A two-step algorithm of smooth spline generation on Riemannian manifolds |
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| Institution: | 1. Institute of Engineering Cybernetics, Wrocłlaw University of Technology, ul. Janiszewskiego 11/17, 50-370 Wrocłlaw, Poland;2. Departamento de Matemática, Universidade de Coimbra, 3000 Coimbra, Portugal;3. Departamento de Física e Matemática, Instituto Superior de Engenharia, Rua Pedro Nunes, 3030-199 Coimbra, Portugal |
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| Abstract: | This paper presents a simple geometric algorithm to generate splines of arbitrary degree of smoothness in Euclidean spaces. Unlike other existing methods, this simple geometric algorithm does not require a recursive procedure and, consequently, introduces a significant reduction in calculation time. The algorithm is then extended to other complete Riemannian manifolds, namely to matrix Lie groups and spheres. |
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