C++ Barycentric coordinates

27 Nov 2018

Doing research to find out how to approach a mesh deformer. I think I can use this to create a free form deformation (FFD) deformer: https://en.wikipedia.org/wiki/Barycentric_coordinate_system

How does it work

In order to deform a point within another shape, we have to remap the point in world space relative to the cage.

1. Binding.

   In this example I use a triangle as the cage, the first step in the process is called ‘binding’, this will loop through all points in a mesh and calculate the coordinates in the cage, once we have those coordinates we can store them and access them later.

2. Update the cage points.

   Change the position of the cage after doing the binding step.

3. Apply new coordinates of the mesh based on the new cage points

    FVector cagePointC = VertexBuffer[0].Position;
    FVector cagePointB = VertexBuffer[1].Position;
    FVector cagePointA = VertexBuffer[2].Position;
   
    float u = barycentric_coordinates[0].X;
    float v = barycentric_coordinates[1].Y;
    float w = barycentric_coordinates[2].Z;
   
    float n = (u * cagePointC.X) + (v * cagePointB.X) + (w * cagePointA.X);