On detecting the orientation of polygons and polyhedra
B. K. Natarajan
Abstract
B. K. Natarajan
Abstract
This paper concerns the use of ray sensors to detect the orientation of polygonal and polyhedral objects moving on a belt or slide. The problem is abstracted to the computational domain and the following results obtained. For polygons of n vertices, n sensors are sufficient and (n/2) necessary. For convex polyhedra of n vertices, (6n) sensors are sufficient and (n/4) necessary. Non-convex polyhedra cannot be effectively handled with such sensors.
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This paper concerns the use of ray sensors to detect the orientation of polygonal and polyhedral objects moving on a belt or slide. The problem is abstracted to the computational domain and the following results obtained. For polygons of n vertices, n sensors are sufficient and (n/2) necessary. For convex polyhedra of n vertices, (6n) sensors are sufficient and (n/4) necessary. Non-convex polyhedra cannot be effectively handled with such sensors.
Key concepts: Polyhedron, Regular polygon, Orientation (vector space), Domain (mathematical analysis), Combinatorics, Computational geometry, Computer science, Mathematics