The main result of the paper is a new and efficient algorithm to compute the closest possible representable intersection point between two lines in the plane. The coordinates of the points that define the lines are given as single precision floating-point numbers. The novelty of the algorithm is the method for deriving the best possible representable floating point numbers: instead of solving the equations to compute the line intersection coordinates exactly, which is a computationally expensive procedure, an iterative binary search procedure is applied. When the required precision is achieved, the algorithm stops. Only exact comparison tests are needed. Interval arithmetic is applied to further speed up the process. Experimental results demonstrate that the proposed algorithm is on the average ten times faster than an implementation of the line intersection computation subroutine using the CORE library exact arithmetic.
Implementing straight skeletons with exact arithmetic: Challenges and experiences