Non-congruent non-degenerate curves with identical signatures

12/20/2019
by   Eric Geiger, et al.
0

We construct examples of non-congruent, non-degenerate simple planar closed curves with identical Euclidean signatures, thus disproving a claim made in Hickman (J. Math Imaging Vis. 43:206-213, 2012) that all such curves must be congruent. Our examples include closed C^∞ curves of the same length and the same symmetry group. We show a general mechanism for constructing such examples by exploiting the self-intersection points of the signature. We state an updated congruence criterion for simple closed non-degenerate curves and confirm that for curves with simple signatures the claim made by Hickman holds.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset