Computer-Aided Design With Spatial Rational B-Spline Motions

Using rational motions it is possible to apply many fundamental B-spline techniques to the design of motions. The present paper summarizes the basic theory of rational motions and introduces a linear control structure for piecewise rational motions suitable for geometry processing. Moreover it provides algorithms for the calculation of the surface which is swept out by a moving polyhedron and examines interpolation techniques. The methods presented in this paper can be applied to various problems in computer animation as well as in robotics.

[1]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[2]  Helmut Pottmann,et al.  Developable rational Bézier and B-spline surfaces , 1995, Comput. Aided Geom. Des..

[3]  F. Park,et al.  Bézier Curves on Riemannian Manifolds and Lie Groups with Kinematics Applications , 1995 .

[4]  Michael G. Wagner.  Planar rational B-spline motions , 1995, Comput. Aided Des..

[5]  Bert Jüttler.  Spatial rational motions and their application in computer aided geometric design , 1995 .

[6]  John K. Johnstone,et al.  Rational control of orientation for animation , 1995 .

[7]  Bahram Ravani,et al.  Computer aided geometric design of motion interpolants , 1994 .

[8]  Bahram Ravani,et al.  Geometric Construction of Bézier Motions , 1994 .

[9]  Bert Jüttler,et al.  Visualization of moving objects using dual quaternion curves , 1994, Comput. Graph..

[10]  Bert Jüttler.  Rationale Bézierdarstellung räumlicher Bewegungsvorgänge und ihre Anwendung zur Beschreibung bewegter Objekte , 1994 .

[11]  Wolfgang Rath.  Matrix groups and kinematics in projective spaces , 1993 .

[12]  R. Mohan,et al.  Design of developable surfaces using duality between plane and point geometries , 1993, Comput. Aided Des..

[13]  K. Mørken.  Some identities for products and degree raising of splines , 1991 .

[14]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[15]  Gregory M. Nielson,et al.  A survey of applications of an affine invariant norm , 1989 .

[16]  G. Nürnberger.  Approximation by Spline Functions , 1989 .

[17]  Fujio Yamaguchi,et al.  Curves and Surfaces in Computer Aided Geometric Design , 1988, Springer Berlin Heidelberg.

[18]  David Handscomb.  Knot-Elimination; Reversal of the Oslo Algorithm , 1987 .

[19]  Ken Shoemake,et al.  Animating rotation with quaternion curves , 1985, SIGGRAPH.

[20]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[21]  K. Strubecker.  Einführung in die Liniengeometrie und Kinematik , 1936 .