Engineering PapersSearch

Engineering topics

Gordon, W. J.

Publications and source records attributed to Gordon, W. J..

A New Technique for System-to-system Transfer of Surface Data

The purpose is to describe a recently developed technique aimed at providing a universal interface between surface types. In brief, a software package was developed which functions a common denominator of CAD/CAM surface types. This software enable one to convert from any given surface representation to any other target representation. The tiles maintain the same slope continuity as the target surface gram, bicubic patches are used since they allow one to match point, slope, and twist vectors to the target surface. Thus, slopes can be continuous or discontinuous as they are on the target surface. The patches can be of lower order if desired. For example, if only point information is available, the patches produced will be bilinear; however, the number of patches required is likely to increase correspondingly. The patches can be of higher order although many systems will not accept patches of more than order four. The final result of the program is a rectangular grid of bicubic patches. The patches fit the target surface exactly at their corners. Also, the patch corners have the same tangent and twist vectors. Adjacent patches will have slope continuity, unless a discontinuity was indicated by the target surface.

Sterling, M. W.

An operator calculus for surface and volume modeling

The mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.

Gordon, W. J.