### Abstract

A standard technique in solid modeling is to represent planes (or lines) by explicit equations and to represent vertices and edges implicitly by means of combinatorial information. Numerical problems that arise from using floating-point arithmetic to implement operations on solids can be avoided by using exact arithmetic . Since the execution time of exact arithmetic operators increases with the number of bits required to represent the operands, it is important to avoid increasing the number of bits required to represent the plane (or line) equation coefficients. Set operations on solids do not increase the number of bits required. However, rotating a solid greatly increases the number of bits required, thus adversely affecting efficiency. One proposed solution to this problem is to round the coefficients of each plane (or line) equation without altering the combinatorial information. We show that such rounding is NP-complete.

Original language | English (US) |
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Title of host publication | Proc Sixth Annu Symp Comput Geom |

Publisher | Publ by ACM |

Pages | 244-252 |

Number of pages | 9 |

ISBN (Print) | 0897913620 |

State | Published - 1990 |

Externally published | Yes |

Event | Proceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA Duration: Jun 6 1990 → Jun 8 1990 |

### Other

Other | Proceedings of the Sixth Annual Symposium on Computational Geometry |
---|---|

City | Berkeley, CA, USA |

Period | 6/6/90 → 6/8/90 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proc Sixth Annu Symp Comput Geom*(pp. 244-252). Publ by ACM.

**Finding compact coordinate representations for polygons and polyhedra.** / Milenkovic, Victor; Nackman, Lee R.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proc Sixth Annu Symp Comput Geom.*Publ by ACM, pp. 244-252, Proceedings of the Sixth Annual Symposium on Computational Geometry, Berkeley, CA, USA, 6/6/90.

}

TY - GEN

T1 - Finding compact coordinate representations for polygons and polyhedra

AU - Milenkovic, Victor

AU - Nackman, Lee R.

PY - 1990

Y1 - 1990

N2 - A standard technique in solid modeling is to represent planes (or lines) by explicit equations and to represent vertices and edges implicitly by means of combinatorial information. Numerical problems that arise from using floating-point arithmetic to implement operations on solids can be avoided by using exact arithmetic . Since the execution time of exact arithmetic operators increases with the number of bits required to represent the operands, it is important to avoid increasing the number of bits required to represent the plane (or line) equation coefficients. Set operations on solids do not increase the number of bits required. However, rotating a solid greatly increases the number of bits required, thus adversely affecting efficiency. One proposed solution to this problem is to round the coefficients of each plane (or line) equation without altering the combinatorial information. We show that such rounding is NP-complete.

AB - A standard technique in solid modeling is to represent planes (or lines) by explicit equations and to represent vertices and edges implicitly by means of combinatorial information. Numerical problems that arise from using floating-point arithmetic to implement operations on solids can be avoided by using exact arithmetic . Since the execution time of exact arithmetic operators increases with the number of bits required to represent the operands, it is important to avoid increasing the number of bits required to represent the plane (or line) equation coefficients. Set operations on solids do not increase the number of bits required. However, rotating a solid greatly increases the number of bits required, thus adversely affecting efficiency. One proposed solution to this problem is to round the coefficients of each plane (or line) equation without altering the combinatorial information. We show that such rounding is NP-complete.

UR - http://www.scopus.com/inward/record.url?scp=0025135647&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025135647&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025135647

SN - 0897913620

SP - 244

EP - 252

BT - Proc Sixth Annu Symp Comput Geom

PB - Publ by ACM

ER -