Robust Adaptive Floating-Point Geometric Predicates

Fast C implementations of four geometric predicates, the 2D and 3D orientation and incircle tests, are publicly available. Their inputs are ordinary single or double precision floating-point numbers. They owe their speed to two features. First, they employ new fast algorithms for arbitrary precision arithmetic that have a strong advantage over other software techniques in computations that manipulate values of extended but small precision. Second, they are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small. These algorithms work on computers whose floating-point arithmetic uses radix two and exact rounding, including machines that comply with the IEEE 754 floating-point standard. Timings of the predicates, in isolation and embedded in 2D and 3D Delaunay triangulation programs, verify their effectiveness.

• Type: Conference
• Year: 1996
• Where: COMPGEOM
• Authors: Jonathan Richard Shewchuk
• Keywords: Arbitrary Precision Arithmetic, COMPGEOM 1996, Discrete Geometry, Double Precision Floating-point, Floating-point Arithmetic Uses