Intersection of a cone of light from point $p=(x,y,z)$ and $xy$-plane
I am working on a programming problem where I want to display a cone of light from a point $p=(x,y,z)$ lying in space to some direction.
For example, if $p=(0,0,1)$, and the light is facing straight down with angle of 90 degrees, the intersection at $xy$-plane would be a circle with radius $r = 1$ (circular cone).
The equation(s) that I am looking for should be parametrized in such way that I can input $x, y, z$ and the two angles (altitude, azimuth), and get the intersection as output.
Please, no straight answers, I want to work this out by myself ;-)
analytic-geometry
asked Nov 18 at 15:28
ZzZzZz
61
add a comment |
I am working on a programming problem where I want to display a cone of light from a point $p=(x,y,z)$ lying in space to some direction.
For example, if $p=(0,0,1)$, and the light is facing straight down with angle of 90 degrees, the intersection at $xy$-plane would be a circle with radius $r = 1$ (circular cone).
The equation(s) that I am looking for should be parametrized in such way that I can input $x, y, z$ and the two angles (altitude, azimuth), and get the intersection as output.
Please, no straight answers, I want to work this out by myself ;-)
analytic-geometry
asked Nov 18 at 15:28
ZzZzZz
61
Start with the standard equation of the cone $z = sqrt{x^2+y^2}$. Then use transformations (first rotations and then translations) to put the cone where you want. Finally set $z=0$ in the equation to see where it intersects the $x,y$-plane.
– Nick
Nov 18 at 15:34
Write the equation for the cone in 3D and than set z=0.
– Moti
Nov 18 at 16:22
add a comment |
I am working on a programming problem where I want to display a cone of light from a point $p=(x,y,z)$ lying in space to some direction.
For example, if $p=(0,0,1)$, and the light is facing straight down with angle of 90 degrees, the intersection at $xy$-plane would be a circle with radius $r = 1$ (circular cone).
The equation(s) that I am looking for should be parametrized in such way that I can input $x, y, z$ and the two angles (altitude, azimuth), and get the intersection as output.
Please, no straight answers, I want to work this out by myself ;-)
analytic-geometry
asked Nov 18 at 15:28
ZzZzZz
61
I am working on a programming problem where I want to display a cone of light from a point $p=(x,y,z)$ lying in space to some direction.
For example, if $p=(0,0,1)$, and the light is facing straight down with angle of 90 degrees, the intersection at $xy$-plane would be a circle with radius $r = 1$ (circular cone).
The equation(s) that I am looking for should be parametrized in such way that I can input $x, y, z$ and the two angles (altitude, azimuth), and get the intersection as output.
Please, no straight answers, I want to work this out by myself ;-)
analytic-geometry
analytic-geometry
asked Nov 18 at 15:28
ZzZzZz
61
asked Nov 18 at 15:28
ZzZzZz
61
asked Nov 18 at 15:28
ZzZzZz
61
asked Nov 18 at 15:28
ZzZzZz
61
asked Nov 18 at 15:28
ZzZzZz
61
61
Start with the standard equation of the cone $z = sqrt{x^2+y^2}$. Then use transformations (first rotations and then translations) to put the cone where you want. Finally set $z=0$ in the equation to see where it intersects the $x,y$-plane.
– Nick
Nov 18 at 15:34
Write the equation for the cone in 3D and than set z=0.
– Moti
Nov 18 at 16:22
add a comment |
Start with the standard equation of the cone $z = sqrt{x^2+y^2}$. Then use transformations (first rotations and then translations) to put the cone where you want. Finally set $z=0$ in the equation to see where it intersects the $x,y$-plane.
– Nick
Nov 18 at 15:34
Write the equation for the cone in 3D and than set z=0.
– Moti
Nov 18 at 16:22
Start with the standard equation of the cone $z = sqrt{x^2+y^2}$. Then use transformations (first rotations and then translations) to put the cone where you want. Finally set $z=0$ in the equation to see where it intersects the $x,y$-plane.
– Nick
Nov 18 at 15:34
Start with the standard equation of the cone $z = sqrt{x^2+y^2}$. Then use transformations (first rotations and then translations) to put the cone where you want. Finally set $z=0$ in the equation to see where it intersects the $x,y$-plane.
– Nick
Nov 18 at 15:34
Write the equation for the cone in 3D and than set z=0.
– Moti
Nov 18 at 16:22
Write the equation for the cone in 3D and than set z=0.
– Moti
Nov 18 at 16:22
add a comment |
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Start with the standard equation of the cone $z = sqrt{x^2+y^2}$. Then use transformations (first rotations and then translations) to put the cone where you want. Finally set $z=0$ in the equation to see where it intersects the $x,y$-plane.
– Nick
Nov 18 at 15:34
Write the equation for the cone in 3D and than set z=0.
– Moti
Nov 18 at 16:22