Approximate Implicitization and CAD-type Intersection Algorithms

Thursday, May 31, 2007 - 2:00pm - 2:30pm
EE/CS 3-180
Tor Dokken (SINTEF)
When developing CAD-type intersection algorithms for
NonUniform Rational B-splines surfaces (NURBS) is important
to ensure that the algorithm identifies all intersection
branches. For transversal intersections this is fairly
straight forward. For singular or near singular intersection,
when the surfaces are close and near parallel, the
traditional approach of recursive subdivision does not
suffice on its own. The use of algebraic surfaces to separate
near parallel not intersecting surfaces reduces the depth of
recursion. Approximate implicitization denotes methods that
approximate piecewise parametric manifolds p(s) with an
algebraic hypersurface q(x)=0. The talk will address the
approach to approximate implicitization already published by
the author and further report on how approximate
implicitization has helped the development of a CAD-type
intersection algorithms addressing self-intersecting
CAD-surfaces, and singular and near singular intersection of
NURBS surfaces.