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| Title | Using Isosurface Methods for Visualizing the Envelope of a Swept Trivariate Solid
(In Proceedings) |
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| in | Proceedings of Pacific Graphics 2000 |
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| Author(s) |
Jason Conkey, Ken Joy |
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| Keyword(s) | Keywords: swept surface; envelopes; boundary surface determination;
trivariate B-spline solids; rank-deficient Jacobians;
marching tetrahedra. |
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| Year |
2000
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| Location | Hong Kong |
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| Date | October 3--5, 2000 |
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| Pages | 272--280 |
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| Download |  |
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| Abstract |
We present a method for calculating the envelope surface
of a parametric solid object swept along a path in three dimensional space. The boundary surface of the solid is
the combination of parametric surfaces and an implicit surface where the Jacobian of the defining function has a rankdeficiency condition. Using this condition, we determine a set of square sub-Jacobian determinants that must all vanish simultaneously on the implicit surface. When the generator of the swept surface is a trivariate tensor-product B-spline solid and the path is a B-spline curve, we can give a robust algorithm to determine the implicit surface. This algorithm is based upon the “marching tetrahedra” method, which is adapted to work on 4-simplices. The envelope of the swept solid is given by the union of the parametric and implicit surfaces.
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