Research On Bas-relief Modeling Method Based On Isogeometric Analysis

Computer-aided design(CAD)and computer-aided engineering(CAE)are important components in advanced manufacturing,and they play an important role in mechanical manufacturing and industrial design.CAD mainly uses the cutting-edge computer technology to assist the geometric shape design of engineering products.CAE mainly uses computer simulation technology to perform functional simulation,performance and safety reliability analysis on engineering design products,so as to find design defects early and optimize product performance.The independent development of CAD technology and CAE technology lead to inconsistencies in the mathematical models describing the geometric objects.In order to bridge the gap between CAD and CAE,isogeometric analysis is proposed.The isogeometric analysis is based on spline theory.Both design model and analysis model are spline representations,which avoids the meshing process in finite element analysis,which seamlessly integrates design and simulation,and significantly improves product design efficiency and quality.Once the isogeometric analysis is proposed,it has become a research hotspot,but it has not been applied to the field of bas-relief modeling.In this paper IGA is applied to construct bas-relief model.The main contents include the following three aspects.1.A general algorithm framework for bas-relief modeling based on isogeometric analysis is proposed.The user inputs hand-drawn sketches or 2D images.The algorithm transforms the input model into a spline representation,and then uses the isogeometric analysis to solve the Poisson equation with constraints on the geometric model to obtain the bas-relief base surface.Finally,the corresponding height field is raised on the basis of the bas-relief base surface to generate a bas-relief with details.2.Through the h-type refinement method of the spline,the degree of freedom of the model is increased to enhance the performance of the detail of the bas-relief model.Increasing the degree of freedom will lead to an increase in the amount of computation.To reduce the computational overhead,the isogeometric collocation method is introduced into the above algorithm framework.3.An algorithm to construct dynamic bas-relief model is proposed.The bas-relief can be divided into two parts:a bas-relief base surface and a bas-relief detail,wherein the bas-relief detail is a given bas-relief pattern,and the bas-relief base surface can be selected as any plane model including a bas-relief pattern.The construction of the dynamic bas-relief model includes the construction of the dynamic base surface and the construction of the static bas-relief model.The dynamic base surface is obtained by solving the time-dependent partial differential equation or the interpolation deformation method.A dynamic bas-relief can be constructed by simply combining a static bas-relief model with a dynamic base surface.This paper demonstrates the effectiveness of the proposed method with some examples of dynamic bas-relief models.