稍后我们会知道，在一个单连通区域上也可以。
那么我们是在哪里利用了，“定义在单连通区域”的假设呢？
OK, so where do we use the assumption of being defined in a simply connected region?
提出一种基于边界标注的单连通区域扫描线填充快速算法。
A novel edge - labeled algorithm for simple connected area scan filling is presented.
借助保形变换将单连通区域及其边界化为上半平面与实轴。
With the help of the conformal transformation, we transform a simply connected region and its boundary into the upper half plane and real axis.
对于它，不用太担心，为了精确起见，需要向量场定义在一个单连通区域中。
Let's not worry too much about it. For accuracy we need our vector field to be defined in a simply connected region.
本文把在单连通区域上成立的曲线积分与路线无关性定理推广到复连通区域。
In this paper the theorem in which a curve integral is independent of the integral path on a single connected region is generalized.
证明了拟常曲率流形中二维极小子流形上一个单连通区域为稳定的充分条件。
Sufficient conditions for a simply-connected domain of 2-dimensional minimal submanifold immerged in 2 + p-dimensional manifold of quasi-constant curvature to be stable were proved.
给出了单连通区域和多连通区域中的一般级数表达式及确定级数项系数的方法。
A series expansion and a method to determine the coefficients of the series expansion are given.
本文提出一种算法实现单连通区域的线性四元树表示转换成区域边界的4 -方向链码描述。
An algorithm is presented for converting the linear quadtree representation of a simply connected region into a 4-direction chain code description of the region's boundary.
一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。
OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.
对比传统单连通区域扫描线填充法，新方法算法效率高，实现简单，对复杂区域的填充同样适用。
Compared with the normal algorithms, the new one is efficient in algorithm, simple in realization for scan filling of simple connected area and also applicable to the filling of the complex area.
如果知道了，向量空间在单连通区域内处处有定义，那么就可以毫无顾忌地，在这个区域里使用格林公式了？
Well, if you know that your vector field is defined everywhere in a simply connected region, then you don't have to worry about this question of, can I apply Green's theorem to the inside?
这里，为了使得完全成立，不得不假设，这定义在一个单连通区域，否则就有可能得到，和先前一样的奇怪事情。
And here, to be completely truthful, I have to say defined in a simply connected region. Otherwise, we might have the same kind of strange things happening as before.
期末考也可能会用得上，实际上，真的不会有十分复杂的问题，不过你们也要大概地了解一下,这个关于单连通区域的知识点。
And, maybe on the final it would be, there won't be any really, really complicated things probably, but you might need to be at least vaguely aware of this issue of things being simply connected.
好滴，目前这里，在有定义的区域里，减掉原点，即移去原点，就不是单连通的。
OK, so for this guy, domain of definition, which is plane minus the origin with the origin removed is not simply connected.
这是检验,该区域不是单连通的一种方法。
So, that's one way to check just for sure that this thing is not simply connected.
该算法能处理多个区域的情况和区域为单连通或复连通区域的情况；
The improved algorithm can deal with multiple regions, single connected domain and multiple connected domain.
文中还定义了平面单连通多边形区域的所谓分层三角剖分，并确定了此剖分下二次样条空间的维数。
Then, a new kind of so-called stratified triangulation of a simply connected planar polygonal region is introduced.
本文是作者在多连通区域单叶函数领域研究成果的总结。
The present article is an account of results on univalent functions in multiply connected domains obtained by the author.
基于区域递归分解算法是一种有效的四边形网格生成算法，能较好地运用于复杂的单连通和多连通图形区域，自动化程度高。
This paper presents an efficient algorithm for creating automatic quadrilateral mesh based on a recursive decomposition domain of quadrilateral elements.
基于区域递归分解算法是一种有效的四边形网格生成算法，能较好地运用于复杂的单连通和多连通图形区域，自动化程度高。
This paper presents an efficient algorithm for creating automatic quadrilateral mesh based on a recursive decomposition domain of quadrilateral elements.
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