MOS surfaces: Medial surface transforms with rational domain boundaries. (English) Zbl 1163.68353

Kosinka, Jiří; Jüttler, Bert

Martin, Ralph (ed.) et al., Mathematics of surfaces XII. 12th IMA international conference, Sheffield, UK, September 4–6, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73842-8/pbk). Lecture Notes in Computer Science 4647, 245-262 (2007).

Summary: We consider rational surface patches \(s(u,v)\) in the four-dimensional Minkowski space \(\mathbb{R}^{3,1}\), which describe parts of the medial surface (or medial axis) transform of spatial domains. The corresponding segments of the domain boundary are then obtained as the envelopes of the associated two-parameter family of spheres. If the Plücker coordinates of the line at infinity of the (two-dimensional) tangent plane of \(s\) satisfy a sum-of-squares condition, then the two envelope surfaces are shown to be rational surfaces. We characterize these Plücker coordinates and analyze the case, where the medial surface transform is contained in a hyperplane of the four-dimensional Minkowski space.
For the entire collection see [Zbl 1122.68007].

MSC:

68U05	Computer graphics; computational geometry (digital and algorithmic aspects)
65D18	Numerical aspects of computer graphics, image analysis, and computational geometry