Incremental computation of planar maps

Abstract

Aplanar map is a figure formed by a set of intersecting lines and curves. Such an object captures both the geometrical and the topological information implicitly defined by the data. In the context of 2D drawing, it provides a new interaction paradigm, map sketching, for editing graphic shapes. To build a planar map, one must compute curve intersections and deduce from them the map they define. The computed topology must be consistent with the underlying geometry. Robustness of geometric computations is a key issue in this process. We present a robust solution to Bézier curve intersection that uses exact forward differencing and bounded rational arithmetic. Then, we describe data structure and algorithms to support incremental insertion of Bézier curves in a planar map. A prototype illustration tool using this method is also discussed.