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Representing higher-order singularities in vector fields on piecewise linear surfaces
Wan-Chiu Li1, Bruno Vallet, Nicolas Ray
1INRIA-Alice, France. wan-chiu.li@loria.fr
IEEE Transactions on Visualization and Computer Graphics
|November 4, 2006
Summary
This study presents a new facet-based method for interpolating vector fields on triangulated surfaces, enabling accurate representation of complex singularities. The approach simplifies visualization and analysis of vector fields on complex geometries.
Area of Science:
- Computer Graphics
- Computational Geometry
- Scientific Visualization
Background:
- Representing singularities in vector fields on piecewise linear surfaces is challenging.
- Existing vertex-based schemes have limitations on singularity complexity based on vertex connectivity.
Purpose of the Study:
- To introduce a concise and complete interpolation scheme for vector fields on arbitrary triangulated surfaces.
- To enable the representation of arbitrary singularities at vertices.
- To develop a facet-based encoding for vector fields on piecewise linear surfaces.
Main Methods:
- Vector fields are described in polar coordinates per facet, using facet edges as angular references.
- A 'period jump' integer is associated with edges to resolve directional ambiguity between facets.
- Linear interpolation of rotation angles along facet graph edges is performed.
- A variant of Nielson's side-vertex scheme is used for surface-wide interpolation.
Main Results:
- The scheme removes limitations on singularity complexity previously imposed by vertex connectivity.
- The index of a vector field vertex can be combinatorially determined using the data structure.
- A GPU-accelerated algorithm for Line Integral Convolution (LIC) visualization was developed.
Conclusions:
- The proposed facet-based interpolation scheme accurately represents higher-order singularities on triangulated surfaces.
- The method simplifies vector field representation and enables efficient, high-complexity singularity visualization.
- The approach is demonstrated on various vector fields on curved surfaces.
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