
Journal for Geometry and Graphics 19 (2015), No. 2, 189200 Copyright Heldermann Verlag 2015 Blending of Spheres by RotationMinimizing 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 rotationminimizing 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 [ Fulltextpdf (2369 KB)] 