曲面

The algorithm makes full use of geometric information of intersecting lines to speed up the calculation according to the arc height tolerance.

在跟踪求交的算法中充分利用了交线的几何特性，按等弓高误差快速精确地求取曲面上的交线。

The algorithm of point of intersection about free surface occupies a position of importance in the CAD/CAM software system,and has a great effect on the efficiency of running software.

自由曲面的求交算法在CAD/CAM软件系统中占有重要的地位，并对软件运行的效率有较大的影响。

Their study is called the intrinsic geometry of the surface.

它们的研究被称做曲面的内蕴几何。

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。

Proposed a representation scheme for 3D face -- Surface UnfoldingFor its irregular sampling in 3D space, 3D face surface cannot be processed by many orthogonal and subspace analysis toolkits directly, i.e. DFT, DCT, PCA, LCA. Surface Unfolding projects the 3D face to a 2D plane while retaining its intrinsic geometry properties of angle and area which issues a surface representation — Unfolded Image.

提出了一个三维人脸的平面表征方法——曲面开折模型不同于传统的数字生物特征，3D人脸数据是非规则采样的，传统的信号处理工具难以对3D数据进行直接处理。

Gauss(1777-1855); Copenhagen ; competition essay ; intrinsic ifferential geometry

本文考察了高斯完成于1822年12月，并于1823年获哥本哈根科学院大奖的论文《将一给定曲面投影到另一曲面上，使得保持它们在无穷小部分相似性的一般解决方法》(1825年出版，以下简称获奖论文)产生的背景及其对内

By using in a sequence the eigen-decomposition,a permutation,the inverse discrete Fourier transformand a truncation on the matrix,an exact and explicit parametrization formula for Loop subdivision surfaces is proposed.

利用控制网格拓扑结构的对称性，通过将奇异点周围1-环和2-环的控制顶点进行离散Fourier变换得到分块对角阵，将其进行特征分解及排序之后，再通过离散Fourier逆变换和截断等操作得到细分矩阵的高次幂的表达式，从而得到Loop 细分曲面新的精确参数化公式

In this paper, a new kind of rational parametric transformationis studied which has the same form of it's inverse transformation.

文摘：研究了一类逆变换具有同样表示形式的有理参数变换，并给出了在此参数变换下的曲面一阶几何连续拼接条件。

In this article,we introduce some ordinary methods for correction of contour irregularity in details,and study was carried out for their implementation.

本文详细地介绍了几种常用的曲面修正方法，并对它的实现进行了研究。

Theorem Let M be a orientable or non-orientable closed surface, and f a C°-flow whose every singular point is isolated. Then f has POTP if and only if the following three conditions hold

定理 设M是任一个可定向或不可定向的闭曲面，f是M上任一个奇点均孤点的C〓-流，则f具有伪轨跟踪性质的充分必要条件是

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。