Triangular Mesh Refinement

This function will refine a triangular mesh with 4-split spline interpolation

This function "refinepatch" can refine any triangular mesh surface ( patch) with 4-split spline interpolation, see screenshot.

Literature:
The spline interpolation of the face edges is done by the Opposite Edge Method, described in: "Construction of Smooth Curves and Surfaces from Polyhedral Models" by Leon A. Shirman

How it works:
The tangents (normals) and velocity on the edge points of all edges are calculated. Which are later used for b-spline interpolation when splitting the edges.
A tangent on an 3D line or edge is under defined and can rotate along the line, thus an (virtual) opposite vertex is used to fix the tangent and make it more like a surface normal.
B-spline interpolate a half way vertices between all existing vertices using the velocity and tangent from the edge points. After splitting a new face list is constructed with 4 times as many faces.

Implementation:
Some Matlab files are also available as MEX files to allow quick refinement of large meshes.

Please Leave a comment, if you find a bug, like the code or know improvements.