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This is my last OpenGL for a project to use the "three-dimensional vector space / point" and related functions, they can use a definition of space vector / points, for the vector translation, zooming and rotation, the use of correlation function can also achieve two vector by the fork, get a Vectors absolute length of a vector unit, received a 3:00 decision vector perpendicular to the plane, a space to be the distance between two points, two vector to be the plot points, to be the angle between two vectors, such as operating for the use of user-friendly, each function is detailed Notes, it is particularly important if the calculation vector plot points, fork also took note, we hope to have useful.

这是我过去进行一个OpenGL项目时使用到的"三维空间向量/点"类及相关函数，使用它们可以定义一个空间向量/点，实现向量的平移，缩放和旋转等，使用相关函数还可以实现两向量的叉乘，得到一个向量的绝对长度，将一个向量单位化，得到一个三点决定的平面的垂直向量，得到空间中两点的距离，得到两向量的点积，得到两向量的夹角等操作，为方便用户的使用，每个函数都有详细的注释，特别重要的向量计算如点积，叉乘还有相关说明，希望对大家有所用处。

Nevertheless, on account of the great benefit of absolution, and because it is otherwise useful to the conscience, Confession is retained among us.

然而，到了十分有益的赦免，因为这是其他有用的良心，忏悔是保留在我们中间。

Higher algebra is an abstract and theoretical subject.In the teaching,it is hard to join the examples with the real life.This gives people the impression that learning algebra is not useful.

高等代数是一门抽象性和理论性较强的学科，在教学中所涉及的例子较少能与实际生活密切相连，让人感觉到学习的内容与生产实践脱节，体现不了数学的应用价值。

It is specifically useful for those students who have difficulties in connecting abstract mathematics symbols and concrete experience.

此外虚拟教具还具有不占空间、容易复制、分享，课堂上易於整理等优点，也是传统实体教具所不及的。

The very abstractness of mathematics makes it useful.

正是数学的抽象性使它大有用处。

Yet the very abstractness of mathematics makes it useful.

然而，正是数学的这种高度抽象性使它变的十分有用。

It is possible to do some almost absurdly difficult-to-understand things with regular expression (but ones that are nonetheless useful).

这是有可能做一些荒唐几乎很难理解的事情经常表达but的仍然是有用的）。

We hope that you find the information abundantly useful in your personal path of ascension.

我们希望，你们发现这些信息非常有助于你个人的提升道路。

And if a College of Physicians is a useful institution, because it contemplates bodily healthy, why is not an Academical Body, though it were simply and solely engaged in imparting vigor and beauty and grasp to the intellectual portion of our nature?...

如果说一所医学院是个有用的机构，因为它考虑的是身体的健康，那么尽管一所学术机构从事的仅仅是给我们人性中的心智部分提供力量、美和理解力，为什么它就不是有用的呢？

This academically sound, practically useful study shows that what you eat is just as important as how much you eat.

这个理论上可行，实际有用的研究表明，你吃的是一样重要多少，你吃。

The commercials enigmatically depicted various scenes from what appeared to be a short narrative that climaxed with a car crashing into a swimming pool.

这次的企划是让一帮共和党人站出来解释，为何自己00年大选选了布什，04年却把票子投给了克里。

If you are wanting the best, designer gold and diamond necklaces are the very best.

如果你想要最好的，设计黄金和钻石项链是最好的。