A piecewise quintic G1 spline surface
interpolating the vertices
of a triangular
surface mesh of arbitrary topological type is presented.
The surface has an explicit triangular Bezier representation, is affine
invariant and has local support.
The twist compatibility problem which arises when joining
an even number of polynomial patches G1 continuously around a common
vertex is solved by constructing C2-consistent boundary curves.
Piecewise C1 boundary curves and a regular
4-split of the domain triangle
make shape parameters available for controlling locally the boundary
curves. A small number of free inner control points can be chosen
for some additional local shape effects.
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