@article{NavaYazdani2013722,
title = "De Casteljauʼs algorithm on manifolds ",
journal = "Computer Aided Geometric Design ",
volume = "30",
number = "7",
pages = "722 - 732",
year = "2013",
note = "",
issn = "0167-8396",
doi = "http://dx.doi.org/10.1016/j.cagd.2013.06.002",
url = "http://www.sciencedirect.com/science/article/pii/S0167839613000551",
author = "E. Nava-Yazdani and K. Polthier",
keywords = "Bézier curve",
keywords = "Canal surface",
keywords = "Ruled surface",
keywords = "Symmetric spaces",
keywords = "Rigid body motion",
keywords = "Euclidean group",
keywords = "Positive definite matrix",
keywords = "Nonlinear subdivision",
keywords = "Lie group",
keywords = "De Casteljauʼs algorithm ",
abstract = "Abstract 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. "
}