On the geometry of rolling and interpolation curves on S-n, SOn, and Grassmann manifolds

Hueper, KnutLeite, F Silva2015-12-101079-2724http://hdl.handle.net/1885/54055We present a procedure to generate smooth interpolating curves on submanifolds, which are given in closed form in terms of the coordinates of the embedding space. In contrast to other existing methods, this approach makes the corresponding algorithm easyKeywords: Constrained variational problems; Grassmann manifold; Orthogonal group; Parallel transport; Rolling mapping; Constraint theory; Geometry; Kinematics; Polynomials; Vectors; Interpolation Constrained variational problems; Geodesics; Geometric splines; Grassmann manifold; Interpolation; Kinematic equation; Orthogonal group; Parallel transport; Rolling mapping; SphereOn the geometry of rolling and interpolation curves on S-n, SOn, and Grassmann manifolds200710.1007/s10883-007-9027-32015-12-09