CAD systems today are feature-based in that they represent geometry via a collection of features, and associated feature parameters. During the design process, feature parameters are optimized to meet various design objectives including functionality, manufacturability, aesthetics, etc. This paper focuses on predicting the impact of parametric feature changes on quantities of interest, such as average stress within a given region, etc. When the parametric change is sufficiently small, one can rely on classic shape sensitivity and reanalysis methods to rapidly predict the desired quantity of interest. However, when the parametric changes are large, both methods are unreliable.

Numerous simplification methods have been proposed for speeding up engineering analysis/ simulation. A recently proposed medial axis reduction is one such method, that is particularly well suited for analyzing thin solids, wherein a governing equation is reduced to the medial axis, leading to significantly smaller stiffness matrices. However, this method involves the non-trivial computation of a piece-wise C1 continuous medial axis that must closely approximate the exact medial axis.In this paper, we propose a new medial mesh reduction that is computationally more efficient than medial axis reduction in that it only requires a C0 continuous tessellation of the medial axis. However, the proposed method retains all the advantages of the explicit medial axis reduction including automation and guaranteed numerical convergence. Furthermore, as the medial mesh converges to the exact medial axis, the computed solution also converges to the exact dimensionally reduced solution. These claims are substantiated through numerical experiments in 2-D and 3-D.

Offsets, sweeps, and Minkowski operations (M-ops) are easy to define in the existential (representation-free) mathematics of point sets, but computing ‘values’ for offset, swept, and M-summed entities is thought to be difficult by many. This article argues that such computations may be easy if (1) they are cast in specific application contexts, and (2) relevant mathematical definitions are discretized and implemented directly. The argument is based on 10 years of research on a range of motional, process-modeling, and visualization problems that involved offsetting, sweeping, and M-ops; the solution paradigm common to all was direct approximation of mathematical definitions, using ray representations and parallel computation as primary media. This article presents no new results; it merely summarizes a body of well documented research that illustrates an approach to problem solving, whose primary tenets are: compute only what you need to solve the problem at hand, and do that as directly as possible.