Paper Info
Title
Alternative interpretation of the Plücker quadric's ambient space and its application.
Abstract
It is well-known that there exists a bijection between the set of lines of the projective 3-dimensional space (P^3) and all real points of the so-called Plucker quadric (varPsi ). Moreover one can identify each point of the Plucker quadric’s ambient space with a linear complex of lines in (P^3). Within this paper we give an alternative interpretation for the points of (P^5) as lines of an Euclidean 4-space (E^4), which are orthogonal to a fixed direction. We study straight lines in (P^5), which correspond in the general case to cubic 2-surfaces in (E^4). These surfaces are geometrically connected with circular Darboux 2-motions in (E^4), as they are basic surfaces of the underlying line-symmetric motions. Finally we present an application of this interpretation in the context of interactive design of ruled surfaces and ruled surface strips/patches based on the algorithm of De Casteljau.
Year
Venue
Field
2018
arXiv: Computational Geometry
Ambient space,Notation,Combinatorics,Bijection,Existential quantification,STRIPS,Euclidean geometry,Quadric,Mathematics,Ruled surface
DocType
Volume
Citations 
Journal
abs/1803.09498
0
PageRank 
References 
Authors
0.34
7
1
Name
Order
Citations
PageRank
Georg Nawratil1225.94