曲面

ABSTRACT This paper summarizes our researches on two key techniques in curve and surface modeling-the geometric approximation techniques and the geometric interpolation techniques. The former includes three types of geometric approximation techniques: Hybrid polynomial approximation to rational curves and surfaces, offset curves and surfaces approximation, interval Bézier curves and surfaces approximation. The latter includes a series of algorithms for shape blending modeling: the MSI algorithm for shape blending between space polylines or trees, the MSI algorithm for shape blending between triangular meshes, and skeleton-based shape blending algorithms using triangular decomposition and star-shape decomposition.

本文是作者对曲线曲面造型中两类核心技术几何逼近技术和几何插值技术的研究成果的总结，其中前者包括有理曲线曲面的Hybrid多项式逼近、等距曲线曲面逼近和区间曲线曲面逼近等三类几何逼近方法；后者包括用于形状混合造型的几何插值方法的一系列算法：空间多边形形状混合的MSI插值算法、三角网格形状混合的MSI插值算法、树的形状混合的MSI插值算法以及基于骨架树形状混合的三角剖分算法和星形剖分算法。

Then, the model is extended to triangular mesh surface. The definition of highlight-line model on triangular mesh surface is put forward.

本文首先在NURBS曲面上实现了连续曲面的高光线模型，然后将高光线模型拓展到三角网格曲面中。

These two kinds of methods resolved many problems in modeling and make it feasible to build the model of triangular Bezier surface.

由于三角曲面对数据拓扑关系具有较宽的适应性和良好的保形性，使三角曲面特别适合于描述产品外形中自由曲面部分，这也正是逆向工程CAD建模中最难处理的部分。

Because there exists a high randomness an easier weighted method is used to establish Grid-format data to approximately describe 3-D space topography, 3-D topography is constructed for Grid-format data by using OpenGL technology, and a free transform of the space curved surface is realized, including parallel move, zoom, circumgyrate. Simultaneously, an algorithm of random incision of 3-D space curved surface containing most six sides is provided, in comhination of geologic evolution, element.

由于存在很大的随机性，采用较为简单的加权方法来建立规则网格Grid格式数据体对三维空间地形进行近似描述，利用OpenGL技术构造Grid数据体三维地形，并对构造出的三维空间曲面进行平移、缩放、旋转等自由变换，提供最多6个切面对三维空间曲面进行任意切割的算法，结合地质演化需要，利用双缓存技术实现了地质要素三维曲面动态演化过程。

In this paper,using the classification for the point of general surface in differential geometry,a new combination that relies on the type of point on real conicoids is studied,and then can know more about the shape of conicoid.

利用微分几何中对一般曲面上点的分类来研究实二次曲面依点的类型的又一重要新组合，从而对二次曲面的形状有进一步的认识。

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。

As it can be expressed easily by argument equations, we use the conicoid as the criteria of points" classification. Based on the point"s normal and the adjacent field, corresponding to the conicoid equation such as plane, ball and cylinder, we search the points that fit the equation along the adjacent field. Using this method, we realized the automatic classification of unorganized points.The experiments using the algoritlim and criteria approved from this thesis are also carried out.

本文采用了可以比较方便地用参数方程表示的二次曲面作为数据点的分类标准，根据点的法向量以及其邻域结点的各种属性，对应于平面、球面、柱面等二次曲面，依据曲面方程的特点，从起始点开始沿邻域深度优先递归寻找符合方程的数据点，实现了散乱数据点的自动分类。

When manufacture part which with curved surface by of contour machining,the shape of profile modeling is not as same as the part,they also without simple relation of minify or magnify.

仿形车、铣加工曲面零件，主要是通过靠模曲线来实现的，靠模曲线形状通过带有滚轮的靠模触头传递到刀具上，加工出零件所需的曲面形状。靠模曲线与零件曲面有什么样的关系？

With a given value of this parameter, the C2 continuous spline given in this pape...

这种曲线和曲面克服了B-样条曲线和曲面在进行曲线和曲面插值中的一些缺点，是对B2样条的一种推广。

It is found that for the same volumetric flow rate, the pressure drop in the shell side of the curved baffle heat exchanger is remarkably lower than that of the traditional one. And the pressure drop percentage deceases even more for a smaller curvature radius of the curved baffle and height of the baffle cut.

结果发现：在流量一定的情况下，曲面弓形折流板换热器的壳程压力降明显低于普通弓形折流板换热器的壳程压力降，而且随着曲面折流板曲率半径和折流板圆缺口高度的减小，曲面弓形折流板换热器的壳程压力降降低的百分比增大。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。