Abstract
We introduce the concept of couple points as a global feature of surfaces. Couple points are pairs of points \(({\mathbf x}_1,{\mathbf x}_2)\) on a surface with the property that the vector \({\mathbf x}_2 - {\mathbf x}_1\) is parallel to the surface normals both at \({\mathbf x}_1\) and \({\mathbf x}_2\). In order to detect and classify them, we use higher order local feature detection methods, namely a Morse theoretic approach on a 4D scalar field. We apply couple points to a number of problems in Computer Graphics: the detection of maximal and minimal distances of surfaces, a fast approximation of the shortest geodesic path between two surface points, and the creation of stabilizing connections of a surface.
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Rössl, C., Theisel, H. (2012). Couple Points – A Local Approach to Global Surface Analysis. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_39
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DOI: https://doi.org/10.1007/978-3-642-27413-8_39
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