Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
A data reduction scheme for triangulated surfaces
Computer Aided Geometric Design
BLaC-Wavelets: a multiresolution analysis with non-nested spaces
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
VIS '97 Proceedings of the 8th conference on Visualization '97
Multiresolution compression and reconstruction
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
Simplification of tetrahedral meshes
Proceedings of the conference on Visualization '98
Construction of vector field hierarchies
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Optimal triangular Haar bases for spherical data
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
Constructing Hierarchies for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
On a Construction of a Hierarchy of Best Linear Spline Approximations Using Repeated Bisection
IEEE Transactions on Visualization and Computer Graphics
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
ACM '68 Proceedings of the 1968 23rd ACM national conference
Fast Multiresolution Surface Meshing
VIS '95 Proceedings of the 6th conference on Visualization '95
Ray casting curved-quadratic elements
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
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We present a method for hierarchical data approximation using quadratic simplicial elements for domain decomposition and field approximation. Higher-order simplicial elements can approximate data better than linear elements. Thus, fewer quadratic elements are required to achieve similar approximation quality. We use quadratic basis functions and compute best quadratic simplicial spline approximations that are C0-continuous everywhere. We adaptively refine a simplicial approximation by identifying and bisecting simplicial elements with largest errors. It is possible to store multiple approximation levels of increasing quality. We have tested the suitability and efficiency of our hierarchical data approximation scheme by applying it to several data sets.