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Linear Interval Estimations for Parametric Objects Theory and Application
Author(s) -
Bühler Katja
Publication year - 2001
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.00520
Subject(s) - bounding overwatch , intersection (aeronautics) , bounding volume , affine transformation , computer science , minimum bounding box , algorithm , parametric statistics , parametric surface , computation , mathematics , computer vision , artificial intelligence , geometry , image (mathematics) , collision detection , statistics , computer security , collision , engineering , aerospace engineering
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.