Taylor models and affine arithmetics-towards a more sophisticated use of reliable methods in computer graphics

A critical discussion of existing applications of reliable methods in computer graphics and the fact that one of the key applications of reliable arithmetics in computer graphics is its use for range analysis provokes a reconsideration of existing ideas of bounding volumes. A novel kind of parametrized bounding volume for parametric surfaces is proposed that informs about the location of each surface point and the corresponding parameters, as well as the location of the surface . Taylor models and the intrinsic structure of affine arithmetic are used to realize the discussed concepts in the form of linear interval estimations (LIEs). The sophisticated use of reliable methods and the characteristics of LIEs allow an effective intersection test for LIEs that also gives information about those parts of the parameter domains possibly affected by an intersection of the enclosed surface patches. A novel subdivision algorithm for the intersection of two parametric surfaces with remarkable experimental results is presented as a possible application for LIEs.