Evolving Guide Subdivision

Abstract

To overcome the well-known shape deficiencies of bi-cubic subdivision surfaces, Evolving Guide subdivision (EG subdivision) generalizes C2 bi-quartic (bi-4) splines that approximate a sequence of piecewise polynomial surface pieces near extraordinary points. Unlike guided subdivision, which achieves good shape by following a guide surface in a two-stage, geometry-dependent process, EG subdivision is defined by five new explicit subdivision rules. While formally only C1 at extraordinary points, EG subdivision applied to an obstacle course of inputs generates surfaces without the oscillations and pinched highlight lines typical for Catmull-Clark subdivision. EG subdivision surfaces join C2 with bi-3 surface pieces obtained by interpreting regular sub-nets as bi-cubic tensor-product splines and C2 with adjacent EG surfaces. The EG subdivision control net surrounding an extraordinary node can have the same structure as Catmull-Clark subdivision: two rings of 4-sided facets around each extraordinary nodes so that extraordinary nodes are separated by at least one regular node.