### Abstract

Practical solid modeling systems are plagued by numerical problems that arise from using floating-point arithmetic. Problems arise when numerical roundoff error in geometric operations causes the geometric information to become inconsistent with the combinatorial information. These problems can be avoided by using exact arithmetic instead of floating-point arithmetic. However, some operations, such as rotation, increase the number of bits required to represent the plane equation coefficients. Since the execution time of exact arithmetic operators increases with the number of bits in the operands, the increased number of bits in the plane equation coefficients can cause performance problems. One proposed solution to this performance problem is to round the plane equation coefficients without altering the combinatorial information. We show that such rounding is NP-complete.

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

Pages (from-to) | 753-769 |

Number of pages | 17 |

Journal | IBM Journal of Research and Development |

Volume | 34 |

Issue number | 5 |

State | Published - Sep 1990 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*IBM Journal of Research and Development*,

*34*(5), 753-769.

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

Research output: Contribution to journal › Article

*IBM Journal of Research and Development*, vol. 34, no. 5, pp. 753-769.

}

TY - JOUR

T1 - Finding compact coordinate representations for polygons and polyhedra

AU - Milenkovic, Victor

AU - Nackman, L. R.

PY - 1990/9

Y1 - 1990/9

N2 - Practical solid modeling systems are plagued by numerical problems that arise from using floating-point arithmetic. Problems arise when numerical roundoff error in geometric operations causes the geometric information to become inconsistent with the combinatorial information. These problems can be avoided by using exact arithmetic instead of floating-point arithmetic. However, some operations, such as rotation, increase the number of bits required to represent the plane equation coefficients. Since the execution time of exact arithmetic operators increases with the number of bits in the operands, the increased number of bits in the plane equation coefficients can cause performance problems. One proposed solution to this performance problem is to round the plane equation coefficients without altering the combinatorial information. We show that such rounding is NP-complete.

AB - Practical solid modeling systems are plagued by numerical problems that arise from using floating-point arithmetic. Problems arise when numerical roundoff error in geometric operations causes the geometric information to become inconsistent with the combinatorial information. These problems can be avoided by using exact arithmetic instead of floating-point arithmetic. However, some operations, such as rotation, increase the number of bits required to represent the plane equation coefficients. Since the execution time of exact arithmetic operators increases with the number of bits in the operands, the increased number of bits in the plane equation coefficients can cause performance problems. One proposed solution to this performance problem is to round the plane equation coefficients without altering the combinatorial information. We show that such rounding is NP-complete.

UR - http://www.scopus.com/inward/record.url?scp=0025480035&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025480035&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0025480035

VL - 34

SP - 753

EP - 769

JO - IBM Journal of Research and Development

JF - IBM Journal of Research and Development

SN - 0018-8646

IS - 5

ER -