Using Bezier Curve To Upsample Scattered Point Model

With the continuous development of computer theory and technology, computer-aided design and manufacturing (CAD/CAM) has become a powerful tool to researchers, which is essential in the design and development of the modern industrial applications all over the machinery manufacturing, engineering design, simulation, medicineHealth and digital entertainment as well as many other fields. Among them, the free curve and surface modeling technology has been widely used in modern industrial product design and innovation, mold improving, and other aspects of automated processing and manufacturing. Implicit or explicit reconstruction of the scattered point cloud surface after the sampling process is the scattered point model of multi-resolution processing of important steps and key technologies. Therefore, direct research about upsampling point set surface is better able to express sophistication of the model surfaces in different level which depends on points’ number. Upsampling technology is of great significance to the model surface refinement.The major contributions of this paper include four areas as follow:1. Summarize in detail the implicit surface fitting method which is based on least squares and radial basis function, as well as the mathematical basis of parametric curve and parametric surface fitting. The description of point set surface is generally divided into two categories:explicit and implicit. The former includes parametric surfaces and triangle (or polygon) mesh surface, which is weak to deal with noise and uneven distribution, in addition to the high cost when expressing complex models. The latter which is built on the implicit surface, is not sensitive to the slight noise and applied to the representation of complex models and a variety of collection operations and mathematical calculations.2. Compare the three data structures of point cloud data in detail:the grid structure, the octree structure and the KD-tree structure. After the analysis, we select the high efficiency and simple encoding KD-tree structure to be the organization of point cloud data, which can complete k-nearest neighbors finding in the point cloud data easily and efficiently. And then two different point cloud model upsampling algorithms are introduced step by step.3. Solve basic geometric information of each data point in the model, including normal vector using covariance analysis which is based on least squares plane and its adjustment by propagation algorithm which makes the total points a unified direction form the point to the outline of the model. The local coordinate transformation set each data point as the origin of the local coordinate system, and project, sort counterclockwise or clockwise as well as removes unreasonable points in all its k-neighbor points in this local coordinate system. Sorted neighbor points and the point in the origin are grouped and become point pair. Upsampling is on the basis of local criteria, to generate new data points between each point pair, from the nearest neighbor.4. Make some improvements on the local operator of local upsampling, in purporse of avoiding repeated sampling. At the same time solve the non-uniform upsampling because of the four mutual neighbor points, which guarantees the upsampling algorithm suitable for processing globally. At last, we verify the effectiveness of the algorithm by experiments and render upsampling pictures of same point cloudmodels.