Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves

Hyeong In Choi, Chang Yong Han, Hwan Pyo Moon, Kyeong Roh, Nam Sook Wee

Research output: Contribution to journalArticle

49 Citations (Scopus)

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 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.

Original languageEnglish (US)
Pages (from-to)59-72
Number of pages14
JournalCAD Computer Aided Design
Volume31
Issue number1
DOIs
StatePublished - Jan 1999
Externally publishedYes

Fingerprint

Medial Axis Transform
Offset Curves
Pythagorean-hodograph Curves
Domain Decomposition
Decomposition
Curve
Splines
Fundamental Domain
Geometric Graphs
Trimming
Rational Curves
Cubic Spline
Minkowski Space
Spline
Lemma
Trivial
Union
Radius
Decompose
Three-dimensional

ASJC Scopus subject areas

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

Cite this

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.

In: CAD Computer Aided Design, Vol. 31, No. 1, 01.1999, p. 59-72.

Research output: Contribution to journalArticle

Choi, Hyeong In ; Han, Chang Yong ; Moon, Hwan Pyo ; Roh, Kyeong ; Wee, Nam Sook. / Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves. In: CAD Computer Aided Design. 1999 ; Vol. 31, No. 1. pp. 59-72.
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