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Nonsplitting Macro Patches for Implicit Cubic Spline Surfaces
Author(s) -
Guo B.
Publication year - 1993
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 - 10.1111/1467-8659.1230433
Subject(s) - polyhedron , quadric , monotone polygon , cubic function , cubic surface , macro , spline (mechanical) , monotone cubic interpolation , mathematics , surface (topology) , algebraic surface , algebraic number , computer science , polynomial , geometry , pure mathematics , bicubic interpolation , mathematical analysis , programming language , structural engineering , linear interpolation , engineering
Macro patches are important for generating quadric or cubic implicit spline surfaces from the input of a polyhedron. All existing macro patches split the triangular facets of the polyhedron; this paper presents cubic nonsplitting macro patches (NMP) that do not split these facets. The NMP's are based on a necessary and sufficient condition for nonsplitting constructions of implicit cubic spline surfaces. This condition can be satisfied for most practical applications, so the NMP's lead to an efficient and powerful spline surface scheme using implicit cubics. The free parameters in an NMP are set using a new technique for excluding topological anomalies such as extraneous sheets, splits, unwanted holes, self‐intersections, and unwanted handles. Each cubic patch obtained by this technique best approximates, in a least‐squares sense, a quadric patch from a single algebraic component of a monotone polynomial derived from the input data.