Multi-dimensional trees for controlled volume rendering and compression
VVS '94 Proceedings of the 1994 symposium on Volume visualization
Real-time, continuous level of detail rendering of height fields
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Visualization of higher order singularities in vector fields
VIS '97 Proceedings of the 8th conference on Visualization '97
ROAMing terrain: real-time optimally adapting meshes
VIS '97 Proceedings of the 8th conference on Visualization '97
Visualization of scalar topology for structural enhancement
Proceedings of the conference on Visualization '98
Feature comparisons of vector fields using earth mover's distance
Proceedings of the conference on Visualization '98
Automatic detection of open and closed separation and attachment lines
Proceedings of the conference on Visualization '98
Wavelets over curvilinear grids
Proceedings of the conference on Visualization '98
Interpolation of triangle hierarchies
Proceedings of the conference on Visualization '98
Construction of vector field hierarchies
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Simplified representation of vector fields
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Feature comparisons of 3-D vector fields using earth mover's distance
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
C1-interpolation for vector field topology visualization
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Cracking the cracking problem with Coons patches
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Collapsing flow topology using area metrics
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Direct numerical simulations of the Navier-Stokes alpha model
Physica D - Special issue originating from the 18th Annual International Conference of the Center for Nonlinear Studies, Los Alamos, NM, May 11&mdash ;15, 1998
A framework for assessing uncertainties in simulation predictions
Physica D - Special issue originating from the 18th Annual International Conference of the Center for Nonlinear Studies, Los Alamos, NM, May 11&mdash ;15, 1998
Topology preserving compression of 2D vector fields
Proceedings of the conference on Visualization '00
A topology simplification method for 2D vector fields
Proceedings of the conference on Visualization '00
Continuous topology simplification of planar vector fields
Proceedings of the conference on Visualization '01
Visualizing Vector Field Topology in Fluid Flows
IEEE Computer Graphics and Applications
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
The Earth Mover''s Distance as a Metric for Image Retrieval
The Earth Mover''s Distance as a Metric for Image Retrieval
A tool for visualizing the topology of three-dimensional vector fields
VIS '91 Proceedings of the 2nd conference on Visualization '91
Vector and tensor field topology simplification on irregular grids
EGVISSYM'01 Proceedings of the 3rd Joint Eurographics - IEEE TCVG conference on Visualization
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We present a hierarchical top-down refinement algorithm for compressing 2D vector fields that preserves topology. Our approach is to reconstruct the data set using adaptive refinement that considers topology. The algorithms start with little data and subdivide regions that are most likely to reconstruct the original topology of the given data set. We use two different refinement techniques. The first technique uses bintree subdivision and linear interpolation. The second algorithm is driven by triangular quadtree subdivision with Coons patch quadratic interpolation. We employ local error metrics to measure the quality of compression and as a global metric we compute Earth Mover's Distance (EMD) to measure the deviation from the original topology. Experiments with both analytic and simulated data sets are presented. Results indicate that one can obtain significant compression with low errors without losing topological information. Advantages and disadvantages of different topology preserving compression algorithms are also discussed in the paper.