Stereographic projection and world bending

Unity Engine
, , ,
1

Hello everyone,

I would like to create a “world-bending” shader using Unity’s Shader Graph Editor (and the Universal Render Pipeline). I want to make a shader that bends the world around you into a sphere.
For that I’m using the stereographic projection to map every vertex of my world to a sphere.
I’m only dealing with a flat plane for now so I’m just mapping using the x and z coordinates only.
The formula to map 2d point (x,y) into a 3d sphere (x,y,z) of radius 1 is the following:

And I tested it in GeoGebra to check if it worked:

1387×663 111 KB

So what I did is :

  • First, create two 2D vectors containing the x and z position of both the camera and the current vertex using Split and Vector2 nodes
  • Then substract those two vectors in order to have the position of the vertex relative to the camera’s position
  • Then, normalize this vector
  • This will be the input to my custom function that take a 2D vector and calculate the 3D position on the sphere using the Custom Function Node (I multiply the output by 100 in order to have a sphere of radius 100 in unity)
  • Finally, convert back the vector to the object’s frame of reference with the Transform node

But I can’t get it to work. Just nothing appears, where am I wrong ?

Here is a screen of my Shader Graph Editor along with my custom function’s code (click on it for a better view):

1891×655 110 KB

Any help is welcome!

2

Curious if you ever made progress on this issue. I was looking into this idea too recently and haven’t found any examples just yet.

3

This tutorial is spot on

It’s the same effect that games like Animal Crossing use for bending the horizon, and the same concept can be extended to 3 dimensions.

Also this asset seems to cover the same idea and take it a few steps further Curved World | VFX Shaders | Unity Asset Store