Charles Loop developed triangular subdivision surfaces. Loop subdivision repeatedly refines a control mesh and updates vertices by weighted averages, producing a smooth limiting shape.[ref]
Smooth Subdivision Surfaces Based on Triangles by Charles Loop. Official thesis publication record, 1987
His later work modifies edge masks to obtain bounded curvature and a convex hull preservation. The analysis depends on eigenvalues of the subdivision operator, especially near extraordinary vertices whose number of neighbors differs from the regular triangular-grid case. Thus a local averaging algorithm has global smoothness and shape-preservation questions.[ref]
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