Marshall Wayne Bern
and David Eppstein

*Computing in Euclidean Geometry*, Lecture Notes Series on Computing, Ding-Zhu Du
and Frank Kwang-Ming Hwang, ed., World Scientific, 1992, pp. 23–90

*Computing in Euclidean Geometry*, Lecture Notes Series on Computing, Ding-Zhu Du
and Frank Kwang-Ming Hwang, ed., World Scientific, 1995, pp. 47–123

Tech. report CSL-92-1, Xerox Palo Alto Research Center, 1992

http://www.ics.uci.edu/~eppstein/pubs/BerEpp-CEG-95.pdf

Cited by:

- Systematic local flip rules are generalized Delaunay rules
- The Delaunay triangulation maximizes the mean inradius
- Numerically robust algorithm for constructing constrained Delaunay triangulation
- Optimal tetrahedralization of the 3d-region “between” a convex polyhedron and a convex polygon
- Selecting heavily covered points
- Automatic mesh generation using the symmetric axis transformation of polygonal domains
- Computational geometry: a retrospective
- Stable finite elements for problems with wild coefficients
- Quality mesh generation in three dimensions
- Mesh generation with provable quality bounds
- Approximating the maxmin-angle covering triangulation
- Refining a triangulation of a planar straight-line graph to eliminate large angles
- Optimal Two-Dimensional Triangulations
- An optimal bound for high-quality conforming triangulations
- Linear-size nonobtuse triangulation of polygons
- Coping with inconsistencies: a new approach to produce quality triangulations of polygonal domains with holes for the finite element method
- Guaranteed-quality mesh generation for curved surfaces
- Optimality of the Delaunay triangulation in $R^d$
- Compatible tetrahedralizations
- The computation of simplicial approximations of implicitly defined two-dimensional manifolds
- Computational geometry column 23
- A Delaunay based numerical method for three dimensions: generation, formulation, and partition
- Printed circuit board simplification: simplifying subdivisions in practice
- Strategies for polyhedral surface decomposition: an experimental study
- Stabbing triangulations by lines in 3D
- A Delaunay refinement algorithm for 2-dimensional mesh generation
- Converting triangulations to quadrangulations
- Quadrangulations of planar sets
- Automatic mesh partitioning
- Finding the constrained Delaunay triangulation and constrained Voronoi diagram of a simple polygon in linear time
- Numerical conformal mapping using cross-ratios and Delaunay triangulation
- Locally-adaptive grid generation using quadtrees
- Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator
- Flipping edges in triangulations
- Partitioning meshes with lines and planes
- A free Lagrange method for gas-dynamics
- Local bisection refinement for $n$-simplicial grids generated by reflection
- Zippered polygon meshes from range images
- Fast separator decomposition for finite element meshes
- Steiner triangulation for isotropic and stretched elements
- Multiple sequence comparison and consistency on multipartite graphs
- An $O(n^2)$ heuristic for Steiner minimal trees in $E^3$
- A framework for advancing front techniques of finite element mesh generation
- Optimal good-aspect-ratio coarsening for unstructured meshes
- The efficient location of neighbors for locally refined $n$-simplicial grids
- Control volume meshes using sphere packing: generation, refinement and coarsening
- Hamiltonian triangulations for fast rendering
- A parallel solution strategy for irregular dynamic problems
- 1-irregular element tessellation in mixed element meshes for the control volume discretization method
- Surface and 3D triangular meshes from planar cross-sections
- The edge-flipping distance of triangulations
- Optimal triangulation problems
- Euclidean Steiner minimal trees, minimum energy configurations, and the embedding problem of weighted graphs in $E^3$
- Generalized unstructured decimation
- Good orders for incremental (re)construction
- Guaranteed-quality Delaunay meshing in 3D
- Minimum strictly-convex quadrangulations of convex polygons
- Computational Geometry: Algorithms and Applications
- Triangulations
- Mesh generation: theory, algorithms, and software
- Numerische simulationen für granulare Medien
- Mesh generation and optimal triangulation in three dimensions
- Mesh refinement via bidirected flows: modeling, complexity, and computational results
- Complexity and modeling aspects of mesh refinement into quadrilaterals
- Solution-based mesh quality for triangular and tetrahedral meshes
- High quality quadrilateral surface meshing without template restrictions: a new approach based on network flow techniques
- Three dimensional Delaunay mesh generation using a modified advancing front approach
- Delaunay Refinement Mesh Generation
- Linear-time reconstruction of Delaunay triangulations with applications
- Improved approximations for minimum cardinality quadrangulations of finite element meshes
- Exploiting domain geometry in analogical route planning
- A large subgraph of the minimum weight triangulation
- Trends and developments in computational geometry
- Decimation of isosurfaces with deformable models
- Fast nested dissection for finite element meshes
- Mesh smoothing using a posteriori error estimates
- Adaptive refinement of unstructured finite-element meshes
- Automatic 3D surface meshing to address today's industrial needs
- Quadtree grid generation: Information handling, boundary fitting and CFD applications
- Flow simulation and high performance computing
- General object reconstruction based on simplex meshes
- A branch-and-cut approach for minimum weight triangulation
