Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
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
MPFR: A multiple-precision binary floating-point library with correct rounding
ACM Transactions on Mathematical Software (TOMS)
Exact and efficient construction of Minkowski sums of convex polyhedra with applications
Computer-Aided Design
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
Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl
Robust Minkowski sums of polyhedra via controlled linear perturbation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
A GPU-based voxelization approach to 3D Minkowski sum computation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
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We present an algorithmic solution to the robustness problem in computational geometry, called controlled linear perturbation, and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Approximate computation in floating point arithmetic is efficient but can assign incorrect signs to geometric predicates, which can cause combinatorial errors in the algorithm output. We make approximate computation accurate by performing small input perturbations, which we compute using differential calculus. This strategy supports fast, accurate Minkowski sum computation. The only prior robust implementation uses a less efficient algorithm, requires exact algebraic computation, and is far slower based on our extensive testing.