Direct methods for sparse matrices
Direct methods for sparse matrices
Long and thin triangles can be good for linear interpolation
SIAM Journal on Numerical Analysis
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
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
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Multistep scattered data interpolation using compactly supported radial basis functions
Journal of Computational and Applied Mathematics - Special issue on scattered data
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
Smooth hierarchical surface triangulations
VIS '97 Proceedings of the 8th conference on Visualization '97
The multilevel finite element method for adaptive mesh optimization and visualization of volume data
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
An efficient algorithm for terrain simplification
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Meshless parameterization and surface reconstruction
Computer Aided Geometric Design
Visualization in Scientific Computing
Visualization in Scientific Computing
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
On a Construction of a Hierarchy of Best Linear Spline Approximations Using Repeated Bisection
IEEE Transactions on Visualization and Computer Graphics
Simplification of Tetrahedral Meshes with Error Bounds
IEEE Transactions on Visualization and Computer Graphics
Fast Multiresolution Surface Meshing
VIS '95 Proceedings of the 6th conference on Visualization '95
Adaptive mesh generation of MRI images for 3D reconstruction of human trunk
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
Hi-index | 0.00 |
We present a method for the hierarchical approximation of functions in one, two, or three variables based on the finite element method (Ritz approximation). Starting with a set of data sites with associated function, we first determine a smooth (scattered-data) interpolant. Next, we construct an initial triangulation by triangulating the region bounded by the minimal subset of data sites defining the convex hull of all sites. We insert only original data sites, thus reducing storage requirements. For each triangulation, we solve a minimization problem: computing the best linear spline approximation of the interpolant of all data, based on a functional involving function values and first derivatives. The error of a best linear spline approximation is computed in a Sobolev-like norm, leading to element-specific error values. We use these interval/triangle/tetrahedron-specific values to identify the element to subdivide next. The subdivision of an element with largest error value requires the recomputation of all spline coefficients due to the global nature of the problem. We improve efficiency by 1) subdividing multiple elements simultaneously and 2) by using a sparse-matrix representation and system solver.