Computational geometry: an introduction
Computational geometry: an introduction
Polygonization of implicit surfaces
Computer Aided Geometric Design
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
A polygonal approximation to direct scalar volume rendering
VVS '90 Proceedings of the 1990 workshop on Volume visualization
Octrees for faster isosurface generation
ACM Transactions on Graphics (TOG)
Geometric triangulations, with application to fully automatic three-dimensional mesh generation
Geometric triangulations, with application to fully automatic three-dimensional mesh generation
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Octree-based decimation of marching cubes surfaces
Proceedings of the 7th conference on Visualization '96
Multiresolution tetrahedral framework for visualizing regular volume data
VIS '97 Proceedings of the 8th conference on Visualization '97
Interval volume tetrahedrization
VIS '97 Proceedings of the 8th conference on Visualization '97
The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics
The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A simple recursive tessellator for adaptive surface triangulation
Journal of Graphics Tools
Interactive Time-Dependent Particle Tracing Using Tetrahedral Decomposition
IEEE Transactions on Visualization and Computer Graphics
The Lazy Sweep Ray Casting Algorithm for Rendering Irregular Grids
IEEE Transactions on Visualization and Computer Graphics
Feature Extraction of Separation and Attachment Lines *
IEEE Transactions on Visualization and Computer Graphics
Adaptive Polygonalization of Implicitly Defined Surfaces
IEEE Computer Graphics and Applications
Generalized Unstructured Decimation
IEEE Computer Graphics and Applications
Concepts and Applications of Finite Element Analysis
Concepts and Applications of Finite Element Analysis
Extraction of crack-free isosurfaces from adaptive mesh refinement data
EGVISSYM'01 Proceedings of the 3rd Joint Eurographics - IEEE TCVG conference on Visualization
Methods and Framework for Visualizing Higher-Order Finite Elements
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
Fusion of depth maps with multiple scales
Proceedings of the 2011 SIGGRAPH Asia Conference
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We describe a general algorithm to produce compatible 3D triangulations from spatial decompositions. Such triangulations match edges and faces across spatial cell boundaries, solving several problems in graphics and visualization including the crack problem found in adaptive isosurface generation, triangulation of arbitrary grids (including unstructured grids), clipping, and the interval tetrahedrization problem. The algorithm produces compatible triangulations on a cell-by-cell basis, using a modified Delaunay triangulation with a simple point ordering rule to resolve degenerate cases and produce unique triangulations across cell boundaries. The algorithm is naturally parallel since it requires no neighborhood cell information, only a unique, global point numbering. We show application of this algorithm to adaptive contour generation; tetrahedrization of unstructured meshes; clipping and interval volume mesh generation.