Computational geometry: an introduction
Computational geometry: an introduction
Computing a ham-sandwich cut in two dimensions
Journal of Symbolic Computation
Edge-skeletons in arrangements with applications
Algorithmica
Topologically sweeping an arrangement
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Constructing higher-dimensional convex hulls at logarithmic cost per face
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
A geometric consistency theorem for a symbolic perturbation scheme
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
Computing a face in an arrangement of line segments
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Visibility-ordering meshed polyhedra
ACM Transactions on Graphics (TOG)
Incremental topological flipping works for regular triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
An efficient approach to removing geometric degeneracies
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Three-dimensional alpha shapes
VVS '92 Proceedings of the 1992 workshop on Volume visualization
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
The union of balls and its dual shape
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A data-parallel algorithm for three-dimensional Delaunay triangulation and its implementation
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Triangulating topological spaces
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
On geometric optimization with few violated constraints
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
ACM Computing Surveys (CSUR)
Polyhedral modelling with exact arithmetic
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Output-sensitive results on convex hulls, extreme points, and related problems
Proceedings of the eleventh annual symposium on Computational geometry
Splitting a complex of convex polytopes in any dimension
Proceedings of the twelfth annual symposium on Computational geometry
On computing Voronoi diagrams by divide-prune-and-conquer
Proceedings of the twelfth annual symposium on Computational geometry
Construction of 1-d lower envelopes and applications
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computing exact geometric predicates using modular arithmetic with single precision
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A perturbation scheme for spherical arrangements with application to molecular modeling
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Snap rounding line segments efficiently in two and three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Classical computational geometry in GeomNet
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
V-Clip: fast and robust polyhedral collision detection
ACM Transactions on Graphics (TOG)
An exact interactive time visibility ordering algorithm for polyhedral cell complexes
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Controlled perturbation for arrangements of polyhedral surfaces with application to swept volumes
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Lower bounds for linear satisfiability problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
A practical approximation algorithm for the LMS line estimator
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On degeneracy in geometric computations
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Linear-time triangulation of a simple polygon made easier via randomization
Proceedings of the sixteenth annual symposium on Computational geometry
Deterministic algorithms for 3-D diameter and some 2-D lower envelopes
Proceedings of the sixteenth annual symposium on Computational geometry
Computing contour trees in all dimensions
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Hierarchical morse complexes for piecewise linear 2-manifolds
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Sink-insertion for mesh improvement
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Testing Homotopy for paths in the plane
Proceedings of the eighteenth annual symposium on Computational geometry
A Multiscale Model for Structure-Based Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
An O(n log n) algorithm for the zoo-keeper's problem
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Computing contour trees in all dimensions
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Perturbations and vertex removal in a 3D delaunay triangulation
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
An Easy to Use Implementation of Linear Perturbations within CGAL
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
Finding an Optimal Path without Growing the Tree
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Dealing with Degeneracy in Triangulation
Computing in Science and Engineering
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Smooth kinetic maintenance of clusters
Proceedings of the nineteenth annual symposium on Computational geometry
Updating and constructing constrained delaunay and constrained regular triangulations by flips
Proceedings of the nineteenth annual symposium on Computational geometry
Interval Set: A Volume Rendering Technique Generalizing Isosurface Extraction
VIS '95 Proceedings of the 6th conference on Visualization '95
Topological quadrangulations of closed triangulated surfaces using the Reeb graph
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Introducing alpha shapes for the analysis of path integral Monte Carlo results
VIS '94 Proceedings of the conference on Visualization '94
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
Finding an optimal path without growing the tree
Journal of Algorithms
Almost-Delaunay simplices: nearest neighbor relations for imprecise points
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Kinetic collision detection between two simple polygons
Computational Geometry: Theory and Applications
Extreme elevation on a 2-manifold
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Tetrahedralization of Point Sets Using Expanding Spheres
IEEE Transactions on Visualization and Computer Graphics
Simplifying Flexible Isosurfaces Using Local Geometric Measures
VIS '04 Proceedings of the conference on Visualization '04
Star splaying: an algorithm for repairing delaunay triangulations and convex hulls
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Smooth kinetic maintenance of clusters
