Technical Report CIS9903

Title: Three Dimensional Freeform Sculpting Via Zero Sets of Scalar Trivariate Functions
Authors: Alon Raviv and Gershon Elber
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 {\em 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.
CopyrightThe above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information

Remark: Any link to this technical report should be to this page (, rather than to the URL of the PDF or PS files directly. The latter URLs may change without notice.

To the list of the CIS technical reports of 1999
To the main CS technical reports page

Computer science department, Technion