Approximation of 3D Shortest Polygons in Simple Cube Curves

Authors:
Thomas Bülow;Reinhard Klette
Affiliations:
-;-
Venue:
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Year:
2001

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Abstract

One possible definition of the length of a digitized curve in 3D is the length of the shortest polygonal curve lying entirely in a cube curve. In earlier work the authors proposed an iterative algorithm for the calculation of this minimal length polygonal curve (MLP). This paper reviews the algorithm and suggests methods to speed it up by reducing the set of possible locations of vertices of the MLP, or by directly calculating MLP-vertices in specific situations. Altogether, the paper suggests an in-depth analysis of cube curves.