【作者】 杜佶；

【导师】 张丽艳；

【作者基本信息】 南京航空航天大学 ， 航空宇航制造工程， 2005， 硕士

【摘要】 对散乱数据点集进行曲面重建是逆向工程中的关键问题,使用体视化思想解决该问题,把散乱数据点集作为体视化中的采样数据,可以重建得到含有物体内部信息的产品模型,并采用隐式曲面的方式来表示重建结果。在隐式曲面方程的构造方法上,使用径向基函数对散乱点集进行插值,表现出良好的精确性和光滑性,因而在近年来得到国内外众多学者的研究。本文从使用径向基函数对散乱点集进行曲面重建出发,对径向基函数在逆向工程中的应用进行了研究,主要工作如下:Θ 研究了基于径向基函数(RBF)和紧支撑径向基函数(CSRBF)的散乱点曲面 重建技术。首先建立插值散乱数据点的隐式曲面方程,然后使用步进立方体 算法提取出曲面的三角网格模型。实验结果表明,这样得到的网格模型较基 于距离场函数的网格曲面重建方法在细节处有更好的描述。Θ 针对径向基函数进行曲面重建的前提条件,对散乱点云的法矢计算和调整进 行了研究。采用微切平面法计算散乱点的法矢,在已有法矢调整算法的基础 上提出并实现了两种新的法矢调整算法,使法矢调整的速度得到明显提高。Θ 应用径向基函数对三角网格曲面中孔洞的修补进行了研究,提出了一种新的 孔洞修补算法。该算法可以处理多种类型的孔洞,并保证修补后的区域同原 始曲面能光滑地融为一体。Θ 通过提取体数据场的等值面,很好地解决了任意拓扑网格曲面的等距曲面生 成问题。该方法的突出优点是生成的等距面不存在曲面自交问题,在快速原 型制造和数控加工中具有非常重要的实用价值。更多还原

【Abstract】 Reconstructing surfaces from digitized points is the pivotal problem of ReverseEngineering. To solve this problem, we can adopt the ideology of VolumeVisualization, regard digitized points as sample data in the process of VolumeVisualization. In this way, a model containing interior information of the object canbe reconstructed and expressed in the form of implicit surface. As the method ofconstruction to be concerned, interpolating digitized points by means of Radial BasisFunction has presented excellent accuracy and smoothness, and been under theresearch by many scholars at home and abroad in recently years. The application ofRadial Basis Function in Reverse Engineering was studied in this thesis. The maincontents are as follows:Θ Surface reconstruction from digitized points based on Radial Basis Functio n (RBF) and Compactly Supported Radial Basis Function (CSRBF) was re searched. The triangle mesh model of surface was extracted by constructin g an implicit surface function. As shown in the experimental result, RBF- based method has better description of details than that of distance-field-b ased method.Θ As the precondition of RBF-based surface reconstruction, normal computation and normal adjustment were investigated. The normal of digitized points was computed use ‘micro-tangent plane’. Based on existing algorithms, two new normal adjustment algorithms were put forward and implemented, which greatly improve the speed of computation.Θ Repairing holes in mesh surfaces was discussed as well. A novel hole- repairing algorithm, which can guarantee the consistency between the holes and the original surface, was put forward. The algorithm can be used to repair different kinds of holes in mesh surfaces.Θ Through extracting iso-surface of volumetric data field, the offset surface of arbitrary topology mesh was obtained. The most prominent merit of this method is that the problem of self-intersection can be avoided, which has important practical value in rapid prototyping manufacturing and numerical controlledmachining.更多还原