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
A Multi-resolution Data Structure for Two-dimensional Morse-Smale Functions
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Preferred directions for resolving the non-uniqueness of Delaunay triangulations
Computational Geometry: Theory and Applications
On finding a widest empty 1-corner corridor
Information Processing Letters
On Histograms and Isosurface Statistics
IEEE Transactions on Visualization and Computer Graphics
Handling degeneracies in exact boundary evaluation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
A practical approximation algorithm for the LMS line estimator
Computational Statistics & Data Analysis
Meshing skin surfaces with certified topology
Computational Geometry: Theory and Applications
Sliver-free perturbation for the Delaunay tetrahedrization
Computer-Aided Design
Topology-Controlled Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Computer-Aided Design
Modeling dynamic developable meshes by the Hamilton principle
Computer-Aided Design
Approximating polyhedral objects with deformable smooth surfaces
Computational Geometry: Theory and Applications
Visibility maps of segments and triangles in 3D
Computational Geometry: Theory and Applications
Delaunay triangulations of imprecise pointsin linear time after preprocessing
Proceedings of the twenty-fourth annual symposium on Computational geometry
Automatic Generation of High-level Contact State Space between 3D Curved Objects
International Journal of Robotics Research
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Reliable Implementation of Real Number Algorithms: Theory and Practice
Testing bipartiteness of geometric intersection graphs
ACM Transactions on Algorithms (TALG)
Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree
Computational Geometry: Theory and Applications
Eliminating contour line artefacts by using constrained edges
Computers & Geosciences
Delaunay triangulation of imprecise points in linear time after preprocessing
Computational Geometry: Theory and Applications
Smooth kinetic maintenance of clusters
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Preferred directions for resolving the non-uniqueness of Delaunay triangulations
Computational Geometry: Theory and Applications
Constrained Delaunay tetrahedral mesh generation and refinement
Finite Elements in Analysis and Design
On Shortest Disjoint Paths in Planar Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On finding a widest empty 1-corner corridor
Information Processing Letters
Discrete critical values: a general framework for silhouettes computation
SGP '09 Proceedings of the Symposium on Geometry Processing
Robust Minkowski sums of polyhedra via controlled linear perturbation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Perturbations for Delaunay and weighted Delaunay 3D triangulations
Computational Geometry: Theory and Applications
A kinetic triangulation scheme for moving points in the plane
Computational Geometry: Theory and Applications
Adaptive skin meshes coarsening for biomolecular simulation
Computer Aided Geometric Design
A general approach to the analysis of controlled perturbation algorithms
Computational Geometry: Theory and Applications
Industrial design using interpolatory discrete developable surfaces
Computer-Aided Design
SIAM Journal on Optimization
SIAM Journal on Computing
Flipping to robustly delete a vertex in a delaunay tetrahedralization
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
A point inclusion test algorithm for simple polygons
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Using three-valued logic to specify and verify algorithms of computational geometry
ICFEM'05 Proceedings of the 7th international conference on Formal Methods and Software Engineering
Dependable polygon-processing algorithms for safety-critical embedded systems
EUC'05 Proceedings of the 2005 international conference on Embedded and Ubiquitous Computing
Visibility maps of segments and triangles in 3d
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Constrained delaunay triangulation using delaunay visibility
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
Approximating polygonal objects by deformable smooth surfaces
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Exact medial axis computation for triangulated solids with respect to piecewise linear metrics
Proceedings of the 7th international conference on Curves and Surfaces
On shortest disjoint paths in planar graphs
Discrete Optimization
Controlled linear perturbation
Computer-Aided Design
Parallel Computation of 3D Morse-Smale Complexes
Computer Graphics Forum
VG'07 Proceedings of the Sixth Eurographics / Ieee VGTC conference on Volume Graphics
How to cover a point set with a V-shape of minimum width
Computational Geometry: Theory and Applications
The complexity of geodesic Voronoi diagrams on triangulated 2-manifold surfaces
Information Processing Letters
On the power of the semi-separated pair decomposition
Computational Geometry: Theory and Applications
Putting holes in holey geometry: topology change for arbitrary surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
QEx: robust quad mesh extraction
ACM Transactions on Graphics (TOG)
gHull: A GPU algorithm for 3D convex hull
ACM Transactions on Mathematical Software (TOMS)
Robust and efficient polygon overlay on parallel stream processors
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
A GPU accelerated algorithm for 3D Delaunay triangulation
Proceedings of the 18th meeting of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Merging polyhedral shapes with scattered features
The Visual Computer: International Journal of Computer Graphics
Short Communication: A rectilinear Gaussian model for estimating straight-line parameters
Journal of Visual Communication and Image Representation
Approximating functions on a mesh with restricted Voronoï diagrams
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Visualizing robustness of critical points for 2D time-varying vector fields
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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This paper describes a general-purpose programming technique, called Simulation of Simplicity, that can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task of providing a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software.