### 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 language | English (US) |
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Pages | 102-111 |

Number of pages | 10 |

State | Published - Jan 1 1996 |

Event | Proceedings of the 1996 14th International Conference of the Computer Graphics Society, CGI'96 - Pohang, South Korea Duration: Jun 24 1996 → Jun 28 1996 |

### Other

Other | Proceedings of the 1996 14th International Conference of the Computer Graphics Society, CGI'96 |
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City | Pohang, South Korea |

Period | 6/24/96 → 6/28/96 |

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### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*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.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - Computing the constrained Euclidean, geodesic and link centre of a simple polygon with applications

AU - Bose, Prosenjit

AU - Toussaint, Godfried

PY - 1996/1/1

Y1 - 1996/1/1

N2 - 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.

AB - 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.

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M3 - Paper

AN - SCOPUS:0029721530

SP - 102

EP - 111

ER -