Three dimensional freeform sculpting via zero sets of scalar trivariate functions

Abstract

This paper presents a three dimensional interactive sculpting paradigm that employs a collection of scalar uniform trivariate Bspline functions. The sculpted object is evaluated as the zero set of the sum of the collection of the trivariate functions defined over a three dimensional working space, resulting in multi-resolution control capabilities. The continuity of the sculpted object is governed by the continuity of the trivariates. The manipulation of the objects is conducted by modifying the scalar control coefficients of the meshes of the participating trivariates. Real time visualization is achieved by incrementally computing a polygonal approximation via the Marching Cubes algorithm. The exploitation of trivariates in this context benefits from the different properties of the Bspline's representation such as subdivision, refinement and convex hull containment. A system developed using the presented approach has been used in various modeling applications including reverse engineering.