- Fully Unstructured Delaunay Mesh Generation Using a Modified Advancing Front Approach for Applications in Technology CAD
- Tools for triangulations and tetrahedralizations and constructing functions defined over them
- Quadrilateral Mesh Generation in Computer-Aided Design
- On the discrete core of quadrilateral mesh refinement
- Mesh generation
- Computational investigations of the optimality of two- and three-dimensional triangulations under several criteria
- Color printer characterization using a computational geometry approach
- Efficient algorithms for Petersen's matching theorem
- Disparity map coding based on adaptive triangular surface modelling
- The natural element method in solid mechanics
- The computation of simplicial approximations of implicitly defined $p$-dimensional manifolds
- Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains
- A solution-based triangular and tetrahedral mesh quality indicator
- Minimum convex partition of a polygon with holes by cuts in given directions
- Finite volume methods on Voronoi meshes
- Bayesian image analysis with Markov chain Monte Carlo and coloured continuum triangulation models
- Mesh generation over curved surfaces with explicit control on discretization error
- On box schemes for elliptic variational inequalities
- Empirical design of geometric algorithms
- How to subdivide pyramids, prisms, and hexahedra into tetrahedra
- Hexahedral mesh generation by successive dual cycle elimination
- Strategies for nonobtuse boundary Delaunay triangulations
- Mesh quality: a function of geometry, error estimates, or both?
- A global minimization-based, automatic quadrilateral meshing algorithm
- LEPP-Delaunay algorithm: a robust tool for producing size-optimal quality triangulations
- Generalized LMT-skeleton heuristics for several new classes of optimal triangulations
- Splitting a complex of convex polytopes in any dimension
- Interactive Rendering of Parametric Spline Surfaces
- Combining hierarchical radiosity and discontinuity meshing
- Construction of a human torso model from magnetic resonance images for problems in computational electrocardiography
- Anisotropic mesh generation with particles
- Visual grid quality assessment for 3D unstructured meshes
- Learning the Voronoi centers of a mobile robot's configuration space
- Tetrahedral meshes from planar cross sections
- A sensory uncertainty field model for unknown and non-stationary mobile robot environments
- Survey of polygonal surface simplification algorithms
- Piecewise linear hypersurfaces using the marching cubes algorithm
- On parallel complexity of planar triangulations
- Algorithms and data structures for handling a fully flexible refinement approach in mesh generation
- A parallel algorithm for finding the constrained Voronoi diagram of line segments in the plane
- A monotone finite element scheme for convection-diffusion equations
- Physical vapor-deposited thin hard films on polymers: sample preparation for SEM analysis
- Shape reconstruction from contours using isotopic deformation
- Micromechanical modeling of concrete response under static loading I: Model development and validation
- Mesh generation for application in technology CAD
- Asymptotics for the length of a minimal triangulation on a random sample
- Adaptive finite element analysis of 2-D static and steady-state electromagnetic problems
- A point-placement strategy for conforming Delaunay tetrahedralization
- Finding minimal triangulations of convex 3-polytopes is NP-hard
- Voronoi diagrams
- Polygon decomposition
- Computational topology
- Delaunay triangulation and Voronoi diagrams for Riemannian manifolds
- Quality mesh generation in higher dimensions
- Unstructured mesh generation: Theory, practice, and perspectives
- Minimal simplicial dissections and triangulations of convex 3-polytopes
- Minimal tetrahedralizations of a class of polyhedra
- Enumerating triangulation paths
- Adaptive simplicial grids from cross-sections of monotone complexes
- Structures of triangulations of points
- Shape similarity by homotopic deformation
- A 3D refinement/derefinement algorithm for solving evolution problems
- Local refinement of simplicial grids based on the skeleton
- Minimum number of pieces in a convex partition of a polygonal domain
- Lipschitzian crowded ball packings and Delaunay spheres
- Force-directed methods for smoothing unstructured triangular and tetrahedral meshes
- Force-directed methods for mesh improvement
- The complexity of finding small triangulations of convex 3-polytopes
- Approximate quality mesh generation based on small edge details
- Tessellations of cuboids with Steiner points
- Static and kinetic geometric spanners with applications
- Anisotropic mesh transformations and optimal error control
- Experimental results on quadrangulations of sets of fixed points
- Multigrid Equation Solvers for Large Scale Nonlinear Finite Element Simulations
- Mesh Generation for Technology CAD in Three Dimensions
- LMT-skeleton heuristics for several new classes of optimal triangulations
- Sliver-Free Three-Dimensional Delaunay Mesh Generation
- Multiresolution shape deformations for meshes with dynamic vertex connectivity
- Optimality and integer programming formulations of triangulations in general dimension
- Approximating uniform triangular meshes in polygons
- Optimal triangulations
- On computing new classes of optimal triangulations with angular constraints
- Managing large terrain data sets with a multiresolution structure
- FIST: Fast industrial-strength triangulation of polygons
- Numerical identification of the potential of whisker- and platelet-filled polymers
- Geometry based triangulation of multiple trimmed NURBS surfaces
