Decompositions of Objects Bounded by Algebraic Curves

We present a.n algorithm to decompose the edges of planar curved object so that the carrier polygon of decomposed boundary is a simple polygon. We also present an algoritbm to compute a simple characteristic carrier polygon. By refining this decomposition further and using the chords and wedges of decomposed edges, we obtain an inner polygon (resp. an outer polygon) which is a simple polygon totally contained in (resp. totally containing) the object. We also consider various applications of these polygons to object decompositions and collision-avoidance planar robot motion planning problems.