The Research On Carving Surface Modeling Based On Planar Random Closed Graph

The main content of this thesis is how to construct 3D carving surface model based on random planar closed curve and a given height (H). The modeling process of carving surface is quite complex in existing general purpose CAD/CAM (Computer-aided design/Computer-aided manufacturing) software. It requires a lot of skill from users. So it's necessary to simplify the carving surface modeling process. For most of the planar carving pattern are multi-layered, one can first modeling them layer by layer, then using combination and interpolation of them to build the final model. The key to this complex carving surface modeling process is constructing carving surface model based on single layered random planar closed curve.Two methods for constructing 3D carving surface based on random planar closed curve have been proposed in this paper. Both of them take the following as their initial steps:transforming random planar closed curve into approximation polygon; performing Constrained Delaunay Triangulation on approximation polygon; extracting skeleton of the approximation polygon. The first method use steps like constructing initial control net; subdividing the control net by subdivision surface scheme to get carving surface model. The second method obtain 3D model by quadratic Bezier curves and ruled surface based on result of the initial processing.We obtain approximation polygon by applying tracking contour algorithm to the closed curve and lining the points which formed the closed curve.In order to extract skeleton of the approximation polygon, we first perform Constrained Delaunay Triangulation, then connect skeleton points. Skeleton points can be located using the following method:the edges of initial polygon are called external edges, while edges added in the triangulation are called internal edges. Triangles can be classified into three categories-terminal triangles, sleeve triangles and junction triangles. The midpoint of internal edges and central point of the junction triangles are the skeleton points. We have improved the existing optimization method of skeleton. For further improvement of skeleton, we proposed new methods.In the first modeling method, the objective is elevating skeleton to the defined height which can be implemented by assigning the defined height to skeleton points and connecting the elevated skeleton points and their nearest boundaries during building process of initial control net based on random planar closed curve. We proposed a method which can automatically build reasonable initial control net by transforming terminal triangles, sleeve triangles and junction triangles into type I(the height of one vertex is H, the others are 0),Ⅱ(the height of two vertices are H, the rest is 0),Ⅲ(the height of 3 vertices are H) triangular meshes. In the last step, we chose the modified butterfly subdivision surface scheme to subdivide the control net based on comparision of several common subdivision scheme. The main characteristic of subdivision surface is applying the subdivision surface scheme iteratively to refine and smooth the surfaces bit by bit until we get the smooth surface we want. So we can get satisfied smooth surface by subdividing the control net iteratively.The second modeling method classified the triangulated approximation polygon into five categories. The common characteristic of them is building quadratic Bezier curves and lining related points on these curves from another direction to form ruled surface on certain area. Finally, we can construct smooth surface model for the whole area covered by random planar closed curve.There are various possibilities for inferring 3D carving surface from planar closed curve. The methods proposed in this thesis produce the same kind of model. The ridge of our model located in the central parts of the 2D closed curve and the lowest part appears on the closed curve. Smooth surface bridge between them. The experimental results show that our model answer the character of most carving surface model. Our methods help to improve the design and modeling process of carving surface model.The main original ideas of this thesis include:improving the existing optimization method of skeleton and proposing new method for further optimization of skeleton and two new methods for constructing carving surface model based on random planar closed curve.