Abstract
Simple cube-curves in a 3D orthogonal grid are polyhedrally bounded sets which model digitized curves or arcs in three-dimensional euclidean space. The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve. A critical edge is a grid edge contained in three consecutive cubes of a simple cube-curve. This paper shows that critical edges are the only possible locations of vertices of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve.
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Klette, R., Bülow, T. (2000). Minimum-Length Polygons in Simple Cube-Curves. In: Borgefors, G., Nyström, I., di Baja, G.S. (eds) Discrete Geometry for Computer Imagery. DGCI 2000. Lecture Notes in Computer Science, vol 1953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44438-6_38
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DOI: https://doi.org/10.1007/3-540-44438-6_38
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