= Charles Loop
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<Charles Loop> developed triangular <subdivision surfaces>. <Loop subdivision> repeatedly refines a control mesh and updates vertices by weighted averages, producing a smooth limiting shape.<Smooth Subdivision Surfaces Based on Triangles by Charles Loop>[Official thesis publication record, 1987]{ref}
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.<Convex Triangular Subdivision Surfaces with Bounded Curvature by Charles Loop>[Abstract and sections 2–4]{ref}
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