We present an efficient and reliable method for computing the unit-in-the-last-place (ulp) of a double precision floating--point number, taking advantage of the standard binary representation for floating--point numbers defined by IEEE Std 754-1985. The ulp is necessary to perform software rounding for robust rounded interval arithmetic (RIA) operations. Hardware rounding, using two of the standard rounding modes defined by IEEE-754, may be more efficient. RIA has been used to produce robust software systems for the solution of systems of nonlinear equations, interrogation of geometric and differential properties of curves and surfaces, curve and surface intersections, and solid modeling.
Key words: binary representation, denormalized number, IEEE Std 754-1985, rounded interval arithmetic, unit-in-the-last-place
We present a method for approximating B-spline curves and surfaces with non-open knot vectors. The approximating curves and surfaces have open knot vectors, which conforms to widely accepted data exchange formats, such as IGES, and the requirements for most commercial CAD/CAM/CAE systems. The curve approximation process interpolates a new curve through a representative set of points defined on the original curve. Surface approximation occurs by extracting, approximating, and then lofting through a family of isoparameter curves of the original surface. These algorithms have been implemented in Praxiteles, a general purpose, NURBS-based geometric modeling system.
MIT Ocean Engineering Design Laboratory
Copyright © 1998, Massachusetts Institute of Technology
URL: http://deslab.mit.edu/DesignLab/abstracts96.html
Revised: August 17, 1998