SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Shapes and implementations in three-dimensional geometry
Shapes and implementations in three-dimensional geometry
SIGGRAPH '96 Proceedings of the 23rd 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
Simplifying surfaces with color and texture using quadric error metrics
Proceedings of the conference on Visualization '98
Fast and memory efficient polygonal simplification
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
New quadric metric for simplifiying meshes with appearance attributes
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Simplification of Tetrahedral meshes with accurate error evaluation
Proceedings of the conference on Visualization '00
Topology preserving and controlled topology simplifying multiresolution isosurface extraction
Proceedings of the conference on Visualization '00
Constructing Hierarchies for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Volume Decimation of Irregular Tetrahedral Grids
CGI '99 Proceedings of the International Conference on Computer Graphics
A Multi-resolution Data Structure for Two-dimensional Morse-Smale Functions
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Simplification and improvement of tetrahedral models for simulation
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Quadric-based simplification in any dimension
ACM Transactions on Graphics (TOG)
A Topological Approach to Simplification of Three-Dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Streaming Simplification of Tetrahedral Meshes
IEEE Transactions on Visualization and Computer Graphics
Extraction and simplification of iso-surfaces in tandem
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Efficient Computation of Morse-Smale Complexes for Three-dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
ASM: An adaptive simplification method for 3D point-based models
Computer-Aided Design
Simplification of unstructured tetrahedral meshes by point sampling
VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
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We consider scientific data sets that describe density functions over three-dimensional geometric domains. Such data sets are often large and coarsened representations are needed for visualization and analysis. Assuming a tetrahedral mesh representation, we construct such representations with a simplification algorithm that combines three goals: the approximation of the function, the preservation of the mesh topology, and the improvement of the mesh quality. The third goal is achieved with a novel extension of the well-known quadric error metric. We perform a number of computational experiments to understand the effect of mesh quality improvement on the density map approximation. In addition, we study the effect of geometric simplification on the topological features of the function by monitoring its critical points.