- Stability and existence of solutions of time-implicit finite volume schemes for viscous nonlinear conservation laws
- Terminal-edges Delaunay (small-angle based) algorithm for the quality triangulation problem
- Accurate integration of surface profile data with quantitative error analysis
- Atomic images – a method for meshing digital images
- Sample shuffling for quality hierarchic surface meshing
- Quality meshing with weighted Delaunay refinement
- Unstructured tetrahedral meshing by an edge-based advancing front method
- Computational geometry - Some easy questions and their recent solutions
- Approximate shape quality mesh generation
- Approximation for minimum triangulations of simplicial convex 3-polytopes
- Tetrahedralization of two nested convex polyhedra
- Multicriteria-optimized triangulations
- Shelling hexahedral complexes for mesh generation
- Constructing differentiable homeomorphisms between isomorphic triangulations
- Diagonal flips in labelled planar triangulations
- Higher order Delaunay triangulations
- Three-dimensional hybrid mesh generation for turbomachinery airfoils
- Triangulations in CGAL
- Delaunay refinement algorithms for triangular mesh generation
- Approximating uniform triangular meshes for spheres
- Spatial embedding of pseudo-triangulations
- Adapting (pseudo)-triangulations with a near-linear number of edge flips
- Quadtree, ray shooting and approximate minimum weight Steiner triangulation
- BSP-assisted constrained tetrahedralization
- Transforming triangulations of polygons on non planar surfaces
- A time efficient Delaunay refinement algorithm
- Volumetric meshes for real-time medical simulations
- Supporting cuts and finite element deformation in interactive surgery simulation
- Free-form shape design using triangulated surfaces
- Grid generation and optimization based on centroidal Voronoi tessellations
- Approximation and Geometric Processing of Digital Images with Adaptive Triangular Meshes
- Optimal tetrahedralizations of some convex polyhedra
- Enumerating triangulations of convex polytopes
- Axisymmetric dynamical models for SAURON and OASIS observations of NGC 3377
- Dynamic capacitated minimum spanning trees
- Generating surface geometry in higher dimensions using local cell tilers
- Optimal Delaunay triangulations
- The long-time behaviour of the thermoconvective flow in a porous medium
- Finite Volume and Finite Volume Element Methods for Nonsymmetric Problems
- Small point sets whose graph of triangulations is not connected (abridged)
- 3d terrain mapping: a stochastic approach
- Multibeam data processing: a detailed algorithm to compute (adaptive) triangulations and potential indicators of data quality
- Multibeam data processing: data reduction, adaptive triangular meshing and comments resulting from Brouns et al. (THJ No. 101, 2001)
- Phase unwrapping with GAMMA ISP
- Quadrilateral meshes for the registration of human brain images
- A new algorithm for generating quadrilateral meshes and its application to FE-based image registration
- On decreased importance of algorithmic strategies in current ACM curricula for graphics & visual computing
- Automatic grid finding in calibration patterns using Delaunay triangulation
- Voxelization of solids using simplicial coverings
- Subdivision Surfaces in Computer Games
- Points and combinatorics
- Orbit determination with very short arcs: admissible regions
- A numerical method for interface tracking
- Edge-constrained marching triangles
- Animationsorientierte Optimierung von Polygonnetzen
- Neue Untersuchungen zur Integration von DGM und DSM mittels Triangulationen zur Berechnung integrierter 2.5D-Landschaftsmodelle
- Konzeption und Implementierung von geometrischen 3D-Datentype
- Surface reconstruction from problem point clouds
- Topology alteration for virtual sculpting using spatial deformation
- Modelling built environments from large range images using adaptive triangular meshes
- Stochastic simulation in surface reconstruction and application to 3D mapping
- Comparison of image-transformation methods used in matching 2d gel electrophoresis images
- A mapping-independent primitive for the triangulation of parametric surfaces
- Direct interface tracking of droplet deformation
- A Delaunay approach to interactive cutting in triangulated surfaces
- Cutting in Deformable Objects
- Precise relative positioning of multiple moving platforms using GPS carrier phase observables
- Delaunay Refinement Algorithms
- From point cloud to surface: the modeling and visualization problem
- Atomic meshes: from seismic images to reservoir simulation
- Robust Surface Reconstruction Strategy for Large Clouds of Points: State of the Art and Concept of Doctoral Thesis
- Energy Minimization Methods for Feature Displacement in Map Generalization
- Information lack localization in architectural laser scanning surveys: the Venice test site
- Schwarz-Christoffel Mapping
- Representation and Detection of Shapes in Images
- Geometric Decompositions and Networks: Approximation Bounds and Algorithms
- Algorithmic problems on proximity and location under metric constraints
- A 2d kinetic triangulation with near-quadratic topological changes
- Connectivity shapes
- Detecting tetrahedralizations of a set of line segments
- Finding a triangular mesh with a constant number of different edge lengths
- Merging range images of arbitrarily shaped objects
- Pseudo-triangulations from surfaces and a novel type of edge flip
- Triangulations and meshes in computational geometry
- Efficient and reliable triangulation of polygons
- Representation and detection of deformable shapes