Abstract
Abstract In the interactive design of freeform surface, assessments of curvatures is an important tool for the analysis of surface shape. Commonly used measures include Gaussian and mean curvatures as well as normal curvatures along a given field of directions and curvatures of nonnormal sections. In the paper, we will discuss the process of surface design based on direct modifications of these curvatures. Mathematically, this amounts to the solution of certain nonlinear partial differential equations, some of which have attracted considerable attention during the preceding twenty-five years.
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