SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A data reduction scheme for triangulated surfaces
Computer Aided Geometric Design
Data point selection for piecewise linear curve approximation
Computer Aided Geometric Design
Multiresolution modeling and visualization of volume data based on simplicial complexes
VVS '94 Proceedings of the 1994 symposium on Volume visualization
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Mesh reduction with error control
Proceedings of the 7th conference on Visualization '96
Dynamic view-dependent simplification for polygonal models
Proceedings of the 7th conference on Visualization '96
View-dependent refinement of progressive meshes
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Progressive simplicial complexes
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Smooth hierarchical surface triangulations
VIS '97 Proceedings of the 8th conference on Visualization '97
Simplifying polygonal models using successive mappings
VIS '97 Proceedings of the 8th conference on Visualization '97
Triangulations from repeated bisection
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Smooth view-dependent level-of-detail control and its application to terrain rendering
Proceedings of the conference on Visualization '98
Simplification of tetrahedral meshes
Proceedings of the conference on Visualization '98
Progressive tetrahedralizations
Proceedings of the conference on Visualization '98
Multiresolution Representation and Visualization of Volume Data
IEEE Transactions on Visualization and Computer Graphics
Constructing Hierarchies for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Generalized Unstructured Decimation
IEEE Computer Graphics and Applications
A procedural approach to authoring solid models
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
TetFusion: an algorithm for rapid tetrahedral mesh simplification
Proceedings of the conference on Visualization '02
Proceedings of the conference on Visualization '02
Feature preserved volume simplification
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
VG '03 Proceedings of the 2003 Eurographics/IEEE TVCG Workshop on Volume graphics
Selective Refinement Queries for Volume Visualization of Unstructured Tetrahedral Meshes
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
LoD Volume Rendering of FEA Data
VIS '04 Proceedings of the conference on Visualization '04
TetSplat Real-Time Rendering and Volume Clipping of Large Unstructured Tetrahedral Meshes
VIS '04 Proceedings of the conference on Visualization '04
Quadric-based simplification in any dimension
ACM Transactions on Graphics (TOG)
Efficient partial-surface registration for 3D objects
Computer Vision and Image Understanding
Hierarchical Clustering for Unstructured Volumetric Scalar Fields
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
View-dependent tetrahedral meshing and rendering
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Geometry-guided computation of 3D electrostatics for large biomolecules
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Streaming Simplification of Tetrahedral Meshes
IEEE Transactions on Visualization and Computer Graphics
Multiresolution heterogeneous solid modeling and visualization using trivariate simplex splines
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Update operations on 3D simplicial decompositions of non-manifold objects
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
SOT: compact representation for tetrahedral meshes
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Geometry-guided computation of 3D electrostatics for large biomolecules
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Efficient partial-surface registration for 3D objects
Computer Vision and Image Understanding
Tetrahedral image-to-mesh conversion for biomedical applications
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
Tetrahedral adaptive grid for parallel hierarchical tetrahedrization
EGMM'04 Proceedings of the Seventh Eurographics conference on Multimedia
An integrated pipeline of decompression, simplification and rendering for irregular volume data
VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
Simplification of unstructured tetrahedral meshes by point sampling
VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
Out-of-core simplification and crack-free LOD volume rendering for irregular grids
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
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We present a method for the construction of multiple levels of tetrahedral meshes approximating a trivariate scalar-valued function at different levels of detail. Starting with an initial, high-resolution triangulation of a three-dimensional region, we construct coarser representation levels by collapsing edges of the mesh. Each triangulation defines a linear spline function, where the function values associated with the vertices are the spline coefficients. Error bounds are stored for individual tetrahedra and are updated as the mesh is simplified. Two algorithms are presented that simplify the mesh within prescribed error bounds. Each algorithm treats simplification on the mesh boundary. The result is a hierarchical data description suited for efficient visualization of large data sets at varying levels of detail.