查询词典 subdivision

Adaptive subdivision is performed only in the areas facing to the viewpoint in the pre-process. And in the each adaptive subdivision, we choose the normal angle of the adjacent faces as the control error to detect whether the approximation is sufficient. Sharp edges are automatically tagged according to the given thresholdθand subdivision masks are designed based on different sharp degrees.

在预处理过程中，只选取面向视点的网格作为能够被进一步自适应细分的网格；在自适应细分过程中，用相邻面片的法向夹角作为控制误差来反映细分的逼近程度是否足够；并根据预设的阈值θ自动标记网格中的尖锐特征边，重新设计尖锐特征处的权值掩模。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component. For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper. For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space state informatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision. Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为（n-1）维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料（单质材料作为特殊的功能梯度材料看待）、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component.For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material .distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper.For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space stateinformatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision.Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为(n-1)维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料(单质材料作为特殊的功能梯度材料看待)、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

In this thesis, we design a subdivision scheme to generate conics and quadrics.

本文设计出了生成除抛物线和抛物面外的二次曲线曲面的Subdivision格式。

By means of homogeneous coordinates, a type of important subdivision—Rational Matrix Subdivision are proposed in chapter 2. Many good geometric properties of the curves with Rational Matrix Subdivision such as convex and variation diminishing properties are proved.

第二章以齐次坐标为工具，提出了一类重要的细分法——有理矩阵细分方法，并证明了其生成曲线的优良性质，例如凸包性、变差缩减性等（参见第二章§2.3节）。

The vertex within control mesh of fitting subdivision surface was located by iterative modification and local adaptive subdivision. This method makes it feasible to avoid the solution of linear equation system. The size of control mesh, which is corresponding to the fitting Loop subdivision surface, is smaller. The surface is reconstructed according to the given precision. It can represent detail characteristics of original model, and is piecewise smooth (C^2 continuous everywhere except at extraordinary vertices where they are C^1 continuous).

系统通过对控制网格顶点的循环修正和局部自适应细分来求解最终拟合细分曲面控制网格，避免了求解线性方程组，提高了拟合曲面的质量，实现了在给定精度下用较少的控制网格反映物体细节特征的分片光滑（片内除奇异点C^1，外其余C^2连续）的Loop细分曲面重建。

The main creative achievements accomplished in this dissertation are as follows: 1. A new method to achieve nanometer-scale resolution for grating-based metrology is developed by improving the discrimination power of method of Computer Tangent Subdivision which makes use of the good linearity of tangent function in small range. 2. A new subdivision technique of moire fringes-Dynamic Tracing Subdivision is proposed.

在本论文的研究过程中，所做的主要创造性工作有：（1）提出了利用正切函数在小范围内线性度较好的特点，采用粗、精结合的方式，扩展计算机正切细分法的细分能力，达到纳米级的测量分辨率的新方法；（2）提出了一种新的莫尔条纹信号细分方法：动态跟踪细分法。

A new scheme was presented to design subdivision curves by introducing three control parameters in the subdivision process. The sufficient conditions of the uniform convergence and Ck continuity of this subdivision scheme were analyzed.

通过在曲线细分过程中引入三个参数，给出一种新的细分曲线构造的算法，并利用生成多项式等方法对细分法的一致收敛性、Ck连续性进行了分析。

The main content reads as follows: Chapter 1 gives a survey on the three methods by which regular geometric modeling can be rended, including parametric curves/surfaces modeling method, algebraic curves/surfaces modeling method and subdivision. Moreover we introduce in greater detail about two means for subdivision which fit into two class: geometric subdivision and algebraic subdivision.

全文主要内容如下：第一章首先对CAGD中构造&规则几何形体&的三类造型方法：参数曲线、曲面造型方法，代数曲线、曲面造型方法及细分法——曲线、曲面的离散化造型方法，作了较系统的综述，并对两类主要的细分法——几何方法与代数方法，作了较详细的介绍。

Three new fringe subdivision methods are first proposed opposing to the restrictions of the traditional subdivision methods. They are fringe subdivision method based on self correlation coefficient, fringe subdivision method based on gene algorithm and fringe subdivision method based on Fourier-transform.

本文针对传统软件细分方法的局限性，首次提出了三种新的条纹细分方法：基于自相关系数的条纹细分法、基于遗传算法的条纹细分方法和基于傅立叶变换的条纹细分方法。

Graf, without question, is the greatest women's player in history.

格拉芙，现在，毫无疑问是女子网坛历史上最伟大的选手。

If not, you will have to look around at all your important data.

如果没有，您将需要检查所有的重要数据。