**Reference**:- Erik D. Demaine, Martin L. Demaine, David A. Huffman, Duks Koschitz, and Tomohiro Tachi, “Conic Crease Patterns with Reflecting Rule Lines”, in
*Origami*, volume 2, Oxford, England, September 5–7, 2018, pages 573–590, Tarquin.^{7}: Proceedings of the 7th International Meeting on Origami in Science, Mathematics and Education (OSME 2018) **Abstract**:- We characterize when two conic curved creases are compatible with each other, when the rule lines must converge to conic foci and reflect at the crease. Namely, two conics are compatible (can be connected by rule segments in a foldable curved crease pattern) if and only if they have equal or reciprocal eccentricity. Thus, circles (eccentricity 0) and parabolas (eccentricity 1) are compatible with only themselves (when scaled from a focus), and ellipses (eccentricity strictly between 0 and 1) and hyperbolas (eccentricity above 1) are compatible with themselves and each other (but only in specific pairings). The foundation of this result is a general condition relating any two curved creases connected by rule segments. We also use our characterization to analyze several curved crease designs.
**Length**:- The paper is 17 pages.
**Availability**:- The paper is available in PDF (5822k).
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Last updated August 19, 2022 by Erik Demaine.