Robust Minkowski sums of polyhedra via controlled linear perturbation

Authors:
Victor Milenkovic;Elisha Sacks;Min-Ho Kyung
Affiliations:
University of Miami, Coral Gables, FL;Purdue University, West Lafayette, IN;Ajou University, Suwon, South Korea
Venue:
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Year:
2010

Citing 9
Cited 1

Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms

ACM Transactions on Graphics (TOG)
Exact geometric predicates using cascaded computation

Proceedings of the fourteenth annual symposium on Computational geometry
A perturbation scheme for spherical arrangements with application to molecular modeling

Computational Geometry: Theory and Applications - special issue on applied computational geometry
Controlled perturbation for arrangements of polyhedral surfaces with application to swept volumes

SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Controlled perturbation for Delaunay triangulations

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Accurate Minkowski sum approximation of polyhedral models

Graphical Models - Special issue on PG2004
Exact and efficient 2D-arrangements of arbitrary algebraic curves

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Covering Minkowski sum boundary using points with applications

Computer Aided Geometric Design
Exact Minkowksi Sums of Polyhedra and Exact and Efficient Decomposition of Polyhedra into Convex Pieces

Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl

Controlled linear perturbation

Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a new approach, called controlled linear perturbation (CLP), to the robustness problem in computational geometry and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Large errors can occur when predicates are assigned inconsistent truth values because the computation assigns incorrect signs to the associated polynomials. CLP enforces consistency by performing a small input perturbation, which it computes using differential calculus. CLP enables us to compute Minkowski sums via convex convolution, whereas prior work uses convex decomposition, which has far greater complexity. Our program is fast and accurate even on inputs with many degeneracies.