TY - JOUR A1 - Nava-Yazdani, Esfandiar A1 - Polthier, Konrad T1 - De Casteljau's Algotithm on Manifolds T2 - Computer Aided Geometric Design N2 - 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. Y1 - 2013 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6909 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-69096 VL - 30 IS - 7 SP - 722 EP - 732 PB - CAGD ER -