Detection and computation of conservative kernels of models consisting of freeform curves and surfaces, using inequality constraints

Abstract

We present an algorithm to compute a tight-as-needed conservative approximation of the kernel domain of freeform curves in R2 and freeform surfaces in R3. Inequality constraints to detect the interior of the kernel domain are formulated as multivariates, and solved with a subdivision-based approach to find the domains in R2 or R3 that satisfy the inequalities and are in the kernel. The convex hull of the computed domains is also included in the kernel, and adopted as the approximated kernel domain. We can apply the presented algorithm to detect the kernel domain of not only C1 continuous closed regular curves and surfaces, but also the kernel domains of multiple piecewise C1 continuous regular freeform curves and surfaces. Further, the presented algorithm can be applied to find the gamma-kernel as well as the kernel domain of open curves and surfaces, under some assumptions. We demonstrate our experimental result using various freeform curves and surfaces, and compare it with the kernel computation algorithm presented in Elber et al. (2006). © 2022 Elsevier B.V.