Minkowski Pythagorean hodograph curves are widely studied in computer-aided geometric design, and several methods exist which construct Minkowski Pythagorean hodograph (MPH) curves by interpolating Hermite data in the ${\mathbb{R}}^{2,1}$ Minkowski space. Extending the class of MPH curves, a new class of Rational Envelope (RE) curve has been introduced. These are special curves in ${\mathbb{R}}^{2,1}$ that define rational boundaries for the corresponding domain. A method to use RE and MPH curves for skinning purposes, i.e., for circle-based modeling, has been developed recently. In this paper, we continue this study by proposing a new, more flexible way how these curves can be used for skinning a discrete set of circles. We give a thorough overview of our algorithm, and we show a significant advantage of using RE and MPH curves for skinning purposes: as opposed to traditional skinning methods, unintended intersections can be detected and eliminated efficiently.

Special curves in the Minkowski space such as Minkowski Pythagorean hodograph curves play an important role in computer-aided geometric design, and their usages are thoroughly studied in recent years. Bizzarri et al. (2016) introduced the class of Rational Envelope (RE) curves, and an interpolation method for G ¹ Hermite data was presented, where the resulting RE curve yielded a rational boundary for the represented domain. We now propose a new application area for RE curves: skinning of a discrete set of input circles. We show that if we do not choose the Hermite data correctly for interpolation, then the resulting RE curves are not suitable for skinning. We introduce a novel approach so that the obtained envelope curves touch each circle at previously defined points of contact. Thus, we overcome those problematic scenarios in which the location of touching points would not be appropriate for skinning purposes. A significant advantage of our proposed method lies in the efficiency of trimming offsets of boundaries, which is highly beneficial in computer numerical control machining.