Computational geometry: an introduction
Computational geometry: an introduction
Solid shape
Pattern Recognition Letters
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Computational Line Geometry
3D surface point and wireframe reconstruction from multiview photographic images
Image and Vision Computing
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A set S is called convex if, for all points P, Q of S, the line segment PQ is contained in S. A simple closed planar curve and a simple closed surface are not convex by this definition, but they are called "convex" if they are boundaries of convex sets, and similarly a planar arc is called "convex" if it is a subset of the boundary of a convex set. This concept of "convexity" is ordinarily defined only for planar arcs, but we show that it can also be used in 3D. Points on the boundary of a convex set--in particular, points of a "convex" curve or surface--have useful visibility and accessibility properties. We establish some of these properties, and also characterize some special classes of "convex" space arcs and curves.