The Local Projective Shape of Smooth Surfaces and Their Outlines
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This article examines projectively-invariant local geometric properties of smooth curves and surfaces. Oriented projective differential geometry is proposed as a general framework for establishing such invariants and characterizing the local projective shape of surfaces and their outlines. It is applied to two problems: (1) the projective generalization of Koenderink’s famous characterization of convexities, concavities, and inflections of the apparent contours of solids bounded by smooth surfaces, and (2) the image-based construction of rim meshes, which provide a combinatorial description of the arrangement induced on the surface of an object by the contour generators associated with multiple cameras observing it.
Keywordsprojective differential geometry oriented projective geometry differential invariants local shape frontier points
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