Splines in geometry and topology

This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to more thorough treatments of the subject. •Many varieties X h...

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Bibliographic Details
Published inComputer aided geometric design Vol. 45; pp. 32 - 47
Main Author Tymoczko, Julianna
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2016
Subjects
Equivariant cohomology
Generalized splines
Generalized splines
Equivariant cohomology
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ISSN0167-8396
1879-2332
1879-2332
DOI10.1016/j.cagd.2015.11.006

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Summary:This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to more thorough treatments of the subject. •Many varieties X have a graph GX that describes their essential geometric features.•The splines S∞0(GX) form the equivariant cohomology ring and encode key data about X.•We describe geometric tools to analyze splines that differ from classical tools.•We give an algebraic and combinatorial generalization called generalized splines.
ISSN:0167-8396
1879-2332
1879-2332
DOI:10.1016/j.cagd.2015.11.006