Refinable G1 functions on G1 free-form surfaces

For two high-quality piecewise polynomial geometrically smooth (G1) surface constructions, explicit G1 functions are derived that form the basis of a function space on the G1 surfaces. The spaces are refinable and nested, i.e. the functions can be re-represented at a finer level. By choosing all bas...

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Bibliographic Details
Published inComputer aided geometric design Vol. 54; pp. 61 - 73
Main Authors Karčiauskas, Kȩstutis, Peters, Jörg
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.05.2017
Subjects
Free-form surfaces
Functions on surfaces
Geometric continuity
Multi-resolution
Refinable space
Multi-resolution
Functions on surfaces
Geometric continuity
Refinable space
Free-form surfaces
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Summary:For two high-quality piecewise polynomial geometrically smooth (G1) surface constructions, explicit G1 functions are derived that form the basis of a function space on the G1 surfaces. The spaces are refinable and nested, i.e. the functions can be re-represented at a finer level. By choosing all basis functions to be first order smooth a maximal set of degrees of freedom is obtained that have small support and near-uniform layout. •For two G1 surface constructions, an explicit G1 basis is derived.•The G1 basis generates functions on these surfaces.•The spaces of functions are refinable and nested.•Enforcing only first-order smoothness yields a maximal set of free functions.•The maximal set has small support and near-uniform layout.
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2017.02.014