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Christian Sigg, Ronny Peikert
Given a set of
geometry objects in 2- or 3-space, a
distance field is defined at each point by the smallest Euclidean
distance to a point
on one of the objects. Objects can be curves in 2-space and
surfaces in 3-space or, more generally, any compact subset. If an
orientable and closed n-1 dimensional manifold is chosen, the
distance field can be given a sign.
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In order to achieve
linear complexity in the number of
grid points, to each primitive we assign a simple polyhedron
enclosing its Voronoi cell. Voronoi cells are known to
contain exactly all points that lay closest to its corresponding
primitive.
Thus, the distance to the primitive only has to be computed
for grid points inside its polyhedron. Although Voronoi cells partition
space, the polyhedrons enclosing these cells do overlap. In
regions where these overlaps occur, the minimum of all computed
distances is assigned to a grid point. In order to speed up
computations,
points inside each polyhedron are determined by scan
conversion of grid slices using graphics hardware. For this task, a
fragment program is used to perform the nonlinear interpolation
and minimization of distance values.
- R. Peikert, C. Sigg, Optimized Bounding Polyhedra For GPU-Based Distance Transform, Proceedings of Dagstuhl Seminar 023231 on Scientific Visualization: Extracting Information and Knowledge from Scientific Data Sets, 2003
[Abstract]
[BibTeX]
[PDF]
- C. Sigg, R. Peikert, M. Gross, Signed Distance Transform Using Graphics Hardware, Proceedings of IEEE Visualization '03, IEEE Computer Society Press, pp. 83-90 (Visualization '03, Seattle, WA, USA, 19-24 October, 2003)
[Abstract]
[PDF]
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