Hierarchical Spherical Distance Fields for Collision Detection
IEEE Computer Graphics and Applications
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Abstract: 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 new kind of parametrized bounding volumes for parametric surfaces is proposed that inform besides of the location of the surface also about the location of each surface point and the corresponding parameters. 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 sophisticate use of reliable methods and the characteristics of LIEs allow an effective intersection test for LIEs that gives also information about those parts of the parameter domains possibly affected by an intersection of the enclosed surface patches. A new subdivision algorithm for the intersection of two parametric surfaces with remarkable experimental results is presented as a possible application for LIEs.