Surface Reconstruction Based On Implicit Function And Its Application

Surfaces reconstruction is a key technology used for complex surface modeling, which is a process transforming the point clouds into continuous and watertight surface and widely used in many research fields. There are many reconstruction methods, but the most challenge comes from the defective sample points due the measurements in practice. The point clouds often have large amount data with noise, holes and overlapping regions. These defective samples make the existing surface reconstruction difficulty to evaluate the oriented information or construct triangular meshes, which is necessary for reconstruction. The know methods only guarantee the accurate result of function surface with geometric standard, but can not realize the physical performance. Aiming at the problems existing above, this paper mainly researches the surface reconstruction modeling, and proposes some effective methods based on implicit function theory for application.Firstly, the known existing methods are lacking in the mathematical description and the suitable standard. Most methods are based on complex oriented information evaluation, hard to apply in practice. Based on the summary of the existed reconstruction methods, a general extremum model based on the metric function and constrains conditions is proposed. This paper analyzes many kinds of metric functions including the definition, conditions, resolving methods. Based on the modeling, a efficient estimation methods for oriented information of defective point clouds is proposed. The approach can handle the holes and overlapping regions, avoiding constructing triangular mesh and pre-processing, which can increase the efficiency.Secondly, many segmentation methods rely on the triangular mesh and are hard to segment defective samples, requiring complex algorithm or data structure. This paper proposes an efficient and automatic segmentation methods based on active contour model, which can reduce the defective influence. The median filter is extended into a narrowband in 3D space to handle the noisy samples. The active contour model in image processing is also extended to create a segmentation model based on curvature and the segmentation is performed by propagating the space curves with adaptive topological changes. This method can avoid reconstruct triangular mesh, not only guarantee the accurate segment results, but also increase the efficiency with simple data structure.Thirdly, many known reconstruction methods need the oriented information previously, however the information is often hard to evaluate automatically and accurately. For avoiding this problem, this paper proposes an implicit surface reconstruction based on dual off-set gradient functions. It does not fit the clouds, instead, it generates dual surfaces which construct a minimal surrounding space to the point clouds firstly and reconstruct the final surface then. The dual gradient functions are constructed by the mathematical morphology quickly, they are then combined as a novel minimal model, and finally the corresponding PDE is solved by fast Fourier transform (FFT) efficiently. Since this method needs not the normals estimation or the triangular mesh construction, it saves lots steps. For the FFT implementation, the compute time of reconstruction is reduced. Through the numerical examples, this method shows much effectiveness to the noise point clouds.Fourthly, the know reconstruction method can not guarantee the physical performance of resulting surface and need complex post-processing including smoothing, modification et.al. Therefore, this paper takes stream surface as example and proposes a stream surface reconstruction method with the fluid velocity function. The main idea is to compute the fluid velocity as global constraint to the traditional minimal model, and use the surface evolution to reconstruct the final surface. It can not only generate a global smooth and accurate resulting surface, but also keep the surface as a corresponding stream modeling. The influences of each parametric are also discussed with an engine intake ports in real world.Finally, based on the general extremum model and the methods proposed in the paper, a numerical platform is developed. The platform is programmed by the combination of VC++and MATLAB environment. It contains many function modules, such as input/output, mathematical function library, many kinds of measurement equipment and software package. Series numerical examples, which all sample from industrial products in real world, are adopted to prove these methods in the paper.