Intersection test and blossoming perturbation for disk parametric curves and ball parametric surfaces

Abstract

Errors in curve and surface representation due to inaccuracies in the data are considered and accounted for by introducing disk parametric curves and ball parametric surfaces. Intersection test algorithms and interval extensions using blossoming are discussed for each of the three cases of Bézier curves, tensor product surfaces, and triangular patches. A stability analysis is also performed for each of the three cases. It is shown that under certain restrictions disk Bézier curves and triangular ball Bézier patches are stable with respect to perturbations of the control disks (balls); whereas tensor product ball Bézier surfaces are in general not.