Journal Article

Envelopes of splines in the projective plane

Krzysztof Andrzej Krakowski

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 22, issue 2, pages 171-180
Published in print June 2005 | ISSN: 0265-0754
Published online June 2005 | e-ISSN: 1471-6887 | DOI:
Envelopes of splines in the projective plane

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In this paper a family of curves—Riemannian cubics—in the unit sphere and the real projective plane is investigated. Riemannian cubics naturally arise as solutions to variational problems in Riemannian spaces. It is remarkable to find that an envelope of lines generated by a Riemannian cubic in one space is (nearly) a Riemannian cubic in another space.

Keywords: Riemannian cubic polynomials; real projective plane; envelopes

Journal Article.  0 words. 

Subjects: Mathematics

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