Viewing Transformations in computer graphics

Before displaying the 3-D picture one more set of “viewing transformations” is to be done. This is to ensure that the viewer would get the depth perspective that has been displayed on the screen. This is done by transforming the image to another coordinate system with axes xe, ye and ze, the origin being the position of the eye and ze being the axis passing from the eye perpendicularly to the screen.

If this transformation is called V, then it is not enough if we simply display the completed picture as it is, but every point is to be transformed to the eye coordinate system.

Calling the original picture coordinate systems as the world system, if a point in it is represented by [ xw yw zw 1] then it should be transformed to the eye coordinate system [xe ye ze 1] using the following transformation

[ xe ye ze 1] = [ xw yw zw 1] V

V is a series of matrix transformations that can be got by including several translations and rotations that are determined by viewing parameters.

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