Kinematic convexity of spherical displacements and its application to collision prediction

Q. J. Ge, Anurag Purwar, Jun Wu
2008 Proceedings of the 2008 ACM symposium on Solid and physical modeling - SPM '08  
In recent years, there has been an increasing interest in developing geometric algorithms for kinematic computations. The aim of this paper is to present the notion of kinematic convexity as a key element for a new framework for spherical kinematic geometry that allows for the development of more elegant and efficient algorithms for geometric computations in kinematic applications. The resulting framework, called computational spherical kinematic geometry, is developed by combining the oriented
more » ... projective geometry with the kinematic geometry of spherical motions. By extending the idea of convexity in affine geometry to an oriented image space of spherical displacements, the notion of kinematic convexity is proposed. A novel application to the collision prediction problem is presented to illustrate the theory developed.
doi:10.1145/1364901.1364955 dblp:conf/sma/GePW08 fatcat:spfog5zdprbjxemtlywjftub74