经过10年的研究，他们在今年年初证明了他们以及其他人已经折了好几年的一个叫双曲线抛物面的曲面实际上并不存在。
After 10 years of research, they proved earlier this year that a curved shape called a hyperbolic paraboloid, which they and others had been folding for years, doesn't actually exist.
单连通和非单连通的概念，研究哪些环路能界定曲面，可以用来对空间内部物体的形状进行分类。
This concept of being simply connected or not, and studying which loops bound surfaces or not can be used to classify shapes of things inside space.
本文主要研究了空间结构中自由曲面的参数化描述及网格划分算法，并编制了相应的程序。
This paper mainly researched on parametric description and meshing algorithm for the free surface of spatial structure with the program development.
本文研究反向工程中曲面重构的几何连续性问题。
This thesis studies the problems of geometric continuity about surfaces reconstruction in Reverse Engineering.
研究了模型边界处理方法及复杂曲面局部特征设计方法。
A design methodology dealing with boundary and local features on the surface model is researched mainly.
针对自由曲面走刀方向数控加工的研究，建立了简化的刀具轨迹时间模型，并对路径规划的系统进行了讨论。
To aim at the research on cutting direction in NC machining of free-form surfaces, a simplified time model for tool trace is established, and the system of tool path programming is discussed.
在这段视频中，我们研究了一些基本的技术将在对象的立场，细分曲面。
In this video segment we investigate some fundamental techniques for turning the stand-in object into a subdivision surface.
本文研究NURBS曲面重构中的几何连续性问题。
This thesis studies the problems of geometric continuity in NURBS surfaces reconstruction.
本文以炮口冲击波场测试系统的测试试验为背景，主要进行了炮口冲击波场压力曲面的插值研究。
Against the background of pressure measurement of the muzzle shock wave, the main work of the article is to study the interpolation methods to describe the pressure surface of the muzzle shock wave.
本文研究了大尺寸零件和复杂曲面的数字化测量方法。
This paper studies a method about digitized measurement of the large-scale parts and the complex curved surfaces.
基于物理的造型方法是当今曲面造型研究的热点之一，并可望成为今后曲面造型的实用工具。
Physics based modeling is one of the keen free form surface modeling method at present, and it should be a practical surface modeling method in the future.
本文系统研究了曲面点接触高副的接触运动学，以及在机器人手点接触抓取操作中的应用。
The kinematics of higher pairs with point contact surfaces and the application on manipulation of multifingered robot hand are researched in this paper.
本文研究了逆向工程的关键技术之一——自由曲面的三维测量技术。
D measurement of free surface, one of key technology of Reverse Engineering, is described in this paper.
NURBS曲面具有许多良好的特性，对它的各方面研究是必要的。
Because of the advantages of the NURBS surface, it important to research into the NURBS surface.
它们的研究被称做曲面的内蕴几何。
Their study is called the intrinsic geometry of the surface.
该文对应用实体造型技术建立船体曲面模型的方法进行了研究。
This paper studies the method of utilizing entity sculpting technique to set up curved hull surface model.
本文研究曲线曲面分形逼近的数学模型及其简单应用。
This thesis studies modeling and the simple application of the fractal approximation of curves and surfaces.
随后论文研究了NURBS曲线曲面的分割算法，进而推导出NURBS三参数实体的离散方法。
The paper studies the tessellating algorithm of NURBS curve and surface, then puts forward the tessellating method of NURBS tri-parametric solids.
在超曲面几何学中，对主曲率的研究是至关重要的。
It is essential to study the principal curvature of hypersurface in the hypersurface geometry.
探索和研究了数学船型构造及解的存在、唯一性，且建立了一套求光顺样条曲面的数值方法。
Also this paper presents the structure of mathematical vessel-model and the existence and uniqueness of the solution and introduces a set of numerical methods to solve the smoothed-spline Surface.
本课题的研究对于空间曲面的复杂工件的扫描测量具有重要的参考价值。
To the scanning measurement of other complicated workpieces with space curved surface, it has very important referenced value.
通过对不可展回转曲面近似展开方法的研究，得到了回转曲面近似展开、精度分析和误差矫正的数学模型。
By study the method of approximate development of surface of revolution, the mathematiccal model of approximate development, precision analysis and error correction has been gained.
经典微分几何研究三维欧氏空间中曲线曲面理论，其最具有特色的研究是主曲率函数满足某些关系的魏因加吞曲面。
In the classical differential geometry which deals with the theory of curves and surfaces of three dimensional Euclidean space, the most distinctive study is the Weingarten surface.
研究了曲线和曲面的光顺准则、方法和评估手段。
The principles, methods and evaluation of the fairing of surfaces and curves are also discussed.
在CAD参数曲线曲面造型方法中，混合曲线曲面技术正被广泛研究，本文分两大部分。
Among the modeling methods used in the CAD parametric curves and surfaces, the technique of blending curves and surfaces is being wildly study.
随着对区间曲线曲面的深入研究，人们开始用区间曲线曲面来逼近曲线曲面。
With the deeper research of interval curves and interval surfaces, people begin to approximate curves (surfaces) with interval curves (surfaces).
从实际应用角度出发，采用线结构光方法进行曲面透明壳体厚度测量的研究。
The thickness measurement of the transparent curved surface object is investigated with the linear structured light method.
通过对典型工程曲面的展开试验，定量地研究了制成展开样板误差的主要因素。
Through developing experiment of typical engineering curved surface, main factors of manufactured developing profile board have been quantitatively researched.
本文研究光滑曲面上曲线的计算机表示、插值与逼近等。
The interpolation, approximation and other things for curves on smooth surfaces with computer are studied.
建立了弹性共轭曲面运动的基本方程，研究了弹性共轭曲面问题的一般求解方法。
The fundamental equation of motion for ECS is set up. The general method to solve the question of ECS is studied.
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