子流形高斯像的几何与拓扑是整体微分几何领域的重要研究课题之一。
It plays an important role in global differential geometry to study the geometric and topological properties of Gaussian image of submanifolds.
所有中国人都应该为中国数学家在微分几何领域所取得的成就，和对庞加莱猜测的贡献而感到骄傲。
All Chinese can be proud of the achievements of their mathematicians in differential geometry and their contributions to the completion of the proof of Poincare conjecture.
在数学学科的很多的领域中算术只是起到次要作用，例如逻辑学和几何学。
There are entire fields of mathematics where numerical manipulation is peripheral: logic and geometry, for example.
柏拉图认为数字(以及一些几何体，例如圆)存在于抽象、永久并且完美的领域中，人们只有通过偶然顿悟中才能领悟。
Plato thought Numbers (and geometric objects such as circles) existed in some abstract, eternal and perfect realm, of which mortals were granted only an occasional glimpse.
几何图形作为一个基本造型元素在现代平面设计领域中发挥着重要作用。
Geometric shape as a basic element in the modern field of graphic design plays an important role.
修改出口几何以减少应力是目前正在开发的一个领域。
Modifying the exit geometry to reduce stress is an area of ongoing development.
本研究是在建构主义学习理论指导下，结合物理学科中的一个具体领域——几何光学进行的一个尝试。
The present research is carried out in combination with disciplinary education under the guidance of constructivist learning theory in one specific domain — geometrical optics.
以几何光学为基础的复射线理论已在激光、微波、声学和地震波等学科领域获得了广泛应用。
Complex ray theory, based on geometrical optics, has been found to have many applications in areas of laser, microwave, acoustics, seismology etc.
本文在分析黎曼的几何思想的基础上，着重论述了它对数学和物理学两个领域所产生的深远影响。
The geometric thinking in the analysis Liman , on the basis of mathematics and physics it focuses on the two areas of the far-reaching implications.
从那时开始，人们发现量子群在很多领域都有着深刻的应用，范围遍及理论物理、辛几何、扭结理论与约化代数群的模表示理论等。
Since then they have found numerous and deep applications in areas ranging from theoretical physics, symplectic geometry, knot theory, and modular representations of reductive algebraic groups.
在三角形域上构造对边界曲线和跨界导数插值的三角曲面是计算机辅助几何设计和计算机图形学等领域中的基本问题。
Constructing triangle surface which interpolates the boundary curve and cross-boundary slopes on a triangle is the basic problem in computer aided geometric design, computer graphics and so on.
本文通过对比研究，发现土地管理空间概念的领域知识，包含几何知识。
In this paper, comparative studies showed that domain knowledge of land management spatial concept covers knowledge of geometry.
几何知识是依据几何特征属性识别的土地管理领域知识之一。
Knowledge of geometry is one of land management domain knowledge that can be identified by the geometric characteristics of attribution.
几何定理证明的前推法能够产生传统形式的可读证明，在定理机器证明领域占有重要的地位。
The forward reasoning for geometry theorem proving can produce the traditional readable proving, thus plays a special role in the mechanical theorem proving.
图像插值是数字图像处理领域的一项重要任务，是图像缩放、旋转、几何矫正等图像操作的基础。
Image interpolation is an important task in the field of digital image processing. It is fundamental to many digital image operations, such as scaling, rotation, and geometric correction.
与领域物体对比，目前的网格几何学被使用作为流动物体。
In contrast to domain objects, the actual mesh geometry is used for fluid objects.
直线汇理论是古典微分几何的一个重要研究领域。
The theory of rectilinear congruence is an important field in differential geometry.
当今的GIS系统的空间数据模型，主要反映地图制图领域的点、线、面对象管理与操作的几何知识。
However, the spatial data model of main GIS systems only reflect knowledge of management and manipulation objects in field of cartography, such as point, line and poly geometry objects.
对具有复杂、不规则轮廓的零件进行精密测量和误差评定，是当前几何量计量领域中的一个重要课题。
In the field of geometrical metrology, one of the important projects is the accurate measurement and error evaluation of parts profile with complicated and irregular surface.
基于零件实物样件的几何模型反求技术已成为CAD/CAM领域中的研究热点之一。
The reverse engineering of geometric model based on product exemplar has become one of the research focuses in CAD/CAM field.
平面点集的(欧几里德)最小权三角剖分问题是计算几何和算法领域的一个长期悬而未决的公开问题。
The (Euclidean) minimum weight triangulation (MWT) of a planar point set is a long-standing open problem in the fields of computational geometry and algorithm design.
特征技术是三维几何建模领域中继实体模型技术后的又一个重要里程碑。
Features 3d geometric modeling technology is the area of solid model relay technology is another important milestone.
由于它与浑沌理论、分形几何等领域有着紧密的联系，因此引起了数学界和其它领域的巨大兴趣和关注。
Because it is closely related to the chaos theory and fractal geometry, there are increasing interest not only in the mathematics but also in the other relating fields.
凸包问题是计算几何的基本问题之一，在许多领域均有应用。
Convex hull problem is one of the fundamental problems in computational geometry, and is used in many fields.
三维几何约束求解对于装配设计、装配工艺规划和并行工程等多个领域的研究具有重要意义。
D geometric constraints solving has important significance for assembly modeling, assembly process planning and concurrent engineering.
几何学家探索的领域是空间，而空间也是艺术家深感兴趣的东西。
Space, the area being explored by geometers, has also received extensive interest in the community of artists.
本论文涉及的是晶体结构几何学领域中晶体空间划分部分的内容。
This dissertation is concerned with classification of crystal space in crystal structure geometry.
顾及地形特征线的散点域(约束数据域)三角剖分是建立高精度数字地面模型的基础，在GIS、地学分析、计算几何、多分辨率DTM等领域中有着广泛的应用。
The triangulation of constrained data set is widely used in Geographic Information System (GIS), geo-science, computational geometry, multi-resolution and high precision DTM, et al.
求两条直线段的交点问题是计算机图形学、计算几何、几何造型等领域的最基本问题之一。
Finding intersection between two line segments is a fundamental problem in computer graphics, computer geometry, geometry modeling, etc.
求两条直线段的交点问题是计算机图形学、计算几何、几何造型等领域的最基本问题之一。
Finding intersection between two line segments is a fundamental problem in computer graphics, computer geometry, geometry modeling, etc.
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