曲面

In this paper,we propose a concept called interval implicitization of rational bézier surfaces,that is ,finding an interval algebraic surface with lower degree which bounds a given parametric rational bézier surface such that some objective function involving the width and the tention term of the interval algebraic surface is minimized.

本文提出有理Bézier曲面的区间隐式化的概念，即找到一条较低次的区间代数曲面使得给出的有理Bézier曲面落在该区间代数曲面内，并使得一包含区间代数曲面的宽度和张量项的目标函数达到最小。

This paper on basis of surface's local principle.Through discussing the Gauss mipping image of the surface's asymptotic curve and the camber between any two directions of surface and the developable surface to illustrate the impact on surface of Gauss mipping.

文章以局部曲面的基本理论为基础，通过对曲面的渐近曲线、曲面上任意两方向的夹角和可展曲面的高斯映射象的讨论来说明高斯映射对曲面的影响。

Applyingthe sufficient and necessary condition of biquadratic Bézier patch being non-negative,a method is presented to see whether two points are the closest points between twobiquadratic NURBS surfaces when the two points are respectively on the two surfaces. Based on the method, the surface split algorithm is improved while the surfaces arebiquadratic NURBS surfaces.

本文利用双二次 Bézier 曲面为非负的充要条件，提出了分别位于两张双二次 NURBS 曲面上的点是否为这两张曲面间距离最近的点的判别方法，并由此在双二次 NURBS 曲面的场合对计算最短距离的曲面分割法作了改进。

A human model using polynomial convolution surface is presented which is modeled by articulated skeletons convolved with some kernel function. The convolution surface and curve correspondence theorem under orthogonal projection is presented. The human contour is approximated with a convolution curve and 3D human pose can be estimated using a nonlinear optimization algorithm.

首先建立了一种新颖的多项式密度卷积曲面人体模型，该模型由连接体线骨架与某种卷积核卷积而成，整个曲面是一张连续曲面，调节多项式和半径参数可以让人体任意变形；给出了正交投影下卷积曲面和曲线对应的概念和相关定理，为二维的图像轮廓和三维人体模型之间建立对应关系；根据正交投影下卷积曲面与曲线对应定理，用卷积曲线去逼近人体的图像轮廓曲线，从而估计和恢复出三维人体运动姿态。

This paper analyzes the deviation of cambered form witch is composed of batten and sheet in concrete construction,and then educes a relationship between width of sheet,deviation of cambered form and curvature radius of camber,in order to solve the problem of assemble spline form work and increase construction quality of concrete curved surface.

分析了用板条和铁皮组装而成的曲面模板在曲面混凝土施工中的误差情况，同时给出了施工中板条宽度、曲面误差、曲面曲率半径之间的关系，以解决好拼装样条模板的问题，从而提高混凝土曲面的施工质量。

We propose a unified method to approximate important geometric attributes, including normal vector, gauss curvature, mean curvature, principal curvatures and principal directions on point sampled surface. Based on MLS projection our method is robust to noise and stable to the sampling density.

曲面的微分性质包括法向量和切平面、高斯曲率、平均曲率、主曲率和主方向，在计算机图形学、机器视觉和计算机辅助设计等领域发挥了重要的作用，比如曲面绘制、内外测试、曲面重建、曲面简化、去除曲面噪声和模型分割等。

We proved that the necessary and sufficient condition that the developable surfaces touch the second focal surface along the orthogonal trajectories was that the base surface S was a developable surface.

证明了线汇中的两系可展曲面交第二叶焦曲面于正交轨线族的充要条件是原曲面是可展曲面，并给出了两叶焦曲面在同一条光线上两焦点相互对应下，保持渐近曲线相互对应的充要条件。

The principle of the fractal-interpolated surface was discussed. The formula and the theorem of fractal dimension of the fractal-interpolated surface were analyzed. The numerical analysis of height anomaly fit by the fractal interpolated surface and the result comparison with the quadric polynomial surface model with practical data were given.

本文论述了分形插值曲面的原理，分析了分形插值曲面的计算公式，讨论了分形插值曲面的维数估计方法和公式，用实际数据进行了分形插值曲面拟合高程异常的数值分析以及与二次多项式曲面拟合模型结果的比较。

To decompose prismoid subject into sweepable sub-volumes, the source vertices project into target surface and decompose target surface to many subdomains. The virtual surfaces are found by linking opposite vertices from source surface and target surface, finally cut volume to sub-volumes. It is also designed spheriform decomposition based on geometry character.

虚拟分解主要是通过将棱柱体的源曲面边界顶点映射到目标曲面，将目标曲面划分成和源曲面一一对应的区域，连接对应的顶点建立虚拟剖分曲面，利用虚拟曲面将复杂的几何体剖分成子几何体。

Traditionally, a surface is usually scatted in an array of 3D data points which are topologically connected by rows and columns to form a rectangular mesh. This method can't meet the requirement of description and measurement for some complex surfaces. On the basis of tracing border points, a new method is proposed to deliver 3D data points of surfaces, which are topologically constructed with optimum rectangular and triangular mesh. In order to measure surface efficiently and safely with NC machine, an optimization of measurement paths is proposed to avoid interference between the measuring tool and the surface with holes. The curve design is the basis of surface modeling.

数控测量技术的发展为测量自动化、集成化、智能化提供了可能，而对于复杂曲面的自动测量规划则是测量技术中的难点问题，平行截面等数目测点分布和四边拓扑测点分布规划方法，不论在测点分布的合理性上还是在网格结构的优化方面，均难以满足形状或边界较复杂曲面的离散化描述和曲面造型的要求，为了实现任意拓扑曲面的自动测量，本文对复杂曲面的合理离散化描述和自动测量问题进行了研究，提出了基于边界跟踪、优化网格的测点自动分布规划和四边、三角混合网格的生成方法：同时对具有孔洞或测量干涉凸台等非完整曲面的测量路径优化问题进行了研究，提出了路径优化方法。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。