Conic curves are planar curves of degree 2 at most: ellipses, hyperbolas, parabolas and of course lines. A finite conic arc is defined by its underlying conic curve and two end-point on that curve.
Many of the algorithms that appear in the literature involve special cases of planar arrangements of conic arcs:
- Arrangements of line segments are used to solve a variety of problems, such as motion planning of a polygonal robot in a room with polygonal obstacles, map overlay, etc.
- Arrangements of line segments and circular arcs are used for motion planning of a disc robot in a room with polygonal obstacles.
- Arrangements of parabolas can be used for answering dynamic nearest-neighbor queries efficiently.
We aim to deal with all these cases, and many more, using a unified approach that insures efficient and robust constructions of arrangements of conic arcs.