An exact, complete and efficient implementation for computing planar maps of quadric intersection curves

Exacus: Efficient and Exact Algorithms for Curves and Surfaces

“…A generalization of Jacobi curves for locating tangential intersections is described by Wolpert [31]. Berberich et al [4] recently extended these techniques to special quartic curves that are projections of spatial silhouette and intersection curves of quadrics and lifted the result back into space. Seidel et al [29] describe a new method for general-degree curves.…”

“…CONIX does not restrict the choice of coordinate system. CUBIX and QUADRIX assume a generic coordinate system to simplify the analysis, see [10,4] for details.…”

“…An Event2 slice is a unified representation of the sequence of arcs over some x-coordinate x 0 , be there an event or not [10,4]. A slice of a pair ( f , g) at x 0 describes the order of points of f and g lying on the fictitious vertical line x = x 0 , sorted by y-coordinate.…”

“…The recent Open Source release contains the full support for conics and conic segments, while existing implementations for cubic curves and a special family of degree four curves are scheduled for later releases. We work currently on extending our results to arrangements of generaldegree curves in the plane [29] and quadric surfaces in space and boolean operations on them [4].…”

“…4 http://www.mpi-inf.mpg.de/EXACUS/ Therefore, we aim for a crisp and clear design, flexibility, modularity, and ease of use of our libraries.…”