LEDA offers geometry kernels for two-dimensional geometry and three-dimensional geometry. These kernels come in two kinds each: a rational kernel and a floating point kernel.
Based on the geometry kernels, LEDA offers a wide variety of data types and algorithms for two- and three-dimensional geometry.
What is a Geometry Kernel?A geometry kernel offers basic geometric objects, such as points, lines, segments, rays, planes, circles, ..., and geometric primitives operating on these objects, e.g., the computation of the area of the triangle defined by three points and the computation of the intersection of two lines.
Difference between Rational and Floating Point KernelIn the rational kernel the Cartesian coordinates of points are rationals (,i.e., rational numbers in the sense of mathematics) and the geometric primitives are exact, i.e., they always give exact results.
In the floating point kernel the Cartesian coordinates of points are double precision floating point numbers and the geometric primitives are approximate, i.e., they usually give exact results but there is no guarantee. Therefore, the use of the floating point kernel is not without risk.
Why Floating Point at all?The floating point kernel is contained in LEDA for the following reasons:
Use the rational kernel exclusively !
Only when a program is stable and the rational kernel does not give the desired performance consider switching to the floating point kernel. A switch to the floating point kernel should be accompanied by a careful analysis of its limits.