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In computer graphics, the implicit surface is an important representation of the geometry, because it is a single analytic function, suitable for many aspects of the collision detection, deformation, fusion, distorted, Boolean operations. , Radial basis function (RBF) implicit surfaces accurate and stable solution to the problem of reconstruction of scattered point data, is the most important in recent years, implicit surface algorithm one. This thesis is an innovative RBF implicit surface is introduced into the field of image-based modeling, minimal surfaces and to study the geometric transformation of the RBF implicit surface. Relevant research results can be applied to virtual reality, scenario modeling, the field of computer vision, graphics, visualization, research on minimal surfaces can be used in plastic surgery and dental surgery, packaging design, molecular engineering and materials many areas of science, art, and modern film project. Therefore, this study has important academic significance and application value. RBF implicit surface research mainline in image-based modeling, RBF implicit surface geometric transformations, three aspects of minimal surfaces in-depth study and propose some new algorithms, the main contents include: 1) three-dimensional model of the field of image-based modeling, a grid-based feature detection algorithm, you can get more match points in the image sequence, and the introduction of the RBF implicit surface reconstruction algorithm to reconstruct the target. The main idea is to manually specify a relatively dense grid in the first frame to determine the most likely to track feature points in the vicinity of the grid point, using an iterative method to get the corner coordinates of the sub-pixel accuracy, and then use the sparse feature set, multi-scale light flow tracking algorithm to track these corners. After using the self-calibration algorithm can reconstruct the relatively uniform and dense 3D point cloud. Finally, the introduction of the RBF implicit surface reconstruction algorithm to generate the target three-dimensional surface model. Reconstruction of multiple image sequences results show that the proposed algorithm is able to obtain a satisfactory surface model richly textured scenes. 2) RBF implicit surface change before and after the geometric transformation coefficient formula is derived. RBF implicit surfaces, you may need it geometric transformation. The traditional RBF Implicit Surfaces geometric transformation algorithm is: at a given point using the inverse transform, and then with the point after the inverse transform, to calculate the function values ??in the original function. The traditional algorithm need to keep the initial RBF centers. Sometimes, you need to geometric transformation of the RBF center. In this case, if still using the traditional algorithm, while maintaining the initial and after the geometric transformation RBF centers. Obviously, this is a problem of wasting storage space. The RBF coefficient of variation is derived formula to solve the problem. The proposed algorithm only needs to keep the transformed RBF centers will save a lot of storage space, and therefore need the transformed RBF centers. Using this formula, we can quickly calculate the new RBF surface, and compactly supported and globally supported RBF. In terms of computing time, a detailed comparison of the algorithm and the traditional algorithm. The theoretical analysis and experimental results show that the proposed algorithm is faster than traditional algorithm in many cases. This algorithm, applied to the RBF implicit surface-based collision detection and Boolean operations. And propose an optimization algorithm, implicit surfaces can accelerate the speed of Boolean operations. Meanwhile, compactly supported RBF implicit surfaces Boolean operations drum kits, the paper also proposed a solution. 3) minimal surfaces problem is the classic conundrum of mathematics, especially its multiple solutions for problems yet to be resolved. This paper presents a new algorithm from an initial surface iterations to get a number of different minimal surfaces (ie a number of different solutions), including unstable minimal surfaces. Given space curve, finding this curve as a boundary area of ??a minimum or minimal surfaces, referred to as the problem of the the Plateau problems or minimal surfaces. From an arbitrary surface of this boundary iteration of a given boundary curve, the proposed algorithm, and finally get a minimal surfaces. With an initial surface when choosing different parameters, the proposed algorithm is likely to get a variety of minimal surfaces. Retrieve other similar algorithm can only converge to a minimal surfaces. The proposed algorithm through the simulation of the dynamic behavior of a nonlinear spring model air resistance, to get the ultimate minimal surfaces. For how to generate the problem of the initial surface, there is little literature related algorithms. This paper presents an algorithm using RBF implicit surface, can semi-automatically generate the specified initial surface of genus, only need a small amount of user operations are valid for any number of boundary curves. In addition, for the rule of a single boundary curve proposed an algorithm to generate the initial surface can be fully automated.
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