Abstract
We show that Möbius transformations preserve the rotation-minimizing frames which are associated with space curves. In addition, these transformations are known to preserve the class of rational Pythagorean-hodograph curves and rational frames. Based on these observations we derive an algorithm for G 1 Hermite interpolation by rational Pythagorean-hodograph curves with rational rotation-minimizing frames.
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Bartoň, M., Jüttler, B., Wang, W. (2010). Construction of Rational Curves with Rational Rotation-Minimizing Frames via Möbius Transformations. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, JL., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2008. Lecture Notes in Computer Science, vol 5862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11620-9_2
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DOI: https://doi.org/10.1007/978-3-642-11620-9_2
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