Abstract: The length of a given rational B'ezier curve is
efficiently estimated. Since a rational B'ezier function is nonlinear,
it is usually impossible to evaluate its length exactly. The
length is approximated by using subdivision and the accuracy
of the approximation n is investigated. In order to improve
the efficiency, adaptivity is used with some length estimator.
A rigorous theoretical analysis of the rate of convergence of
n to is given. The required number of subdivisions to
attain a prescribed accuracy is also analyzed. An application
to CAD parametrization is briefly described. Numerical results
are reported to supplement the theory.
Abstract: The objective is to split a simply connected polygon
into a set of convex quadrilaterals without inserting new
boundary nodes. The presented approach consists in repeatedly
removing quadrilaterals from the polygon. Theoretical results
pertaining to quadrangulation of simply connected polygons are
derived from the usual 2-ear theorem. It produces a quadrangulation
technique with O(n) number of quadrilaterals. The
theoretical methodology is supplemented by practical results
and CAD surface segmentation.