Möbius Transformation

[insignia]

For the past few weeks I've been trying to figure out a method for rendering hyperbolic geometry using Love 2d. At this point I figured out how to use Möbius transformations and here is my product. The equation I used should hopefully (If God himself is willing...) be a precursor to effectivly helping render hyperbolic geometry.

Controls: Left, Right, Up, Down, to Move the dots. LShift to speed up the dots.

[pgimeno]

Looks cool! I couldn't quite understand why the yellow square is off centre with respect to the purple square though. I managed to centre it and make it symmetric but I'm not sure what I was doing as I haven't checked the math.

The equation I used should hopefully (If God himself is willing...) be a precursor to effectivly helping render hyperbolic geometry.

An obvious route is to make the square a mesh and the dots vertices; assign UVs to each vertex and then apply the transform to the vertices, perhaps using a vertex shader, I'm not sure of that.

Another possibility is to apply the transform with a fragment shader, but for that you will need the inverse transform I presume.

[insignia]

Looks cool! I couldn't quite understand why the yellow square is off centre with respect to the purple square though. I managed to centre it and make it symmetric but I'm not sure what I was doing as I haven't checked the math.

The equation I used should hopefully (If God himself is willing...) be a precursor to effectivly helping render hyperbolic geometry.

An obvious route is to make the square a mesh and the dots vertices; assign UVs to each vertex and then apply the transform to the vertices, perhaps using a vertex shader, I'm not sure of that.

Another possibility is to apply the transform with a fragment shader, but for that you will need the inverse transform I presume.

The reason for this artifact is because, That's just how the math works. No bugs or anything.