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a question about shadow mapping

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hello everybody: i am studying how to generate shadow by shadow mapping.and i have read the paper<<hardware shadow mapping>>( and now I am confused by the scale-bias matrix(S) as follow: | ½ 0 0 ½ | | 0 ½ 0 ½ | | 0 0 ½ ½ | | 0 0 0 1 | I don’t know why need multiply this matrix when it generate the texture coordinate[s,t,r,q]T. what is the function of this marix in the shadow mapping? Please help me! And thanks .

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