
Title  Using Isosurface Methods for Visualizing the Envelope of a Swept Trivariate Solid
(In Proceedings) 
in  Proceedings of Pacific Graphics 2000 
Author(s) 
Jason Conkey, Ken Joy 
Keyword(s)  Keywords: swept surface; envelopes; boundary surface determination;
trivariate Bspline solids; rankdeficient Jacobians;
marching tetrahedra. 
Year 
2000

Location  Hong Kong 
Date  October 35, 2000 
Pages  272280 
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BibTeX  
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 subJacobian determinants that must all vanish simultaneously on the implicit surface. When the generator of the swept surface is a trivariate tensorproduct Bspline solid and the path is a Bspline 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 4simplices. The envelope of the swept solid is given by the union of the parametric and implicit surfaces.
