As Debra Stewart said, graduate education is primarily funded via research, especially research grants and contracts.Thus, I shall focus on some national trends in research itself, which has the obvious

This paper provides a basic overview of NURBS and their application to numerical grid generation. Curve/surface smoothing, accelerated grid generation, and the use of NURBS in a practical grid generation system are discussed.

This text includes papers covering topics in geometry processing applications, such as surface-surface intersections and offset surfaces. Present methods fundamental to geometric modelling are highlighted.

Two classes of methods are presented for interpolating scattered data sampled in a spatial domain at different times. Instead of treating time as another Euclidean variable, time is treated as a special variable in our two approaches. These methods make use of scattered data interpolants over the spatial domain and univariate interpolants over the time domain. When compared with existing scattered data interpolation methods, the new methods are more effective.

6.1. IntroductionContouring is an often used and important approach to the problem of visualizing and interrogating surfaces. Even with the present sophistication of interactive color graphics for displaying bivariate surfaces, it is needed to examine the reflection lines of a bivariate function [5]. Reflection lines offer a useful technique for interrogating a surface and are used extensively in the car industry for judging the aesthetic quality of a surface [8].

A method for blending two parametric surfaces is presented. It is based an an algorithm which calculates the intersection of two offset surfaces using only the first-order derivatives of the progenitors. The method converges quadratically in non-singular cases.

We present a new technique for interpolation of scattered data on arbitrary surfaces. The interpolant is obtained as the restriction of a trivariate function and is piecewise defined over triangular surface patches. The smoothness of the resulting function over the domain surface is visualized by application of interrogation tools for surfaces on surfaces.

Given data defined on a (domain) surface, we construct an interpolant, which is a “surface defined on a surface.” we provide four different solutions to this multidimensional problem.