morphing simple polygons
In this paper we investigate the problem of morphing (i.e. continuously deforming) one simple polygon into another. We assume that our two initial polygons have the same number of sides n , and that corresponding sides are parallel. We show that a morph is always possible by a varying simple interpolating polygon also of n sides parallel to those of the two original ones. If we consider a uniform scaling or translation of part of the polygon as an atomic morphing step, then we show that O ( n 4/3+&egr; ) such steps are sufficient for the morph.
morph polygon paper parallel interpolation scale translation atom