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 # 坐标简介（A brief about coordinates）
 
-本章节中我们将讨论坐标和坐标系，尝试以简单的方式介绍一些基本的数学概念，为后面章节将要介绍的技术和内容提供支持。我们将一些内容简化，为了易于学习而牺牲准确性。
+本章节中我们将讨论坐标和坐标系（coordinate system），尝试以简单的方式介绍一些基本的数学概念，为后面章节将要介绍的技术和内容提供帮助。我们将一些内容简化，为了易于学习而牺牲准确性。
 
-我们通过指定坐标来确定物体在空间中的位置。类比地图。通过
-We locate objects in space by specifying its coordinates. Think about a map. You specify a point on a map by stating its latitude or longitude. With just a pair of numbers a point is precisely identified. That pair of numbers are the point coordinates (things are a little bit more complex in reality, since a map is a projection of a non perfect ellipsoid, the earth, so more data is needed but it’s a good analogy).
+我们通过指定坐标来确定物体在空间中的位置。想想地图。通过在地图上指定纬度和经度来确定一个点。只需一对数字，就可以精确的确认一个点。这对数字就是点坐标（实际上有些复杂，因为地图是一个不完美的椭圆球体（地球是不完美的椭圆球体）的投影，所以需要更多的数据，但这是一个很好的类比）
 
-A coordinate system is a system which employs one or more numbers, that is, one or more coordinates to uniquely specify the position of a point. There are different coordinate systems (Cartesian, polar, etc.) and you can transform coordinates from one system to another. We will use the Cartesian coordinate system.
+坐标系是一个系统，它使用一个或多个数字，即一个或多个坐标来唯一地指定一个点的位置。存在着多种不同的坐标系（如笛卡尔坐标系，极坐标系等），并且可以将坐标从一个坐标系转换到另一个坐标系。我们将使用笛卡尔坐标系。
 
-In the Cartesian coordinate system, for two dimensions, a coordinate is defined by two numbers that measure the signed distance to two perpendicular axes, x and y.
+在笛卡尔坐标系中，对于二维，坐标由两个数字定义，它们表示到两个相互垂直的X、Y轴的距离。
 
-![Cartesian Coordinate System](cartesian_coordinate_system.png) 
+![Cartesian Coordinate System](_static/3/cartesian_coordinate_system.png) 
 
-Continuing with the map analogy, coordinate systems define an origin. For geographic coordinates the origin is set to the point where the equator and the zero meridian cross. Depending on where we set the origin, coordinates for a specific point are different. A coordinate system may also define the orientation of the axis. In the previous figure, the x coordinate increases as long as we move to the right and the y coordinate increases as we move upwards. But, we could also define an alternative Cartesian coordinate system with different axis orientation in which we would obtain different coordinates.
+继续类比地图，坐标系定义一个原点。对于地理坐标，原点被设置为赤道和零度经线交叉的点。根据我们原点设置的位置，特定点的坐标是不同的。坐标系也可以定义轴的方向。在上图中，X坐标随着点向右移动而增加，Y坐标随着点向上移动而增加。但是，我们也可以定义一个与笛卡尔坐标系不同的，具有不同的轴取向的坐标系，我们将得到不同的坐标。
  
 ![Alternative Cartesian Coordinate System](alt_cartesian_coordinate_system.png)
 
-As you can see we need to define some arbitrary parameters, such as the origin and the axis orientation in order to give the appropriate meaning to the pair of numbers that constitute a coordinate.  We will refer to that coordinate system with the set of arbitrary parameters as the coordinate space. In order to work with a set of coordinates we must use the same coordinate space. The good news is that we can transforms coordinates from one space to another just by performing translations and rotations.
+正如你所看到的那样，我们需要定义一些参数，例如原点和轴方向，以便给构成坐标的数字对给出适当的含义。为了使用一组坐标，我们必须使用对应的坐标系。好消息是我们可以通过平移和旋转来将坐标从一个坐标系转换到另一个坐标系。
 
-If we are dealing with 3D coordinates we need an additional axis, the z axis. 3D coordinates will be formed by a set of three numbers (x, y, z). 
+如果我们要处理三维坐标，我们需要增加一个轴，即Z轴。三维坐标将由三个数字(x, y, z)构成。
  
 ![3D Cartesian Coordinate System](3d_cartesian_coordinate_system.png)
 
-As in 2D Cartesian coordinate spaces we can change the orientation of the axes in 3D coordinate spaces as long as the axes are perpendicular. The next figure shows another 3D coordinate space.
+在二维笛卡尔坐标系中，只要轴相互垂直，我们就可以改变三维坐标系中的轴的方向。下图展示了另一个三维坐标系。
  
-![Alternative 3D Cartesian Coordinate System](alt_3d_cartesian_coordinate_system.png)
+![Alternative 3D Cartesian Coordinate System](_static/3/alt_3d_cartesian_coordinate_system.png)
 
