Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
A randomized algorithm for closest-point queries
SIAM Journal on Computing
Arrangements and their applications in robotics: recent developments
WAFR Proceedings of the workshop on Algorithmic foundations of robotics
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Handbook of discrete and computational geometry
A perturbation scheme for spherical arrangements with application to molecular modeling
Computational Geometry: Theory and Applications - special issue on applied computational geometry
Dynamic Trees and Dynamic Point Location
SIAM Journal on Computing
Controlled perturbation for arrangements of polyhedral surfaces with application to swept volumes
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Robust Proximity Queries: An Illustration of Degree-Driven Algorithm Design
SIAM Journal on Computing
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Efficient algorithms for line and curve segment intersection using restricted predicates
Computational Geometry: Theory and Applications
Constructing Planar Cuttings in Theory and Practice
SIAM Journal on Computing
The design and implementation of panar maps in CGAL
Journal of Experimental Algorithmics (JEA)
Polygon decomposition for efficient construction of Minkowski sums
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
A Singly-Expenential Stratification Scheme for Real Semi-Algebraic Varieties and Its Applications
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Almost Tight Upper Bounds for Vertical Decompositions in Four Dimensions
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the computation of an arrangement of quadrics in 3D
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
Heuristics for estimating contact area of supports in layered manufacturing
Journal of Experimental Algorithmics (JEA)
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Computer Aided Geometric Design
On the computation of an arrangement of quadrics in 3D
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
Geometric optimization and sums of algebraic functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Geometric optimization and sums of algebraic functions
ACM Transactions on Algorithms (TALG)
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We present new results concerning the refinement of three-dimensional arrangements by vertical decompositions. First, we describe a new output-sensitive algorithm for computing the vertical decomposition of arrangements of n triangles in O(nlog2 n+Vlog n) time, where V is the complexity of the decomposition. This improves significantly over the best previously known algorithms. Next, we propose an alternative sparser refinement, which we call the partial vertical decomposition and has the advantages that it produces fewer cells and requires lower degree constructors. We adapt the output-sensitive algorithm to efficiently compute the partial decomposition as well. We implemented algorithms that construct the full and the partial decompositions and we compare the two types theoretically and experimentally. The improved output-sensitive construction extends to the case of arrangements of n well-behaved surfaces with the same asymptotic running time. We also extended the implementation to the case of polyhedral surfaces---this can serve as the basis for robust implementation of approximations of arrangements of general surfaces.