TitleUsing Isosurface Methods for Visualizing the Envelope of a Swept Trivariate Solid (In Proceedings)
inProceedings of Pacific Graphics 2000
Author(s) Jason Conkey, Ken Joy
Keyword(s)Keywords: swept surface; envelopes; boundary surface determination; trivariate B-spline solids; rank-deficient Jacobians; marching tetrahedra.
Year 2000
LocationHong Kong
DateOctober 3--5, 2000
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.