8}{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{3,5}{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
answered 2 days ago
Thomas
654212
With this definitions every surface can be colored.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
defKOEA{2.5,2}
defFOEA{radiusK,radiusK}
defKOEB{2,1}
defFOEB{radiusK,radiusK}
defKOEC{3,1}
defFOEC{radiusK,radiusK}
defKOEO{2.5,1.375}
defFOEO{2.5,2.5}
%uncomment the following lines to have ellipses
%defKOEA{1.9,2.2}
%defFOEA{1.4,1}
%
%defKOEB{3.3,2.2}
%defFOEB{1.2,1}
%
%defKOEC{2.75,1.4}
%defFOEC{1.4,1}
%
%defKOEO{2.5,2}
%defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
begin{document}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EndeEllipsen*{$Asetminus C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVI
EndeEllipsen*{$Acap Bcap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
arealVI
EndeEllipsen*{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EreignisC*%
EndeEllipsen*{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
arealIV
arealVIII
EndeEllipsen*{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVIII
EndeEllipsen*{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealII
arealV
arealVI
arealVII
EndeEllipsen*{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
EndeEllipsen*{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
Perhaps you want to check out this.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
%defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
%
%defKOEA{2.5,2}
%defFOEA{radiusK,radiusK}
%
%defKOEB{2,1}
%defFOEB{radiusK,radiusK}
%
%defKOEC{3,1}
%defFOEC{radiusK,radiusK}
%
%defKOEO{2.5,1.375}
%defFOEO{2.5,2.5}
%uncomment the following lines to have ellipses
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
begin{document}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EndeEllipsen{$Asetminus C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVI
EndeEllipsen{$Acap Bcap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
arealVI
EndeEllipsen{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
EreignisC*%
EndeEllipsen{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealI
arealIV
arealVIII
EndeEllipsen{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealVIII
EndeEllipsen{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealII
arealV
arealVI
arealVII
EndeEllipsen{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}[shift=-4](0,-1)(5,4)
arealIII
arealV
EndeEllipsen{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
With the help of xint-package using xintFor and xintForpair you can write
VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
so every surface becomes an own color, or you write
VennIII[blue](0.5){2,4,6,8}{Text}%
and all becomes color blue with opacity 0.5.
documentclass[pstricks]{standalone}
usepackage{pst-node}
usepackage{xparse,xintexpr}
defKOEA{1.9,2.2}
defFOEA{1.4,1}
defKOEB{3.3,2.2}
defFOEB{1.2,1}
defKOEC{2.75,1.4}
defFOEC{1.4,1}
defKOEO{2.5,2}
defFOEO{2.5,2.0}
NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
psellipse(KOEA)(FOEA)}%
}
NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
psellipse(KOEB)(FOEB)}%
}
NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
psellipse(KOEC)(FOEC)}%
}
NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
IfBooleanTF{#1}{%
psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
psellipse(KOEO)(FOEO)}%
}
NewDocumentCommand{EndeEllipsen}{sm}{%
EreignisOmega%
pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
EreignisA
EreignisB
EreignisC
rput[t](E){#2}%
IfBooleanF{#1}{%
rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
}%
}
NewDocumentCommand{codeclip}{m}{%
pscustom[linestyle=none]{%
code{/clip /eoclip load def}%
psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
#1
}%
}
%ExplSyntaxOn
NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
}%
codeclip{%
EreignisB
}%
codeclip{%
EreignisC
}%
}%
EreignisOmega*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIII}{!O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisC
}%
codeclip{%
EreignisC
}%
}%
EreignisB*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisB
}%
}%
EreignisA*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
psclip{EreignisB}%
psclip{EreignisC}%
EreignisA*[#1][#2]%
endpsclip
endpsclip
}
NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
EreignisC
}%
codeclip{%
EreignisA
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
psclip{%
codeclip{%
EreignisA
EreignisB
}%
codeclip{%
EreignisB
}%
}%
EreignisC*[#1][#2]%
endpsclip
}
%ExplSyntaxOff
NewDocumentCommand{VIIIarea}{O{cyan}O{0.8}m}{%
xintifboolexpr{#3=1}{arealI[#1][#2]}{}%
xintifboolexpr{#3=2}{arealII[#1][#2]}{}%
xintifboolexpr{#3=3}{arealIII[#1][#2]}{}%
xintifboolexpr{#3=4}{arealIV[#1][#2]}{}%
xintifboolexpr{#3=5}{arealV[#1][#2]}{}%
xintifboolexpr{#3=6}{arealVI[#1][#2]}{}%
xintifboolexpr{#3=7}{arealVII[#1][#2]}{}%
xintifboolexpr{#3=8}{arealVIII[#1][#2]}{}%
}
NewDocumentCommand{VennIII}{oD(){0.8}m!g}{%
IfValueTF{#1}%
{%
xintFor ##1 in {#3}do {VIIIarea[#1][#2]{##1}}%
}%
{%
xintForpair ##1##2 in {#3}do {VIIIarea[##2][#2]{##1}}%
}%
EndeEllipsen{IfValueT{#4}{#4}}%
}
begin{document}
begin{pspicture}(0,-1)(5,4)
VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[orange]{6}{$Acap Bcap C$}%
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{3,5,6}{$Acap (Bcup C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[magenta](0.5){1,5,6,7}{$(overline{A}cap overline{B})cup C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[green](0.2){1,4,8}{$overline{A}setminus (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{8}{$(overline{A}setminus B)cap C$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(Asetminus B)cup (Bcap C)$}
end{pspicture}
begin{pspicture}(0,-1)(5,4)
VennIII[cyan]{3,5}{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
end{pspicture}
end{document}
answered 2 days ago
Thomas
654212
edited 2 days ago
answered 2 days ago
Thomas
654212
answered 2 days ago
Thomas
654212
answered 2 days ago
Thomas
654212
654212
Hey bro, is there a shorter way? Your code seem being enormously complex.
– chishimotoji
2 days ago
This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
– Thomas
2 days ago
A answer sentence is very good.
– chishimotoji
2 days ago
add a comment |
Hey bro, is there a shorter way? Your code seem being enormously complex.
– chishimotoji
2 days ago
This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
– Thomas
2 days ago
A answer sentence is very good.
– chishimotoji
2 days ago
Hey bro, is there a shorter way? Your code seem being enormously complex.
– chishimotoji
2 days ago
Hey bro, is there a shorter way? Your code seem being enormously complex.
– chishimotoji
2 days ago
This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
– Thomas
2 days ago
This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
– Thomas
2 days ago
A answer sentence is very good.
– chishimotoji
2 days ago
A answer sentence is very good.
– chishimotoji
2 days ago
add a comment |
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@ Dũng Vũ Thank you.
– chishimotoji
Nov 30 at 6:39