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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
PubMed
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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.

Related Experiment Videos

  • 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.