查询词典 enumerative geometry

The idea of Gauss initiated the study of "intrinsic geometry" and made differential geometry an independent subject of mathematics.

由此开创了曲面的内蕴几何学的研究，使微分几何成为一门真正独立的学科。

Contemporary differential geometry is intrinsic , meaning that space is a manifold and structure is given by a Riemannian metric , or analogue, locally determining a geometry that is variable from point to point.

微分几何，这是简单的几何的曲率，已越来越重要，因为对数学物理的建议空间不是平坦的空间。

Gauss（1777—1855）; intrinsic differential geometry ; non-Euclidean geometry ; Gaussian curvature ; Gauss-Bonnet Theorem

高斯（C.F.Gauss ； 1777—1855）；内蕴微分几何学；非欧几何；高斯曲率；高斯-博内定理

In this method, a feature vector with desirable characteristics including spatial locality, frequency and orientation selectivity is obtained by DT-CWT. Then, the dimension of the vector is linearly reduced by ONPP, thus effectively preserving the intrinsic neighborhood geometry of the vector and the global geometry.

先通过DT－CWT得到具有空间、频率以及方向特征的人脸特征表示，然后使用ONPP对特征向量进行线性降维，有效地保持了数据的局部与全局的几何特征，最后进行识别测试。

Gauss （ 1777-1855 ）; intrinsic differential geometry; non-Euclidean geometry ; Gaussian curvature ;Gauss-Bonnet Theorem

高斯（C.F.Gauss，1777—1855）内蕴微分几何学非欧几何高斯曲率高斯-博内定理

Gauss(1777—1855);intrinsic differential geometry;non-Euclidean geometry;Gaussian curvature;Gauss-Bonnet Theorem

Gauss，1777-1855；内蕴微分几何学；非欧几何；高斯曲率；高斯-博内定理

Based on the summarizing of the exiting algorithms of the texture mapping and antialiasing, this paper goes deeply into the basic theory and processing of texture mapping. The texture compress algorithm which can satisfy the need of the memory and time is given for the stochastic sampling in the inverse texture mapping; the geometry transformation in the texture mapping are discussed and the concepts of the unitary parametrization and the patch parametrization is proposed, some kinds of the unitary parametrization methods of parametric surfaces and the geometry transformation in the patch parametrization are also presented; in order to solve the aliasing in the parametrization of intermediate surface-sphere in two-part texture mapping, an area-preserving transformation is presented also; to improve the quality of the graph the aliasing in the texture mapping is analyzed from the aspect of signal process, and the modified summed-area tables algorithms is proposed; the distortion of the scanline conversion algorithms under perspective transformation is analyzed and the proper interpolation algorithm is presented so the aliasing problem of the polyhedral object after the unitary parametrization is efficiently solved.

本文在总结现有的纹理映射和反走样算法的基础上，深入研究了纹理映射的基本原理与过程，根据反向纹理映射对纹理随机采样的特殊要求，提出了一种可满足存储空间和寻址时间的纹理压缩存储算法；通过对纹理映射中几何变换理论的进一步深入探讨，提出了整体参数化和面片参数化的概念，并给出了参数化曲面的各种整体参数化方法和面片参数化的几何变换形式；针对现有的两步映射算法所存在的中间曲面—球面的参数化问题，提出一种等积映射方法，较好地实现了由非参数化面片拼接而成的多面体表面的纹理映射；从信号采样的角度深入分析了纹理映射中走样产生的原因，提出了改进的区域求和表算法，使图形生成的效果有所提高；还分析了一般的扫描线算法在透视变换中所存在的问题，提出了一种正确的插值算法，从而解决了整体参数化后多面体表面纹理映射的几何变形问题。

Function graphing and analyzing: 2D, 2.5D functiongraphs and animations, extrema, root, tangent, limit,derivative, integral, inverse; sequence of number: arithmetic progression, geometric progression; analytic geometry: vector, line, circle, ellipse,hyperbola and parabola; solid geometry: spatial line, prism, pyramid, cylinder, cone, dado and sphere; Ability to save graph as data file or bmp file; Ability to save animation as AVI file; Ability to move, zoom in, zoom out and rotate the scene.

函数图表和分析：2D， 2.5D 函数图表和动画，极值，根，正切，极限，导数；序列号：等差数列，等比级数；解析几何：向量，矢量，直线，圆，椭圆，双曲线和抛物线；立体几何：空间线，棱柱，三角锥，圆柱，圆锥体，梯形台和球体；保存图形为数据文件或者图像文件的功能；保存动画为 AVI 文件的功能；移动，缩小，放大和旋转场景的功能。

Because of mechanism parameters unknown and complicated mathematical calculations,it is very difficult for us to identify screw system independence. However,Klein projective geometry theory is used to discuss screw system dependence in this paper. As a result,it is very easy for us to identify screw system dependence by Klein projective geometry theory,so the problem of discriminating input selecting reasonability is solved.

将Klein映射理论应用到多自由度输入选取的判别中，讨论了3力3偶螺旋系的相关性，给出了相关性的判据，使相关性判别变得非常简单，避免了输入选取判别中复杂的数学运算和机构参数未知的问题，从而解决了输入选取的判别难题。

On this basis, it deeply analyzesed the spatial geometry structure of hyper spectral data lattice distribution, concluded that high\|dimensional space of remote sensing hyper spectral data belong to low\|dimensional geometry structure \|"hyperplane" shape, and anomaly point group which includes alteration information usually dissociates out the "hyperplane".

在此基础上，对高光谱数据点阵分布的空间几何结构进行了深入的研究分析，推断出遥感高光谱数据集合的高维空间属于低维几何结构"超平面"形态，而包含蚀变信息在内的异常点群通常会游离在"超平面"之外。

There had been a moment during the breakfast meeting, though, after the backslapping and the small talk and when all of us were seated, with Vice President Cheney eating his eggs Benedict impassively and Karl Rove at the far end of the table discreetly checking his BlackBerry, that I witnessed a different side of the man.

那次早餐会期间，在表示过关心和寒暄以后，我们所有人坐了下来，我注意观察了一下，副总统切尼面无表情地吃着班尼迪克蛋（Eggs benedict，源自美国，以英式松饼、火腿、水煮蛋以及荷兰酱组合而成），卡尔。罗夫在餐桌的远端谨慎地经常查看他的黑莓手机，我目睹了他所不为人知的一面。

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