Construction of Rational Curves with Rational Rotation-Minimizing Frames via Möbius Transformations

We show that Mobius 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 G1 Hermite interpolation by rational Pythagorean-hodograph curves with rational rotation-minimizing frames.

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