Journal for Geometry and Graphics 19 (2015), No. 2, 189--200
Copyright Heldermann Verlag 2015
Blending of Spheres by Rotation-Minimizing Surfaces
Miklós Hoffmann
Institute of Mathematics and Computer Science, Károly Eszterházy University, Eger, Hungary
hofi@ektf.hu
Juan Monterde
Dep. de Geometria i Topologia, Universitat de Valčncia, Avd. Vicent Andrés Estellés 1, 46100 Burjassot, Spain
monterde@uv.es
Ede Troll
Institute of Mathematics and Computer Science, Károly Eszterházy University, Eger, Hungary
troll.ede@ektf.hu
Computation of the blending surface of two given spheres is discussed in this paper. The blending surface (or skin), although not uniquely defined in the literature, is normally required to touch the given spheres in plane curves (i.e., in circles). The main advantage of the presented method over the existing ones is the minimization of unwanted distortions of the blending surface. This is achieved by the application of rotation-minimizing frames for the transportation of a vector along a given curve, which technique, beyond its theoretical interest, helps us to determine the corresponding points along the touching circles of the two spheres. Parametric curves of the blending surface are also defined by the help of the rotation minimizing transportation.
Keywords: Sphere based surface design, skinning, blending surface, rotation minimizing frame.
MSC: 68U05; 65D17, 53A04
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