The overall objective of this project is to lay the framework for a new generation of robust solid modelers for representing and interrogating solid models with curved boundaries in the context of imprecise (discete) computer arithmetic. This future robust modeler is aimed to replacing the current inconsistence-prone modelers used in industry. To accomplish this general objective, we have developed a robust and efficient non-linear polynomial solver for overconstrained, underconstrained, and balanced systems. This non-linear solver is based on Bernstein subdivision and rounded interval artihmetic and leads naturally to the concept of interval polynomial representations. Using the robust solver and interval spline representations, we have introduced and developed a consistent 2D and 3D interval curved solid modeler (ISM), in which objects are bounded by interval polynomial curves and surfaces. Based on the polynomial solver, we have developed a unified algorithm for general geometric intersections including ill-conditioned intersections such as tangential contact point, tangential intersection curve, and overlap of curves and surfaces. We have also developed a graph-based data structure incorporating the special features of ISM. Finally, we have developed Boolean operations for 2D and 3D manifold objects, and extended to 2D and 3D non-manifold objects resulting from ill-conditioned intersections. This condensed paper outlines our recent work for this project.
MIT Ocean Engineering Design Laboratory
Copyright © 1997, Massachusetts Institute of Technology
URL: http://deslab.mit.edu/DesignLab/abstracts96.html
Revised: July 23, 1997