Beyond the Celestial Sphere: Oriented Projective Geometry and Computer Graphics

2002 ◽  
Vol 75 (5) ◽  
pp. 351 ◽  
Author(s):  
Kevin G. Kirby
Keyword(s):  
Computer Graphics ◽  
Projective Geometry ◽  
Oriented Projective Geometry ◽  
Celestial Sphere

Kinematic Convexity of Rigid Body Displacements

2010 ◽  
Author(s):  
Anurag Purwar ◽  
Jeff Ge
Keyword(s):  
Rigid Body ◽  
Projective Space ◽  
Projective Geometry ◽  
Geometric Analysis ◽  
Image Space ◽  
Geometric Algorithms ◽  
Oriented Projective Geometry ◽  
Swept Volumes ◽  
Rigid Body Motions ◽  
Interference Checking

In this paper, we explore the notion of kinematic convexity for rigid body displacements. Previously, we have shown that when spatial rigid body displacements are represented by dual quaternions, an oriented projective space is better suited for the image space of displacements. Geometric algorithms for rigid body motions become more general and elegant when developed from the perspective of oriented projective geometry. By extending the concept of convexity in affine geometry to oriented projective geometry of the image space of rigid body displacements, we define the concept of kinematic convexity. This concept, apart from being theoretically significant, facilitates localization of a displacements and provides a measure of the kinematic separation useful in collision prediction, interference checking, and geometric analysis of swept volumes.

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