Bézier curves and C 2 interpolation in Riemannian manifolds
Tài liệu tham khảo
J. Ahlberg, E. Nilson, J. Walsh, The Theory of Splines and Their Applications, Mathematics in Science and Engineering, No. 38. Academic Press, New York, 1967.
Belta, 2002, On the computation of rigid body motion, Electron. J. Comput. Kinematics, 1
Belta, 2002, Euclidean metrics for motion generation on SE(3), J. Mech. Eng. Sci. Part C, 216, 47, 10.1243/0954406021524909
Bézier, 1986
M. Camarinha, The geometry of cubic polynomials on Riemannian manifolds, Ph.D. Thesis, University of Coimbra, 1996.
Camarinha, 1995, Splines of class Ck on non-Euclidean spaces, IMA J. Math. Control Inform., 12, 399, 10.1093/imamci/12.4.399
Camarinha, 2001, On the geometry of Riemannian cubic polynomials, Differential Geom. Appl., 15, 107, 10.1016/S0926-2245(01)00054-7
Crouch, 1999, The de Casteljau algorithm on Lie groups and spheres, J. Dyn. Control Syst., 5, 397, 10.1023/A:1021770717822
Crouch, 1995, The dynamic interpolation problem: on Riemannian manifolds, Lie groups and symmetric spaces, J. Dyn. Control Syst., 1, 177, 10.1007/BF02254638
P. de Casteljau, Outillages méthodes de calcul’, Technical Report, André Citroën Automobiles, Paris, 1959.
do Carmo, 1992
Duff, 1986, Splines in animation and modelling
Farin, 1999
Farin, 2001
Gabriel, 1985, Spline interpolation in curved space, 1
Ge, 1994, Geometric construction of Bézier motions, Trans. ASME J. Mech. Des., 116, 749, 10.1115/1.2919446
Ge, 1994, Computer aided geometric design of motion interpolants, Trans. ASME J. Mech. Des., 116, 756, 10.1115/1.2919447
Giambo, 2002, An analytical theory for Riemannian cubic polynomials, IMA J. Math. Control Inform., 19, 445, 10.1093/imamci/19.4.445
Giambo, 2004, Optimal control on Riemannian manifolds by interpolation, Math. Control Signals and Syst., 16, 278, 10.1007/s00498-003-0139-3
Hofer, 2004, Energy-minimizing splines in manifolds, ACM Trans. Graphics, 23, 284, 10.1145/1015706.1015716
Jüttler, 1996, Computer-aided design with spatial rational B-spline motions, Trans. ASME J. Mech. Des., 118, 193, 10.1115/1.2826869
Kim, 1995, A general construction scheme for unit quaternion curves with simple high order derivatives, 369
Kim, 1995, Interpolating solid orientations with circular blending quaternion curves, Comput. Aided Des., 27, 385, 10.1016/0010-4485(95)96802-S
Kim, 1996, Hermite interpolation of solid orientations with circular blending quaternion curves, J. Visualization Comput. Animation, 7, 95, 10.1002/(SICI)1099-1778(199604)7:2<95::AID-VIS138>3.0.CO;2-8
K. Krakowski, Geometrical Methods of Inference, Ph.D. Thesis, University of Western Australia, 2002.
Krakowski, 2005, Envelopes of splines in the projective plane, IMA J. Math. Control Inform., 22, 171, 10.1093/imamci/dni014
Lane, 1980, A theoretical development for the computer generation and display of piecewise polynomial surfaces, IEEE Trans. Pattern Anal. Mach. Intell., 2, 35, 10.1109/TPAMI.1980.4766968
J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51. Princeton University Press, Princeton, 1963.
Nielson, 1993, Smooth interpolation of orientation, 75
Nielson, 1992, Animated rotations using quaternions and splines on a 4D sphere, Programming Comput. Software, 18, 145
Noakes, 1997, Riemannian quadratics, 319
Noakes, 1998, Nonlinear corner-cutting, Adv. Comput. Math., 8, 165, 10.1023/A:1018940112654
Noakes, 1999, Accelerations of Riemannian quadratics, Proc. Amer. Math. Soc., 127, 1827, 10.1090/S0002-9939-99-04809-1
Noakes, 2003, Null cubics and Lie quadratics, J. Math. Phys., 44, 1436, 10.1063/1.1537461
Noakes, 2004, Non-null Lie quadratics in E3, J. Math. Phys., 45, 4334, 10.1063/1.1803609
Noakes, 2006, Duality and Riemannian cubics, Adv. Comput. Math., 25, 195, 10.1007/s10444-004-7621-4
Noakes, 2006, Lax constraints in semisimple Lie groups, Quart. J. Math., 57, 527, 10.1093/qmath/hal002
Noakes, 1989, Cubic splines on curved spaces, IMA J. Math. Control Inform., 6, 465, 10.1093/imamci/6.4.465
Noakes, 2005, Null Riemannian cubics in tension in SO(3), IMA J. Math. Control Inform., 22, 477, 10.1093/imamci/dni040
Noakes, 2006, Quadratures and cubics in SO(3) and SO(1,2), IMA J. Math. Control Inform, 23, 463, 10.1093/imamci/dni069
Park, 1995, Bézier curves on Riemannian manifolds and Lie groups with kinematic applications, Trans. ASME J. Mech. Des., 117, 36, 10.1115/1.2826114
Park, 1997, Smooth invariant interpolation of rotations, ACM Trans. Graphics, 16, 277, 10.1145/256157.256160
Popiel, 2006, C2 spherical Bézier splines, Comput. Aided Geom. Des., 23, 261, 10.1016/j.cagd.2005.11.003
Pottmann, 2005, A variational approach to spline curves on surfaces, Comput. Aided Geom. Des., 22, 693, 10.1016/j.cagd.2005.06.006
Schlag, 1991, Using geometric constructions to interpolate orientation with quaternions, 377
Shoemake, 1985, Animating rotations with quaternion curves, ACM SIGGRAPH Comput. Graphics, 19, 245, 10.1145/325165.325242
Silva Leite, 2000, Elastic curves as solutions of sub-Riemannian control problems, Math. Control Signals Systems, 13, 140, 10.1007/PL00009863
Wallner, 2006, Smoothness analysis of subdivision schemes by proximity, Constr. Approx., 24, 289, 10.1007/s00365-006-0638-3
Wallner, 2005, Convergence and C1 analysis of subdivision schemes on manifolds by proximity, Comput. Aided Geom. Design, 22, 593, 10.1016/j.cagd.2005.06.003
Žefran, 1998, Interpolation schemes for rigid body motions, Comput. Aided Design, 30, 179, 10.1016/S0010-4485(97)00060-2
Žefran, 1998, On the generation of smooth three-dimensional rigid body motions, IEEE Trans. Robotics & Automat., 14, 576, 10.1109/70.704225
