Geometric mean, splines and de Boor algorithm in geodesic spaces
作者： Esfandiar Nava-Yazdani
DOI:
关键词:
摘要: We extend the concepts of de Casteljau and Boor algorithms as well splines to geodesic spaces present some applications in geometric modeling. The concept weighted mean provides another approach splines. compare corresponding Bezier curves show that for Riemannian manifolds, their endpoint tangents coincide.
harvard.edu
arxiv.org
128.84.21.199参考文章(28)
Krzysztof Krakowski, K Huper, J Manton, On the Computation of the Karcher Mean on Spheres and Special Orthogonal Groups Workshop on Robotics and Mathematics (RoboMat 2007). ,(2007)
Klaus Höllig, Jörg Hörner, Approximation and Modeling with B-Splines Society for Industrial and Applied Mathematics. ,(2013) , 10.1137/1.9781611972955
Jürgen Jost, Nonpositive Curvature: Geometric and Analytic Aspects ,(1997)
Kuniaki Kawabata, Liang Ma, Jianru Xue, Chengwei Zhu, Nanning Zheng, A path generation for automated vehicle based on Bezier curve and via-points Robotics and Autonomous Systems. ,vol. 74, pp. 243- 252 ,(2015) , 10.1016/J.ROBOT.2015.08.001
P. Crouch, G. Kun, F. Silva Leite, The De Casteljau Algorithm on Lie Groups and Spheres Journal of Dynamical and Control Systems. ,vol. 5, pp. 397- 429 ,(1999) , 10.1023/A:1021770717822
Nicolas Boumal, P.-A. Absil, A discrete regression method on manifolds and its application to data on SO(n) IFAC Proceedings Volumes. ,vol. 18, pp. 2284- 2289 ,(2011) , 10.3182/20110828-6-IT-1002.00542
F. C. Park, B. Ravani, Bézier Curves on Riemannian Manifolds and Lie Groups with Kinematics Applications Journal of Mechanical Design. ,vol. 117, pp. 36- 40 ,(1995) , 10.1115/1.2826114
Johannes Wallner, On Convergent Interpolatory Subdivision Schemes in Riemannian Geometry Constructive Approximation. ,vol. 40, pp. 473- 486 ,(2014) , 10.1007/S00365-014-9264-0
Esfandiar Nava-Yazdani, Thomas P. Y. Yu, On Donoho’s Log-Exp Subdivision Scheme: Choice of Retraction and Time-Symmetry Multiscale Modeling & Simulation. ,vol. 9, pp. 1801- 1828 ,(2011) , 10.1137/100804838
Michael Hofer, Helmut Pottmann, Energy-minimizing splines in manifolds ACM Transactions on Graphics. ,vol. 23, pp. 284- 293 ,(2004) , 10.1145/1015706.1015716