曲面

The available camera self-calibration is based on the image of the dual absolute quadric, but its elements have so large differences in magnitude that solutions are extremely sensitive to noise.

现有的自定标技术一般都是基于对偶绝对二次曲面像，由于对偶绝对二次曲面像元素在数量级上相差较大，在求解时必然会导致鲁棒性较差。

On the basis of B-Rep of CAD data and ACIS library,a technology of surface filling based on loop feature handling and outlines smoothing is presented in the paper,filling for the surface with complex concave edges is also studied in the paper.

以CAD数据的边界表示法和ACIS几何开发库为基础，提出了基于环特征处理和外边界光顺的曲面填充技术，对含有复杂凹缘的汽车覆盖件曲面填充进行了研究。

this article discusses the integral theorem of mean the promoted question, mainly has two aspects: On the one hand in analyzes in the teaching material under the first integral theorem of mean condition, had proven lies between the value spot to have to be possible to obtain in the open-interval, further discusses this knot promotes to the generalized Riemann integral, and further proved the conclusion also establishes to the promoted first integral theorem of mean; Promotes on the one hand in addition the integral theorem of mean to in the curve and the curved surface, and has proven the curvilinear integral theorem of mean and the surface integral theorem of mean.

本文讨论积分中值定理的推广问题，主要有二个方面：一方面在分析教材中第一积分中值定理的条件下，证明了介值点必可在开区间内取得，进一步将这个结论推广到广义Riemann积分，并进一步证明结论对推广的第一积分中值定理也成立；另一方面，将积分中值定理推广到曲线和曲面中，并证明了曲线积分中值定理和曲面积分中值定理。

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。

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。

Regularity is an important algebraic property of parametric curve and surface, which depends on the parameterization of parametric curve and surface.

正则性是参数曲线曲面的重要代数性质，是由参数曲线曲面的参数化决定的。

Thesis is devoted to construct and analysis piecewise rational splines, algebraic curve and surface for interpolation.

首先对参数曲线曲面、代数曲线曲面等问题的历史背景和研究现状进行了综述，并归纳了本文所做的工作。

In the four section, from the interpolationdimension of an algebraic curve and an algebraic surface,using theoryand method of algebraic geometry, we get some interpolation of analgebraic curve and an algebraic surface, and we prove the reasonableof the interpolation dimension of an algebraic curve and an algebraicsurface.

第四章我们从沿代数曲线曲面空间的插值维数出发，利用代数几何理论与方法，给出了代数曲线曲面上的基本插值结构，并证明了我们长期应用的其上的插值维数公式的合理性。

The theory of surfaces made a slow start. It began with the subject of geodesics on surfaces.

曲面理论也经历了一个漫长的开端，曲面理论是从曲面上的测地线的研究开始的。

This paper is mainly focused on data segmentation and model reconstruction problems in Reverse Engineering fields,The main contents include Sharp Featurebased quadrilateral domain extraction from a mesh model,connectivity between multiple B-spline surfaces,fast algorithm for fitting multiple B-spline surfaces on model with arbitrary topology,setting up a hierarchically structured constraintbased data model and binary cubic interpolation of splines with C~2 connectivity for type-Ⅱtriangulations on rectangular domain.

主要内容包括：网格数据的数据分割及矩形片的提取、多个B样条曲面间光滑拼接、任意模型的多个B样条曲面拟合的分块快速算法、基于二元三次样条函数在TYPE-Ⅱ分割下的曲面重建方法、基于约束和层次结构的模型表示及一个小型逆向工程软件系统的建立等。

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。