Projection

 Until now,we have described our objects and eye in 3 dimensions,Our next step is to understand how to turn into a 2D image as would be seen from eye. To do this we will need to model a simple camera, Throughout, we will assume that the camera is placed at original of eye frame  and that it is looking down the eye's negative z-axis.We will use the notation to refer to eye coordinate of point.

    直到现在，我们已经在3D空间中描述了物体及视角的位置。下一步我们将要把这个3D空间变换到一张2D图片上。为了达到这一点，我们需要放置一个简单的相机。至始至终，将假定相机被放置在视空间（）的原点。朝向视空间-Z方向，使用表示视空间的一个点。

10.1 针孔相机：（PinHole Camera）

     The simplest possible camera is a pinhole camera(see Figure 10.1).As Light tralvels towards the film plane,most is blocked by an opaque surface placed at  plane. But we place a very small hole in the center of the surface, at the point with eye coordinate

Only rays of light that pass through this point reach the film plane and have their intensity recorded on film. The image is reocord at film plane placed at ,say,

         针孔相机可能是最简单的相机，当光射向胶片平面时，大部分光背放置在原点处的一个平面挡住了。但是，如果我们放置一个小洞在原点处。那些透过的光就能被放置在1处的胶片平面记录到。

       

       

为了得到正确的图像（无需反转），计算时把胶片平面放置在了相机的前面

 Once the picutre has been created,if we hold up photograph at the  plane,and

observe it with our own eye placed at origin(see Figure10.3),it will look to us just like the original scene would have.We are exactly reproducing the data that would have reached our eye if we had stood there and looked at the scene. if we move the picture around in space,say colser or farther from our eye,we will no longer be exactly reproducing the original scene-stimulus,but it will appear like a reasonably valid visual representation  of orginal scene.

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10.3 Variations 

         By changing the entries in the projection matrix we can slightly alter the geometry of the camera transformation.

          通过改变投影矩阵的元素，我们可以稍微的改变投影矩阵的几何结构。

10.3.1 Scales

In computer graphics this non-uniformity is useful when dealing with non-square windows on the screen,Suppose the window is wider than it is high. In our camera transform ,we need to squish things  horizontally so a wider horizontal field of view fits into retained canonical. when the data is later mapped to the window,it will be stretched out corresponding and will not appear distorted.

10.3.2 Shifts

     该部分主要考虑的是是椎体左右上下不是完全对称的情况，事实上，该部分的内容更具有广泛的适用性