Introduction to theoretical kinematics
Introduction to theoretical kinematics
Oriented projective geometry
Computational geometry in C
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Spherical averages and applications to spherical splines and interpolation
ACM Transactions on Graphics (TOG)
Collision prediction for polyhedra under screw motions
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
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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 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.