This paper describes an algorithm for generating a
guaranteed-intersection-free interpolation sequence between any pair
of compatible polygons. Our algorithm builds on prior results from
linkage unfolding, and if desired it can ensure that every edge length
changes monotonically over the course of the interpolation sequence.
The computational machinery that ensures against self-intersection is
independent from a distance metric that determines the overall
character of the interpolation sequence. This decoupled approach
provides a powerful control mechanism for determining how the
interpolation should appear, while still assuring against intersection
and guaranteeing termination of the algorithm. Our algorithm also
allows additional control by accommodating a set of algebraic
constraints that can be weakly enforced throughout the interpolation
sequence.