Geometric Modelling by Discrete Surface Patches Based on Geometric Partial Differential Equations

We construct discrete three- and four-sided surface patches with specified C⁰ or C¹ boundary conditions, using several geometric intrinsic curvature driven flows. These flow equations are solved numerically based on discretizations of the involved differential-geometry operators, which are derived from parametric approximations. The constructed surface patches satisfy certain geometric partial differential equations, and therefore have desirable shape. These patches are assembled together for constructing complicated geometric models for shape design. Multi-resolution representations of the models are achieved using repeated subdivision and evolution.