Shape sensitivity of constructively represented geometric models

Most solid models are archived using boundary representations, but they are created, edited, and optimized using high level constructive methods that rely on parameterized Boolean set operations and feature-based techniques. Downstream applications often require optimization of integral-valued performance measures over such models that include volume, mass, and energy properties, as well as more general distributed fields (stress, temperature, etc.). A key computational utility in all such applications is the computation of the sensitivity of the performance measure with respect to the parameters in the solid's construction history. We show that for a class of performance measures defined as domain integrals, the sensitivity with respect to a parameter requires integration over a subset of the solid's boundaries that is affected by that parameter. In contrast to earlier methods, the proposed approach for computing sensitivities does not require solid's boundary to remain homeomorphic, and may be used with most types of constructive representations, including CSG and feature-based representations, where the defining Boolean expression may not be known. The simplicity and effectiveness of the proposed technique are illustrated on several common shape optimization problems.