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We can actually use hardware to help in calculating the weights for the pixels. Typically, a pixel consists of four channels: red, green, blue, and alpha. Whereas the first three channels are used store the color information, the alpha usually stores the opacity (or transparency). But really, you can store anything you want to the alpha channel, and we use it to store the weights.
The quality weight is applied into the alpha channel of each triangle's color. The blending weight is applied to the alpha channel of the texture map. When the texture is pasted onto the triangle mesh, their alphas get multiplied together by the graphics hardware. Once the views have been rendered, we have to read them in from the frame buffer. While reading, we can scale the contents of the alpha channel by the view-dependent directional weight.