Bezier Deformation

Premise and End Result

I wanted to make a vertex shader that deforms 3D models along bezier curves, to create bent text and adaptive curves on models.

Process

I calculate a localspace line from one end of the model to another, then appoint each vertex an offset to their closest point on that line. I then calculate a three-dimensional Bezier Curve, use this curve's normals to rotate the original line's vertex displacements and normals, then apply the result of those to the vertices.