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Flatness criteria for subdivision of rational Bézier curves and surfaces
Author(s) -
Dyllong E.,
Luther W.
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200108115132
Subject(s) - subdivision , bézier curve , subdivision surface , flatness (cosmology) , computation , geometric design , mathematics , piecewise , context (archaeology) , piecewise linear function , computer science , mathematical optimization , algorithm , geometry , mathematical analysis , paleontology , physics , archaeology , cosmology , quantum mechanics , biology , history
Many of well‐known algorithms in the context of Computer Aided Geometric Design are based on subdivision techniques. Unfortunately, termination criteria for subdivision mostly require a time‐consuming computation of the maximum deviation between any given curve segment and its linear approximation at each subdivision step. We generalize results by Wang for Bézier curves ]3[ and present an approach which in advance specifies the number of necessary subdivision steps to obtain a piecewise linear approximation within an assumed accuracy for a given rational Bézier curve or surface.