Skinning of circles and spheres

Skinning of an ordered set of discrete circles is discussed in this paper. By skinning we mean the geometric construction of two G1 continuous curves touching each of the circles at a point, separately. After precisely defining the admissible configuration of initial circles and the desired geometric properties of the skin, we construct the future touching points and tangents of the skin by applying classical geometric methods, like cyclography and the ancient problem of Apollonius, finding touching circles of three given circles. Comparing the proposed method to a recent technique (Slabaugh et al.,2008; Slabaugh et al.,2009), larger class of admissible data set and fast computation are the main advantages. Spatial extension of the problem for skinning of spheres by a surface is also discussed in detail.