Reflection coefficient representation for convex planar sets

We combine certain results from two disparate areas, kinematics and geophysics, to obtain a convenient representation for the class of convex compact planar sets, in terms of a sequence of complex valued reflection coefficients. This gives a one-to-one relation between any convex compact planar set S and any set of parameters comprising: a) the coordinates of a reference point in 𝒮, b) the circumference of the set, and c) a complex reflection coefficient sequence, {k₁, k ₂,...}, such that 1) k₁=0, 2) |k_n|⩽1, ∀n, 3) if |k_N|=1 for some N then k_n=0, ∀n>N. For a finite duration reflection coefficient sequence, where k_n=0, ∀n>N, if 0<|k _N|<1 then the boundary of S is an infinitely differentiable convex curve, and if |k_N|=1, then the boundary is an N-sided convex polygon