Geometric Motion Design

We describe the use of rational B--spline motions for the solution of motion design problems. It is shown that such motions possess two kinds of control structures suitable for interactive design or geometry processing, respectively. A main advantage of the proposed technique over previous approaches is that it is built directly onto standard CAD algorithms and thus it inherits their advantages. As examples, we briefly examine interpolation problems and relations to rational curves and surfaces with rational offsets. 1. Introduction This paper reports on recent progress in a research direction that tries to combine methods from kinematics and computer aided geometric design in order to solve motion design problems. This has applications in several areas. For example, in computer animation one often wants to design a smooth motion of a camera that interpolates or approximates some given positions (key frames). Other applications are in mechanical systems animation or motion planning fo..