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-YazdaniORCiD, 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 |
