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Line segment intersection testing. (English) Zbl 1080.65018
The authors test numerical algorithms for determining the line segment intersections. They claim to use “exact” arithmetic methods. No, these methods are not exact. Their algorithm is based on the 40 years old Gill-Möller (not Knuth) algorithm for the optimal correction of sum computation [cf. O. Möller, Nordisk Tidskr. Inform. Behandl. 5, 37–50 (1965; Zbl 0131.15805)] and on the algorithm by M. Pichat [Ph.D. Thèse, Univ. Grenoble (1976)] for the correction of product computation in floating-point arithmetic.
The use of the IEEE 754 denormalized standard and of the double precision is usual. To improve the precision it will be suitable to use the Bayley package for arbitrary length floating format and, parallel, the Cuyt-Verdonk (Anvers University) package of optimal precision in IEEE floating point calculations, but it seems then the authors ignore these developments. However, the methods proposed by the authors reduce the cost of the running time of the usual numerical methods commonly used in the last time.

MSC:
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65B10 Numerical summation of series
65G50 Roundoff error
Software:
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