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Two-dimensional offsets and medial axis transform

Authors :
Kyeong Hah Roh
Tae-wan Kim
Hyeong In Choi
Hwan Pyo Moon
Chang Yong Han
Nam-Sook Wee
Song-Hwa Kwon
Sung Woo Choi
Source :
Advances in Computational Mathematics. 28:171-199
Publication Year :
2007
Publisher :
Springer Science and Business Media LLC, 2007.

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.

Details

ISSN :
15729044 and 10197168
Volume :
28
Database :
OpenAIRE
Journal :
Advances in Computational Mathematics
Accession number :
edsair.doi...........64218d0a4142f6551b3b5cf281994efa