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An Operator Calculus for Surface and Volume Modeling

source

IEEE Computer Graphics and Applications October, 1983. vol. 3: pp. 18-22 : ill. includes bibliography.

summary

This article briefly describes the mathematical techniques underlying surface and volume modeling techniques in current practice. The first part outlines what might be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable. This operator calculus uses operator multiplication and Boolean addition to compound the linear operators associated with simple bivariate and multivariate interpolation/approximation schemes. The result is a distributive lattice of approximation operators. The other two sections of the article contain specific examples of how this operator calculus leads to practical techniques for sculptured surface and volume modeling