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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Couple Points – A Local Approach to Global Surface Analysis
verfasst von : Christian Rössl, Holger Theisel
Erschienen in: Curves and Surfaces
Verlag: Springer Berlin Heidelberg
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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.