Research Of The Generation Of Control Mesh For Subdivision Surface From Curve Network

Freeform surface is the most complicated and most frequently used surface in engineering application, like the surfaces of turbine blades, car bodies and boat hulls. These freeform surfaces can’t be simply described by mathematical expressions. While designing freeform surface in CAD software, the contour of surface can usually be described by using curves network. Subdivision surface, as a new technology in surface generation, has been widely used to generate freeform surface because of its convenience to deal with complicated topology networks. From curves network, constructing initial control mesh is an essential step for the generation of subdivision surfaces. When designing subdivision surfaces with the existing CAD software, initial control mesh is usually constructed manually by user, which consists of patch cycle selecting and control points connecting. The process is time-consuming and it takes a lot of operations, which decreases the efficiency of surface design process. So far, the existing research work focus more on developing new subdivision scheme, analysis of convergence and smoothness, or applications of subdivision in different surfaces generation. However, there are few articles that focus on the generation of initial control mesh for subdivision surface.In order to improve the efficiency of surface generation from curve network and contribute to research work in initial control mesh generation, this paper proposes a framework to generate initial control mesh for subdivision from arbitrary topological curves network. This framework contains three steps. Firstly, generate a discrete polygonal network from input curve network to form the boundary of initial control mesh while keeping these two networks in same topology. Secondly, search patch cycles in the generated polygonal boundary network to represent the whole surface of the designed product described by the curve network. Thirdly, fill all the patch cycles found in the second step to form a polygonal control mesh.The framework proposed in the thesis was realized with Java in the company’s development platform. Several curves networks were tested, generating corresponding control mesh for each of them. And these generated control mesh were subdivided with the Catmull-Clark scheme, resulting smooth surfaces that approximate the original curve network. Aiming at improving the quality of control mesh which may contain irregular quads, an energy function was used to fairing the control mesh. By analyzing the quality of the generated meshes and the generation efficiency, it verifies the effectiveness of our framework and illustrates indirectly the engineering significance.