Research On N-Sided Hole Filling In Closed Surface Construction

The manufacturing industry is the pillar industry of China’s national economy and it plays an important role in the growth of China’s national economy. Geometric modeling is the core area in the development of the manufacturing, providing essential technical support for innovation and the development of the manufacturing industry, Surface construction techniques give convenience for multiple model adjustments and modifications to ensure that the model designers can better describe his ideas, so it has been studied extensively.Surface Construction can be divided into several parts:discrete data acquisition, data preprocessing, data slicing, surface fitting and CAD modeling, this article mainly focus on theoretical research and experiment results of surface construction including parametric surfaces, N-sided hole filling, the slicing surface blending continuity problems.For given three-dimension points, we divided them into different meshes. According to the meshing, we classify the points into two categories:regular points and irregular points; By extracting features of regular points, we obtain two first order partial derivative and a second order mixed partial derivatives, then we get the bicubic Coons Surfaces of regular points. For irregular points, we reparameterize them to reestimate the derivative of these points using Least Square Method, ensuring the compatibility of cross-boundary derivatives on the connecting points of neighboring piecewise surfaces, by this we get the definition of Bezier surfaces, Finally, we get continuous surfaces by solving the constraints of continuity.The proposed method has the following advantages:this method only involves simple equation solver, so the construction is fast. Surfaces we get have a simple form with low degree of three, which gives more convenience for the following construction. Generated surface is C1continuous which ensures that the smoothness and aesthetic nature.