Local shape control for free-form solids in exact CSG representation

Abstract

We present a shape control scheme for free-form solids represented in CSG as Boolean combinations of low-degree algebraic halfspaces. In this scheme, we can create manifold solids of arbitrary topology through polyhedral smoothing, and the resulting shapes may be modified by changing control points and/or control weights, with each control point and weight having a local effect. As a solid changes shape, incremental B-rep-CSG conversions are used for fast updates of the corresponding CSG representation. A key ingredient of our scheme, and a main contribution of this paper, is an algorithm that uses Kuhn-Tucker conditions to efficiently compute valid control points. Published by Elsevier Science Ltd.