Two-dimensional offsets and medial axis transform

Hyeong In Choi, Sung Woo Choi, Chang Yong Han, Tae Wan Kim, Song Hwa Kwon, Hwan Pyo Moon, Kyeong Roh, Nam Sook Wee

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We present a mathematical theory of the two-dimensional offset curves from the viewpoint of medial axis transform. We explore the local geometry of the offset curve in relation with the medial axis transform, culminating in the classification of points on the offset curve. We then study the domain decomposition from the viewpoint of offsets, and in particular introduce the concept of monotonic fundamental domain as a device for detecting the correct topology of offsets as well as for stable numerical computation. The monotonic fundamental domains are joined by peaks or valleys of the medial axis transform, or by what we call the critical horizonal section whose algebro-geometric properties are rigorously treated as well.

Original languageEnglish (US)
Pages (from-to)171-199
Number of pages29
JournalAdvances in Computational Mathematics
Volume28
Issue number2
DOIs
StatePublished - Feb 1 2008

Keywords

  • Computer aided geometric design
  • Domain decomposition
  • Medial axis transform
  • Offset curves

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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    Choi, H. I., Choi, S. W., Han, C. Y., Kim, T. W., Kwon, S. H., Moon, H. P., Roh, K., & Wee, N. S. (2008). Two-dimensional offsets and medial axis transform. Advances in Computational Mathematics, 28(2), 171-199. https://doi.org/10.1007/s10444-007-9036-5