基于稀疏优化的网格简化问题研究

发布时间：2018-01-02 05:05

本文关键词：基于稀疏优化的网格简化问题研究　出处：《中国科学技术大学》2017年硕士论文　论文类型：学位论文

【摘要】：简化复杂的网格模型,减少模型的数据量,对于数字几何处理技术的各个研究领域技术的发展以及推广都有非常重要的意义,尤其是模型的实时渲染和传输。由于科技的发展,可视化技术的需求也是逐渐增强,对于网格模型的简化逼近技术的需求也就变得更加的迫切。本文介绍一种网格逼近方法,使得输入的模型可以由少量的多边形平面网格来近似表示,在保持模型轮廓和特征的同时,大大减少模型的数据量。本文就三维网格简化逼近工作出发,介绍一种新的基于稀疏优化的网格简化逼近方法,使得三维几何物体可以用平面多边形网格来近似表示,得到一个由用户指定的合理的面片数的多边形平面网格来表示三维模型。本文提出的方法主要包含两大方面:一方面是对输入的模型进行法向优化,进而根据优化后的法向信息驱动顶点位置更新。也就是首先对输入的三维网格的面片法向进行L0模最小的稀疏优化,使得面片法向在一个区域内是分片常值的,然后根据优化后的面片法向信息通过网格变型的思想来更新顶点位置。另一方面是,对现有模型进行面片分割聚类,通过随机选择种子面片的方法,设定相邻面片法向之间的差异的截断值,迭代的进行分割聚类。最后根据聚类出来的分类,提出一个基于全局顶点的稀疏优化模型,通过聚类边界顶点梯度L0模最小对网格的聚类进行平面多边形网格逼近。本文提出的优化策略有广泛的应用前景,在几何处理、3D渲染、数据存储等行业中都有广泛的需求。大量的网格简化结果也证明了所提出的优化模型与算法的有效性以及算法的稳定性。多分辨率网格技术以及实时渲染技术的不断发展和壮大,这都要归功于网格简化逼近技术的不断完善和创新。随着图形技术的需求不断加强,拓展更加优秀的网格简化方法依然是科研工作者们重要的研究课题。
[Abstract]:Simplifying the complex grid model and reducing the data volume of the model are of great significance for the development and promotion of various research fields of digital geometric processing technology. Especially the real-time rendering and transmission of the model. With the development of science and technology, the demand of visualization technology is gradually enhanced. The need for simplified approximation of grid model becomes more and more urgent. In this paper, a mesh approximation method is introduced, so that the input model can be approximately represented by a small number of polygonal planar meshes. While preserving the contour and features of the model, the data volume of the model is greatly reduced. In this paper, a new mesh simplification approximation method based on sparse optimization is introduced. The 3D geometric objects can be approximately represented by planar polygonal meshes. A polygonal planar mesh with reasonable number of surfaces specified by the user is obtained to represent the 3D model. The method proposed in this paper mainly includes two aspects: on the one hand, the input model is normally optimized. Then the vertex position is updated according to the optimized normal information. That is to say, the minimum sparse optimization of L0 norm is carried out for the input 3D mesh in the normal direction. So that the normal face in a region is a slice constant, and then according to the optimized face normal information to update the vertex position through the idea of grid modification. On the other hand, the existing models are segmented and clustered. Through the random selection of seed slices, the truncation value of the normal differences between adjacent patches is set, and then the segmentation and clustering are carried out iteratively. Finally, the classification is based on the clustering. A sparse optimization model based on global vertices is proposed, which approximates the mesh clustering by the minimum L0 norm of the edge vertex gradient. The optimization strategy presented in this paper has a wide application prospect. 3D rendering in geometric processing. Data storage and other industries have a wide range of requirements. A large number of mesh simplification results also prove the effectiveness of the proposed optimization model and algorithm and the stability of the algorithm. Multi-resolution grid technology and real-time rendering technology. Continue to grow and grow. This is due to the continuous improvement and innovation of mesh simplification and approximation technology. With the increasing demand for graphic technology, it is still an important research topic for researchers to expand more excellent mesh simplification methods.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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