### Abstract

In manufacturing industry, finding an orientation for a mold that eliminates surface defects and ensures a complete fill after termination of the gravity casting process is an important and difficult problem. We study the problem of determining a favorable position of a mold (modeled as a polyhedron) such that, when it is filled, no air pockets and ensuing surface defects arise. Given a polyhedron in a fixed orientation, we present a linear time algorithm that determines whether the mold can be filled from that orientation without forming air pockets. We also present an algorithm that determines the most favorable orientation for a polyhedral mold in O(n_{2}) time. A reduction from a well-known problem indicates that improving the O(n_{2}) bound is unlikely for general polyhedral molds. We relate fillability to some well known classes of polyhedra. For some of these classes of objects, an optimal direction of fillability can be determined in linear time. Finally, for molds that satisfy a local regularity condition, we give an improved algorithm that runs in time O(nklog_{2} nlog log(n/k)), where k is the number of venting holes needed to avoid air pockets in an optimal orientation.

Original language | English (US) |
---|---|

Pages (from-to) | 245-254 |

Number of pages | 10 |

Journal | CAD Computer Aided Design |

Volume | 30 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1998 |

### Fingerprint

### Keywords

- Algorithms
- Casting
- Computational geometry
- Filling
- Polyhedral molds

### ASJC Scopus subject areas

- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Industrial and Manufacturing Engineering

### Cite this

*CAD Computer Aided Design*,

*30*(4), 245-254. https://doi.org/10.1016/S0010-4485(97)00075-4

**Filling polyhedral molds.** / Bose, Prosenjit; Van Kreveld, Marc; Toussaint, Godfried.

Research output: Contribution to journal › Article

*CAD Computer Aided Design*, vol. 30, no. 4, pp. 245-254. https://doi.org/10.1016/S0010-4485(97)00075-4

}

TY - JOUR

T1 - Filling polyhedral molds

AU - Bose, Prosenjit

AU - Van Kreveld, Marc

AU - Toussaint, Godfried

PY - 1998/1/1

Y1 - 1998/1/1

N2 - In manufacturing industry, finding an orientation for a mold that eliminates surface defects and ensures a complete fill after termination of the gravity casting process is an important and difficult problem. We study the problem of determining a favorable position of a mold (modeled as a polyhedron) such that, when it is filled, no air pockets and ensuing surface defects arise. Given a polyhedron in a fixed orientation, we present a linear time algorithm that determines whether the mold can be filled from that orientation without forming air pockets. We also present an algorithm that determines the most favorable orientation for a polyhedral mold in O(n2) time. A reduction from a well-known problem indicates that improving the O(n2) bound is unlikely for general polyhedral molds. We relate fillability to some well known classes of polyhedra. For some of these classes of objects, an optimal direction of fillability can be determined in linear time. Finally, for molds that satisfy a local regularity condition, we give an improved algorithm that runs in time O(nklog2 nlog log(n/k)), where k is the number of venting holes needed to avoid air pockets in an optimal orientation.

AB - In manufacturing industry, finding an orientation for a mold that eliminates surface defects and ensures a complete fill after termination of the gravity casting process is an important and difficult problem. We study the problem of determining a favorable position of a mold (modeled as a polyhedron) such that, when it is filled, no air pockets and ensuing surface defects arise. Given a polyhedron in a fixed orientation, we present a linear time algorithm that determines whether the mold can be filled from that orientation without forming air pockets. We also present an algorithm that determines the most favorable orientation for a polyhedral mold in O(n2) time. A reduction from a well-known problem indicates that improving the O(n2) bound is unlikely for general polyhedral molds. We relate fillability to some well known classes of polyhedra. For some of these classes of objects, an optimal direction of fillability can be determined in linear time. Finally, for molds that satisfy a local regularity condition, we give an improved algorithm that runs in time O(nklog2 nlog log(n/k)), where k is the number of venting holes needed to avoid air pockets in an optimal orientation.

KW - Algorithms

KW - Casting

KW - Computational geometry

KW - Filling

KW - Polyhedral molds

UR - http://www.scopus.com/inward/record.url?scp=0032045810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032045810&partnerID=8YFLogxK

U2 - 10.1016/S0010-4485(97)00075-4

DO - 10.1016/S0010-4485(97)00075-4

M3 - Article

VL - 30

SP - 245

EP - 254

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 4

ER -