二次曲面

In this paper, we discuss parameterization of implicit blending algebraic surfaces of three quadratic surfaces.

本文研究了三个二次曲面的隐式光滑拼接代数曲面的参数化。

A typical 3-RPS parallel platform manipulator mechanism is firstly studied by means of the above theory. The principal screws of this mechanism under three different configurations are identified by means of the conic section and the quadric degenerating theory, respectively.

以上述理论为武器首先分析典型的3-RPS并联平台机构，分别应用二次曲线分解理论和二次曲面分解理论，识别了该机构在三种位形下的主螺旋。

Another new spatial 3-RPS parallel pyramid manipulator mechanism is studied. The principal screws of this mechanism under three different configurations are identified by means of the conic section and the quadric degenerating theory, respectively. The planar conics representing the relations between the pitches of the output twists and the three linear inputs are described, and the three-dimensional distribution of the axes of all the twists with the same pitch is illustrated under each of the configurations.

研究了另一种新的空间三自由度3-RPS并联角台机构，分别用二次曲线和二次曲面分解法识别该机构在三种位形下的主螺旋，绘制了其在每种位形下的输出运动螺旋的节距与输入之间的平面图以及具有相同节距的所有运动螺旋轴线在每种位形下的空间分布的立体图。

This article used the truncation mark law to discuss the common quadratic surface on the coordinate plane projection, based on this gave by the surface encircles three-dimensional asks the law on the coordinate plane projection one kind, this kind asked method the superiority lay in does not draw the range of integration graph also to be able to determine it on the coordinate plane projection.

本文利用截痕法讨论了常见二次曲面的在坐标面上的投影，在此基础上给出由曲面所围立体在坐标面上的投影的一种求法，这种求法的优越性在于不画出积分区域图形也能确定它在坐标面上的投影。最后以实例说明这种求投影的方法在计算三重积分中的应用。

It is the first time that the rational Bézier surfaces modeling problem has been proposed and approached successfully, which make it possible for us to research on minimal surface modeling of general conicoid.

在CAGD领域内首次提出了有理Bézier极小曲面造型问题并进行了成功的尝试，使得统一地研究一般二次曲面的极小曲面造型成为可能。

With regard to CAD modeling in reverse engineering, some key techniques, including feature extraction from point cloud and parametric representation, are studied.

本文针对反求工程CAD建模路线：从点云提取特征曲面，再进行曲面参数化CAD造型过程中非常关键的步骤——特征提取进行了深入研究，着重研究了二次曲面特征的提取，并对点云中的全局特征约束优化技术进行了有益的探索。

Some questions in digital elevation model were discussed detailedly, such as the obtaining of data points, the fast searching of reference points, the interpolation algorithm of quadric surface, the abnormal data eliminating, and so on. And this paper has realized the 3D vectorization of 2D terrain maps, the 3D display and edit of DEM data with the help of secondary development of CAD.

文中详细讨论了数字高程模型中数据点获得、参考点的快速搜索、二次曲面的插值算法、粗差剔除等内容，并运用AutoCAD二次开发技术，实现了二维地形图的三维矢量化以及DEM数据的三维显示和编辑修改。

On ray tracing algorithm, line-surface intersection is the basic operation. we have studied the intersection method between line and plane region, quadric surface, NURBS surface.

在光线跟踪算法方面，对精确模型下曲面的直接光线跟踪进行了尝试，提出了对平面区域、简单二次曲面及NURBS曲面直接进行光线跟踪的算法。

Based on data cloud, which is measured from 3-coordinate measuring machine or so, an algorithm to search lopological structure from 3D unorganized points using Envelopment-box technology is proposed in this thesis. Based on this method, we searching neighbor points of sampling point. We also improve the Max-Min angle criteria to realize local triangulation, and then get the normal of sampling point from the triangulation. Using the normal and neighbor relationship, classification of scattered data points is realized according to the quadric surface.

本文以测量得到的曲面数据点点云为基础，提出了一种基于包围盒的自动寻找三维散乱数据点之间拓扑结构的方法，采用该方法寻找采样点的邻域结点，并对三角剖分中的典型优化准则—最小内角最大准则提出了改进，按照改进后的优化准则实现了采样点的局部三角划分，并进一步求解得到采样点的法向量，依据法向量及邻域拓扑关系在二次曲面的基础上实现了散乱数据曲面重构中的数据点的自动分类。

The problems include Catmull-Clark subdivision surfaces can"t precisely represent standard conicoid except paraboloid, and it can"t modify the shape of limited surfaces when the original control mesh be given.

Catmull-Clark细分曲面无法精确表示除抛物面外的常规二次曲面；在给定初始控制网格的情况下，难以调整所生成曲面的形状等。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。