Computing the constrained Euclidean, geodesic and link centre of a simple polygon with applications

Prosenjit Bose, Godfried Toussaint

Research output: Contribution to conferencePaper

Abstract

In the manufacturing industry, finding a suitable location for the pin gate (the pin gate is the point from which liquid is poured or injected into a mold) is a difficult problem when viewed from the fluid dynamics of the molding process. However, experience has shown that a suitable pin gate location possesses several geometric characteristics, namely the distance from the pin gate to any point in the mold should be small and the number of turns on the path from a point in the mold to the pin gate should be small. We address the problem of computing locations that possess these geometric characteristics. Given a mold M (modeled by an n vertex simple polygon) we show how to compute the Euclidean center of M constrained to lie in the interior of M or on the boundary of M in O (n log n + k) time where k is the number of intersections between M and the furthest point Voronoi diagram of the vertices of M. We show how to compute the geodesic center of M constrained to the boundary in O (n log n) time and the geodesic center of M constrained to lie in a polygonal region in O (n(n + k)) time. Finally, we show how to compute the link center of M constrained to the boundary of M in O (n log n) time.

Original languageEnglish (US)
Pages102-111
Number of pages10
StatePublished - Jan 1 1996
EventProceedings of the 1996 14th International Conference of the Computer Graphics Society, CGI'96 - Pohang, South Korea
Duration: Jun 24 1996Jun 28 1996

Other

OtherProceedings of the 1996 14th International Conference of the Computer Graphics Society, CGI'96
CityPohang, South Korea
Period6/24/966/28/96

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Fluid dynamics
Molding
Liquids
Industry

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Bose, P., & Toussaint, G. (1996). Computing the constrained Euclidean, geodesic and link centre of a simple polygon with applications. 102-111. Paper presented at Proceedings of the 1996 14th International Conference of the Computer Graphics Society, CGI'96, Pohang, South Korea, .

Computing the constrained Euclidean, geodesic and link centre of a simple polygon with applications. / Bose, Prosenjit; Toussaint, Godfried.

1996. 102-111 Paper presented at Proceedings of the 1996 14th International Conference of the Computer Graphics Society, CGI'96, Pohang, South Korea, .

Research output: Contribution to conferencePaper

Bose, P & Toussaint, G 1996, 'Computing the constrained Euclidean, geodesic and link centre of a simple polygon with applications', Paper presented at Proceedings of the 1996 14th International Conference of the Computer Graphics Society, CGI'96, Pohang, South Korea, 6/24/96 - 6/28/96 pp. 102-111.
Bose P, Toussaint G. Computing the constrained Euclidean, geodesic and link centre of a simple polygon with applications. 1996. Paper presented at Proceedings of the 1996 14th International Conference of the Computer Graphics Society, CGI'96, Pohang, South Korea, .
Bose, Prosenjit ; Toussaint, Godfried. / Computing the constrained Euclidean, geodesic and link centre of a simple polygon with applications. Paper presented at Proceedings of the 1996 14th International Conference of the Computer Graphics Society, CGI'96, Pohang, South Korea, .10 p.
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