Discoball!
Discoball!
...or a shader that demonstrates a parabolic transformation in the upper half space model of hyperbolic 3-space. The flat plane is the "plane at infinity". The sphere is a horosphere that kisses the plane at the origin, which is also the ideal center of the horosphere and the single fixed point of the transformation. Interact with and edit the shader here: http://bit.ly/2Cd8Cuq
I hope to extend this shader to allow displaying other classes of transformations of hyperbolic space (elliptic, hyperbolic, loxodromic).
This was my first go at using Shadertoy. It's pretty cool and relatively easy to use, especially because there is such a large library of examples. I recommend the tutorial at the following link to get started.
http://jamie-wong.com/2016/07/15/ray-marching-signed-distance-functions/
https://youtu.be/ZKL9lGX9XHc
...or a shader that demonstrates a parabolic transformation in the upper half space model of hyperbolic 3-space. The flat plane is the "plane at infinity". The sphere is a horosphere that kisses the plane at the origin, which is also the ideal center of the horosphere and the single fixed point of the transformation. Interact with and edit the shader here: http://bit.ly/2Cd8Cuq
I hope to extend this shader to allow displaying other classes of transformations of hyperbolic space (elliptic, hyperbolic, loxodromic).
This was my first go at using Shadertoy. It's pretty cool and relatively easy to use, especially because there is such a large library of examples. I recommend the tutorial at the following link to get started.
http://jamie-wong.com/2016/07/15/ray-marching-signed-distance-functions/
https://youtu.be/ZKL9lGX9XHc
Möbius transformation revealed
ReplyDeleteyoutube.com - Moebius Transformations Revealed
There's a flower with petals on the plane of that which would be fun to see highlighted.
ReplyDeleteCool! :)
ReplyDelete