Hoffmann, Miklós

Kunkli, Roland

Kunkli Roland

Hoffmann Miklós

University of Szeged

Skinning of Circles Using BiarcsRoland Kunkli and Miklós HoffmannInterpolation of points is a momentous problem in Computer Aided Geometric Design(CAGD). We have several (now standard) methods to solve this kind of problem [1]. If weconsider circles instead of points, the interpolation will be transferred to ”skinning”. By skin-ning we mean the geometric construction of two curves (often G1 or C1 continuous) touchingeach of the circles and provide a result, which is visually ”satisfactory”. It is very hard to definethis problem with mathematical formulae, and we have not got precise definition yet. Further-more, we have not got a well-known, ubiquitously method to get a solution. With the help ofskinning we can easily design tubular structures, and it can be useful by covering problemstoo. There is recent numerical approach of the problem [2], but it has a lot of weaknesses bycertain positions of the circles. We have submitted a manuscript [3] to the journal ComputerAided Geometric Design, in which we present a method. With this presented algorithm we caneasily compute skinning curves and it works in the above-mentioned problem cases too.In this paper we present a new method, where the skinning curves are composed of biarcs.A biarc is a G1 continuous curve, which is composed of two arcs [4]. The real power of thismethod is, that it uses only biarcs for the construction and it also works in the above-mentionedproblem cases too. So it can be useful by applications, where this is essential, e.g. CNC cutting.It can easily implemented and it can be used by an interactive, dynamic software, because it isfast. Furthermore, the user must determine only the circles.Figure 1: Skinning of circles using biarcsKeywords: skinning, circles, interpolation, biarcsReferences[1] G. Farin, Curves and Surface for Computer-Aided Geometric Design, 4th edition, AcademicPress, New York, 1997.[2] G. Slabaugh, G. Unal, T. Fang, J. Rossignac, B. Whited, Variational Skinning of an OrderedSet of Discrete 2D Balls, Lecture Notes on Computer Science, 450–461, 2008.[3] R. Kunkli, M. Hoffmann, Skinning of circles and spheres, Computer Aided Geometric Design,submitted.[4] K. M. Bolton, Biarc curves, Computer–Aided Design, 7, 89–92, 1975.[5] Z. Šír, R. Feichtinger, B. Jüttler, Approximating curves and their offsets using biarcs andPythagorean hodograph quintics Computer–Aided Design, 38, 608–618, 2006.47

Skinning of circles using Biarcs

http://acta.bibl.u-szeged.hu/59971/1/cscs_2010_047.pdf

Skinning of circles using Biarcs

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