仿射曲面

The geometric detail is represented as the set of the local affine coordinates of the base surface and extracted effectively and efficiently in user specified frequency band of geometric signal.

通过基曲面上的局部仿射坐标，则可以得到与之对应的多分辨率几何细节表示，曲面的低频信息和高频信息易被用户所指定的频段分离。

In the classification of QSIC, the notion of affine finiteness of a space curve is put forward.

在对两二次曲面交线的拓扑分类中，本文提出了空间曲线的仿射有限性这一性质。

So it is not easy to turn this idea into reality. We creatively give our parameterization by using the expression of the blending surface in affine coordinate system ([9]) and the plane pencil together.

在仿射坐标系下，二次有轴曲面的表达式相对简单，我们基于厉玉容[9]给出仿射坐标系下拼接曲面的表达形式、不分块直接对混合拼接曲面进行参数化。

3D reconstruction is one of the most challenging problems in computer vision. This project uses CAD model to increase the accuracy,robustness and speed of 3D reconstruction and five different works are conducted: 1 research on space curve 3D reconstruction method based on high curvature point nad turning point; 2 free-form curve 3D reconstruction based on B-spline and BURBS; 3 Active surface affine reconstruction based on single frame; 4 Matching and reconstruction of 3D sparse points; Data fitting method based on the iteration of nearest point.

三维重建是计算机视觉中公认的难题，本项目使用CAD模型来提高三维重建的精度、稳健性和速度的思路，围绕着空间曲线和曲面的三维重建和匹配开展了以下五个方面的研究：1）基于高曲率点和拐点分割的空间曲线三维重建方法研究；2）基于B样条和NURBS表示的空间自由曲线三维重建方法研究；3）基于单帧图像的有源曲面仿射重建；4）三维离散数据的匹配与重建；5）基于迭代最近点的数据拟合方法。

It has been widely used in recent years, for it not only preserves several advantages of B-spline surface, especially the affine- invariance, but also has some special advantages such as adaptability to arbitrary topology which parameter surface doesn't have.

它不仅具备B样条曲面仿射不变性等良好性质，还具有参数曲面所没有的任意拓扑适应性等特点，因而近年来得到了广泛的应用。

This technology not only preserves the properties of localness and affine-invariance of B-spline surface, but also has some special advantages such as adaptability to arbitrary topology which parameter surfaces dont have. These good qualities makes subdivision surface used widely in recent years.

它不仅具备B样条曲面的局部支承性、仿射不变性等良好性质，而且具有参数曲面所没有的任意拓扑适应性等特点，因而近年来得到广泛的应用。

It has been widely used in recent years, for it not only solves some problems in computer graphics, such as arbitrary topology and compatibility, but also retains several advantages of traditional NURBS, including the properties of localness and affine-invariance.

由于细分曲面不但解决了计算机图形学中遇到的任意拓扑和一致性表示问题，而且还保留了传统NURBS曲面表示所具有的局部性、仿射不变性等良好性质，因而近年来得到广泛的应用。

In Chapter 1,we recall the history of the motions of curves and surfaces in briefly.

S~2，S~3和仿射几何中的曲面形变是本文第二章的主要内容。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。