Three-dimensional freeform sculpting via zero sets of scalar trivariate functions

This paper presents a three-dimensional interactive sculpting paradigm that employs a collection of scalar uniform trivariate B-spline functions. The sculpted object is evaluated as the zero set of the sum of the collection o f the trivariate functions defined over a three-dimensional working space, resulting in multi-resolution control capabilities. The continuity of the s culpted object is governed by the continuity of the trivariates. The manipu lation of the objects is conducted by modifying the scalar control coeffici ents of the meshes of the participating trivariates. Real time visualizatio n is achieved by incrementally computing a polygonal approximation via the Marching Cubes algorithm. The exploitation of trivariates in this context b enefits from the different properties of the B-spline's representation such as subdivision, refinement and convex hull containment. A system developed using the presented approach has been used in various modeling application s including reverse engineering. (C) 2000 Published by Elsevier Science Ltd . All rights reserved.