De Casteljau's Algotithm on Manifolds

Please always quote using this URN: urn:nbn:de:0297-zib-69096
  • This paper proposes a generalization of the ordinary de Casteljau algorithm to manifold-valued data including an important special case which uses the exponential map of a symmetric space or Riemannian manifold. We investigate some basic properties of the corresponding Bézier curves and present applications to curve design on polyhedra and implicit surfaces as well as motion of rigid body and positive definite matrices. Moreover, we apply our approach to construct canal and developable surfaces.

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Author:Esfandiar Nava-Yazdani, Konrad Polthier
Document Type:Article
Parent Title (English):Computer Aided Geometric Design
Volume:30
Issue:7
First Page:722
Last Page:732
Publisher:CAGD
Date of first Publication:2013/10/01
Published in:Computer Aided Geometric Design
DOI:https://doi.org/10.1016/j.cagd.2013.06.002