We describe a method that serves to simultaneously determine the topological configuration of the intersection curve of two parametric surfaces and generate compatible decompositions of their parameter domains, that are amenable to the application of existing perturbation schemes ensuring exact topological consistency of the trimmed surface representations. To illustrate this method, we begin with the simpler problem of topology resolution for a planar algebraic curve F (x, y) = 0 in a given domain, and then extend concepts developed in this context to address the intersection of two tensor-product parametric surfaces p(s, t) and q(u, v) defined on (s, t) ∈ [0, 1] 2 and (u, v) ∈ [0, 1] 2 . The algorithms assume the ability to compute, to any specified precision, the real solutions of systems of polynomial equations in at most four variables within rectangular domains, and proofs for the correctness of the algorithms under this assumption are given.
This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot insertion, differentiation, and degree elevation. Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for "multi-degree"). MD-splines are a generalization of B-spline curves in that if all curve segments in an MD-spline have the same degree, it reduces to a B-spline curve. The paper focuses on MD-splines of degree 1, 2, and 3, as well as degree 1 and n. MD-splines have local support, obey the convex hull and variation diminishing properties, and are at least C n−1 , where n is the smaller of the degrees of two adjoining curve segments.
A new type of nonsmooth surface inspired by the shape of barchan dunes has been proposed and is intended to reduce skin friction, a major cause of overall drag. Simulations were carried out to obtain skin friction reduction characteristics for the nonsmooth surface using the commercial computational fluid dynamics software Fluent. A realizable k-ε model was employed to assess the influence of the nonsmooth structure on turbulent flow and velocity fields. The numerical simulation results showed that the new nonsmooth surface possesses the desired skin friction reduction effect and that the maximum skin friction reduction percentage reached 33.63% at a fluid speed of 30 m/s. Various aspects of the skin friction reduction mechanism were discussed, including the distribution of velocity vectors and shear stress contours and the variations in boundary layer thickness. The accuracy of the flow field for the nonsmooth unit was further verified by particle image velocimetry test results. The new bionic nonsmooth surface, which exceeds the limitations of existing nonsmooth bionic structures, can effectively reduce skin friction and should provide insights into engineering applications in the future.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.