Paper Info
Title
Theoretical analytics of stereographic projection on 3D objects' intersection predicate
Abstract
Based on stereographic projection (SP), a novel and systematic three-dimensional (3D) objects' intersection predicate theory is inferred and formularized. The theory is deduced from the intersection of quasi-convex bodies. Since composite mapping has omnidirectional one-to-one mapping properties for any quasi-convex bodies, they can be accurately projected to the equatorial plane, and their intersection predicate can be simplified into two dimensions. Those predicate conclusions are further applied to common polyhedrons by the introduction of the radial dividing point concept. 'Point inclusion' and 'line traversing' are mathematically abstracted as the primary intersection predicate types for all kinds of 3D objects, even including curved line and curved surface. As a special case of 'point inclusion', 'polyhedron entirely included' is also pointed out. Meanwhile, the process of intersection predicate is heuristically optimized at object and face levels with well-matched bounding boxes: bounding sphere and projective cone.
Year
DOI
Venue
2010
10.1080/13658810802687327
International Journal of Geographical Information Science
Keywords
Field
DocType
composite mapping,intersection predicate,stereographic projection,curved surface,curved line,point concept,quasi-convex body,theoretical analytics,intersection predicate theory,point inclusion,primary intersection predicate type,predicate conclusion,three dimensional,convex body,two dimensions
Data mining,Combinatorics,Algebra,Projective cone,Computer science,Polyhedron,Bounding sphere,Stereographic projection,Intersection,Predicate (grammar),Intersection (Euclidean geometry),Bounding overwatch
Journal
Volume
Issue
ISSN
24
1
1365-8816
Citations 
PageRank 
References 
2
0.40
5
Authors
2
Name
Order
Citations
PageRank
Shuqing Zhang1306.18
Junyan Zhang220.40