Geometry processing: Numerical multiple integration. (English) Zbl 0715.65014

Barnhill, Robert E.; Watson, Stephen H.

The mathematics of surfaces III, Proc. 3rd Conf., Oxford/UK 1988, Inst. Math. Appl. Conf. Ser., New Ser. 23, 49-69 (1989).

[For the entire collection see Zbl 0709.00016.]
An adaptive triangular cubature algorithm due to R. E. Barnhill and F. F. Little [Rocky Mt. J. Math. 14, 53-75 (1984; Zbl 0555.65016)] is extended to parametric patches and generalized to trivariate integration. It is applied to problems of computer-aided geometric design (where surfaces are usually defined over polygonal domains). Diverse examples are tested using Radon and Cowper cubature rules.

Reviewer: A.de Castro

MSC:

65D32	Numerical quadrature and cubature formulas
65D17	Computer-aided design (modeling of curves and surfaces)
41A55	Approximate quadratures
65D18	Numerical aspects of computer graphics, image analysis, and computational geometry
41A63	Multidimensional problems

Keywords:

adaptive triangular cubature algorithm; parametric patches; trivariate integration; computer-aided geometric design; Radon and Cowper cubature rules

Citations:

Zbl 0709.00016; Zbl 0555.65016