### Abstract

We present a new approach to medial axis transform and offset curve computation. Our algorithm is based on the domain decomposition scheme which reduces a complicated domain into a union of simple subdomains each of which is very easy to handle. This domain decomposition approach gives rise to the decomposition of the corresponding medial axis transform which is regarded as a geometric graph in the three dimensional Minkowski space R^{2,1}. Each simple piece of the domain, called the fundamental domain, corresponds to a space-like curve in R^{2,1}. Then using the new spline, called the Minkowski Pythagorean hodograph curve which was recently introduced, we approximate within the desired degree of accuracy the curve part of the medial axis transform with a G^{1} cubic spline of Minkowski Pythagorean hodograph. This curve has the property of enabling us to write all offset curves as rational curves. Further, this Minkowski Pythagorean hodograph curve representation together with the domain decomposition lemma makes the trimming process essentially trivial. We give a simple procedure to obtain the trimmed offset curves in terms of the radius function of the MPH curve representing the medial axis transform.

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

Pages (from-to) | 59-72 |

Number of pages | 14 |

Journal | CAD Computer Aided Design |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1999 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Industrial and Manufacturing Engineering
- Geometry and Topology

### Cite this

*CAD Computer Aided Design*,

*31*(1), 59-72. https://doi.org/10.1016/S0010-4485(98)00080-3

**Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves.** / Choi, Hyeong In; Han, Chang Yong; Moon, Hwan Pyo; Roh, Kyeong; Wee, Nam Sook.

Research output: Contribution to journal › Article

*CAD Computer Aided Design*, vol. 31, no. 1, pp. 59-72. https://doi.org/10.1016/S0010-4485(98)00080-3

}

TY - JOUR

T1 - Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves

AU - Choi, Hyeong In

AU - Han, Chang Yong

AU - Moon, Hwan Pyo

AU - Roh, Kyeong

AU - Wee, Nam Sook

PY - 1999/1

Y1 - 1999/1

N2 - We present a new approach to medial axis transform and offset curve computation. Our algorithm is based on the domain decomposition scheme which reduces a complicated domain into a union of simple subdomains each of which is very easy to handle. This domain decomposition approach gives rise to the decomposition of the corresponding medial axis transform which is regarded as a geometric graph in the three dimensional Minkowski space R2,1. Each simple piece of the domain, called the fundamental domain, corresponds to a space-like curve in R2,1. Then using the new spline, called the Minkowski Pythagorean hodograph curve which was recently introduced, we approximate within the desired degree of accuracy the curve part of the medial axis transform with a G1 cubic spline of Minkowski Pythagorean hodograph. This curve has the property of enabling us to write all offset curves as rational curves. Further, this Minkowski Pythagorean hodograph curve representation together with the domain decomposition lemma makes the trimming process essentially trivial. We give a simple procedure to obtain the trimmed offset curves in terms of the radius function of the MPH curve representing the medial axis transform.

AB - We present a new approach to medial axis transform and offset curve computation. Our algorithm is based on the domain decomposition scheme which reduces a complicated domain into a union of simple subdomains each of which is very easy to handle. This domain decomposition approach gives rise to the decomposition of the corresponding medial axis transform which is regarded as a geometric graph in the three dimensional Minkowski space R2,1. Each simple piece of the domain, called the fundamental domain, corresponds to a space-like curve in R2,1. Then using the new spline, called the Minkowski Pythagorean hodograph curve which was recently introduced, we approximate within the desired degree of accuracy the curve part of the medial axis transform with a G1 cubic spline of Minkowski Pythagorean hodograph. This curve has the property of enabling us to write all offset curves as rational curves. Further, this Minkowski Pythagorean hodograph curve representation together with the domain decomposition lemma makes the trimming process essentially trivial. We give a simple procedure to obtain the trimmed offset curves in terms of the radius function of the MPH curve representing the medial axis transform.

UR - http://www.scopus.com/inward/record.url?scp=0032666527&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032666527&partnerID=8YFLogxK

U2 - 10.1016/S0010-4485(98)00080-3

DO - 10.1016/S0010-4485(98)00080-3

M3 - Article

AN - SCOPUS:0032666527

VL - 31

SP - 59

EP - 72

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 1

ER -