原文链接

OpenGL expects all the vertices, that we want to become visible, to be in normalized device coordinates after each vertex shader run. That is, the x, y and z coordinates of each vertex should be between -1.0 and 1.0; coordinates outside this range will not be visible.

坐标系统变换图解

将坐标变换为标准化设备坐标，接着再转化为屏幕坐标的过程通常是分步进行的，也就是类似于流水线那样子。在流水线中，物体的顶点在最终转化为屏幕坐标之前还会被变换到多个坐标系统(Coordinate System)。将物体的坐标变换到几个过渡坐标系(Intermediate Coordinate System)的优点在于，在这些特定的坐标系统中，一些操作或运算更加方便和容易，这一点很快就会变得很明显。对我们来说比较重要的总共有5个不同的坐标系统：

• 局部空间(Local Space，或者称为物体空间(Object Space))
• 世界空间(World Space)
• 观察空间(View Space，或者称为视觉空间(Eye Space))
• 裁剪空间(Clip Space)
• 屏幕空间(Screen Space)

1. Local coordinates are the coordinates of your object relative to its local origin; they're the coordinates your object begins in.
2. The next step is to transform the local coordinates to world-space coordinates which are coordinates in respect of a larger world. These coordinates are relative to a global origin of the world, together with many other objects also placed relative to the world's origin.
3. Next we transform the world coordinates to view-space coordinates in such a way that each coordinate is as seen from the camera or viewer's point of view.
4. After the coordinates are in view space we want to project them to clip coordinates. Clip coordinates are processed to the -1.0 and 1.0 range and determine which vertices will end up on the screen.
5. And lastly we transform the clip coordinates to screen coordinates in a process we call viewport transform that transforms the coordinates from -1.0 and 1.0 to the coordinate range defined by glViewport. The resulting coordinates are then sent to the rasterizer to turn them into fragments.

You probably got a slight idea what each individual space is used for. The reason we're transforming our vertices into all these different spaces is that some operations make more sense or are easier to use in certain coordinate systems. For example, when modifying your object it makes most sense to do this in local space, while calculating certain operations on the object with respect to the position of other objects makes most sense in world coordinates and so on. If we want, we could define one transformation matrix that goes from local space to clip space all in one go, but that leaves us with less flexibility.