The four points were teselated into two triangles.

Each triangle was handeled seperatly

New points were generated between each vertex and the centroid

Three quadralaterals were formed with the original three verticies and the new verticies.

Torroid with small holes

Torroid with thin offset (wall thickness)

Torroid with thick offset (wall thickness)

To demonstrate the versitility, our algorithm works with any surface (spheres shown here)