Abstract:
Given a solid S Ì Â³ with a piecewise smooth boundary, we compute an approximation of the boundary surface of the volume which is swept by S under a smooth one-parameter motion. Using knowledge from kinematical and elementary differential geometry, the algorithm computes a set of points plus surface normals from the envelope surface. A study of the evolution speed of the so called characteristic set along the envelope is used to achieve a prescribed sampling density. With a marching algorithm in a grid, the part of the envelope which lies on the boundary of the swept volume is extracted. The final boundary representation of the swept volume is either a triangle mesh, a B-spline surface or a point-set surface.
Bibtex:
@article{peternell-sv-2005,
author = "Martin Peternell and Helmut Pottmann and Tibor
Steiner and Hongkai Zhao",
title ="Swept Volumes",
journal = "Computer-Aided Design Appl.",
volume = 2,
pages = "599-608",
year = 2005,
url="/peternell/envelope_v4.pdf",
}
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