Linear Interval Estimations for Parametric Objects Theory and Application

Abstract

The new concept of parametrized bounding volumes for parametric objects is proposed to replace the common compact bounding volumes like axis aligned bounding boxes and parallelepipeds. Linear Interval Estimations (LIEs) are developed as a realization of the discussed ideas. Two reliable methods for the computation of LIEs are introduced based on a new understanding of the use of affine arithmetics and a special application of Taylor Models. The particular structure of LIEs allows an effective intersection test of LIEs with rays, boxes and other LIEs. The test gives besides of a possible location of the intersection in object space information about affected parts in the parameter spaces of the enclosed objects. A subdivision algorithm for the intersection of two parametric surface patches with remarkable experimental results is presented as a possible application.