-3D coordinates can be classified in two types: left handed and right handed. How do you know which type it is? Take your hand and form a “L” between your thumb and your index fingers, the middle finger should point in a direction perpendicular to the other two. The thumb should point to the direction where the x axis increases, the index finger should point where the y axis increases and the middle finger should point where the z axis increases. If you are able to do that with your left hand, then its left handed, if you need to use your right hand is right-handed.
+三维坐标可分为左手系和右手系两种类型。你怎么知道它是什么类型的？用你的手在你的拇指和食指之间形成一个“L”，中指应指向垂直于其他两个手指的方向。拇指应该指向X轴的正方向，食指应该指向Y轴的正方向，而中指应该指向Z轴的正方向。如果你能用左手做到，那么它就是左手系，如果你需要用右手，那它就是右手系。
 
-![Right Handed vs Left Handed](righthanded_lefthanded.png) 
+![Right Handed vs Left Handed](_static/3/righthanded_lefthanded.png) 
 
-2D coordinate spaces are all equivalent since by applying rotation we can transform from one to another. 3D coordinate spaces, on the contrary, are not all equal. You can only transform from one to another by applying rotation if they both have the same handedness, that is, if both are left handed or right handed.
+二维坐标系是相同的，因为通过旋转，我们可以从一个坐标系转换到另一个坐标系。但是，三维坐标系并不都是相同的。如果它们可以使用相同的手来表示，也就是说，如果两者都是左手系或者右手系，那么就能通过旋转一个坐标系到另一个坐标系。
 
-Now that we have defined some basic topics let’s talk about some commonly used terms when dealing with 3D graphics. When we explain in later chapters how to render 3D models we will see that we use different 3D coordinate spaces, that is because each of those coordinate spaces has a context, a purpose. A set of coordinates is meaningless unless it refers to something. When you examine this coordinates (40.438031, -3.676626) they may say something to you or not. But if I say that they are geometric coordinates (latitude and longitude) you will see that they are the coordinates of a place in Madrid.
+现在我们已经确定了一些基本的概念，让我们来讲解一些在处理三维图形时常用的术语。当我们在之后的章节中解释如何渲染三维模型时，我们将看到我们使用不同的三维坐标系，这是因为每个坐标系都有不同的设定，不同的目的。一组坐标是没有意义的，除非明确它是某个坐标系的坐标。当你看到这个坐标(40.438031, -3.676626)时，你可能会有一个大胆的想法。但是如果我说他们是几何坐标（经度和纬度），你就会发现它们是马德里某个地方的坐标。
 
-When we will load 3D objects we will get a set of 3D coordinates. Those coordinates are expressed in a 3D coordinate space which is called object coordinate space. When the graphics designers are creating those 3D models they don’t know anything about the 3D scene that this model will be displayed in, so they can only define the coordinates using a coordinate space that is only relevant for the model.
+当我们加载三维物体时，我们将得到一组三维坐标。这些坐标在被称为物体坐标系（object coordinate space）的三维坐标系中表达。当建模师在设计这些三维模型的时候，他们对该模型将显示的三维场景毫不知情，因此只能使用与模型相关的坐标系来定义坐标。
 
-When we will be drawing a 3D scene all of our 3D objects will be relative to the so called world space coordinate space. We will need to transform from 3D object space to world space coordinates. Some objects will need to be rotated, stretched or enlarged and translated in order to be displayed properly in a 3D scene.
+当我们将绘制一个三维场景时，我们所有的三维物体将与被称为世界的坐标系对应。我们需要将三维物体的坐标系转换到世界坐标系。一些物体需要旋转、拉伸、放大和转换，以便在三维场景中能够正确地显示。
 
-We will also need to restrict the range of the 3D space that is shown, which is like moving a camera through our 3D space. Then we will need to transform world space coordinates to camera or view space coordinates. Finally these coordinates need to be transformed to screen coordinates, which are 2D, so we need to project 3D view coordinates to a 2D screen coordinate space.
+我们还需要限制所显示的三维空间的范围，例如移动摄像机穿梭在我们的三维空间中。然后我们需要将世界坐标转换成摄像机或视口坐标。最后，这些坐标需要转换为二维的屏幕坐标，所以我们需要将三维视图坐标投影到二维屏幕坐标系。
 
-The following picture shows OpenGL coordinates, (the z axis is perpendicular to the screen) and coordinates are between -1 and +1.
+下面的图片展示了OpenGL坐标系（Z轴垂直于屏幕），坐标在-1和+1之间。
 
-![OpenGL coordinates](opengl_coordinates.png) 
-
-Don’t worry if you don’t have a clear understanding of all these concepts. They will be revisited during next chapters with practical examples. 
+![OpenGL coordinates](_static/3/opengl_coordinates.png) 
 
+如果你不能清晰的理解这些概念，别担心。在下一章节中，它们将用实例表现出来。