
Title  Generating the Envelope of a Swept Trivariate Solid
(In Proceedings) 
in  Proceedings of IASTED International Conference on Computer Graphics and Imaging 
Author(s) 
Claudia Madrigal, Ken Joy 
Keyword(s)  trivariate splines; sweeping; envelopes; solid modeling. 
Year 
1999

Location  Palm Springs, California 
Date  October 2527 
Pages  59 
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Abstract 
We present a method for calculating the envelope of the swept surface of a solid along a path in threedimensional space. The generator of the swept surface is a trivariate tensorproduct B`ezier solid and the path is a nonuniform rational Bspline curve. The boundary
surface of the solid is the combination of parametric surfaces and an implicit surface where the determinant of the Jacobian of the defining function is zero. We define methods to calculate the envelope for each type of boundary surface, defining characteristic curves on the envelope and connecting them with triangle strips. The envelope of the swept solid is then calculated by
taking the union of the envelopes of the family of boundary surfaces, defined by the surface of the solid in motion along the path.
