I've found a simple way to create UVs for my ceiling geometry, built from Bezier triangles.
For each triangle I compute a LookAt matrix with the normal of the triangle as the view direction. For the up vector I use one edge of the triangle. The UV coordinates can then be calculated by applying this matrix to each sampled points and discarding the Z component.
let mut ps = [
self.room.surface_point(*face, 0.0, 0.0, 1.0),
self.room.surface_point(*face, 1.0, 0.0, 0.0),
self.room.surface_point(*face, 0.0, 1.0, 0.0),
];
ps.sort_by(|x, y| x.y.partial_cmp(&y.y).unwrap());
let v1 = ps[1] - ps[0];
let v2 = ps[2] - ps[0];
let n1 = v1.cross(&v2);
let lt = Matrix3::look_to_rh(n1.normalize().into(), v1.normalize().into());
UV coordinates on pillars and floor working. I've tinkered with UVs for the ceiling surfaces but have not found a solution yet. There are always discontinuities. The ceiling is created with quadratic Bezier triangles.
I've tried to come up with my own parametric surface description but failed. Today I've looked up and implemented Bézier triangle. No I can sample the surface I want to have. Next I will have to do create an actual geometry out of this.
Combined the Delaunay triangulation with the Bezier curves to create the "walls" of a room. Next step will be figuring out how to create surfaces between curves.
