filename     : p_Pei05.pdf
entry        : inproceedings
conference   : Dagstuhl Seminar 023231 on Scientific Visualization: Extracting Information and Knowledge from Scientific Data Sets, 2003.
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title        : Optimized Bounding Polyhedra For GPU-Based Distance Transform
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author       : Ronald Peikert and Christian Sigg
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ISSN/ISBN    : 3-540-26066-8
editor       : G.-P. Bonneau, T. Ertl, and G.M. Nielson
publisher    : Springer
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language     : English
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abstract     : Many problems in areas such as computer graphics, scientific visualization,
computational geometry, or image processing require the computation of a
distance field. The distance field indicates at each point in space the shortest
distance to a given object. Depending on the problem setting, the object
is described either by a voxel attribute within a volume data set or by a
surface representation such as a triangle mesh. The two cases require separate
approaches, and only the case of the triangle mesh is studied in this paper.
Often, the distance field is needed as a regular grid of samples. The samples
can be computed either in image space or object space, referring to the outer
loop of the algorithm, which iterates over all samples or all triangles of the
mesh, respectively. Object space methods can be competitive, especially for
higher resolutions. An ideal object space method would compute a generalized
Voronoi diagram (GVD) of the mesh and then scan convert its cells. At each
sample location, the distance to the Voronoi site associated with the cell would
yield the field value. A practical method however, avoids the expensive GVD
computation and instead works with bounding polyhedra for the Voronoi cells.
In this paper, we propose a new type of bounding polyhedra. This reduces
the number of polyhedra and simplifies their geometry. The choice of these
bounding polyhedra pays oŽ especially if scan conversion is run on graphics
hardware.