Find the normalization transformation that maps a window whose lower left corner is at (1, 1) and upper right corner is at (3, 5) onto a view port that is…
Find the normalization transformation that maps a window whose lower left corner is at (1, 1) and upper right corner is at (3, 5) onto a view port that is the entire normalized device screen
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Correct answer: (A) [1/2 0 −1/2] [0 1/4 −1/4] [0 0 1]
Explanation
Window: xwmin = 1, ywmin = 1, xwmax = 3, ywmax = 5. Viewport (normalized screen): xvmin = 0, yvmin = 0, xvmax = 1, yvmax = 1. Scale factors sx = (1 − 0)/(3 − 1) = 1/2 and sy = (1 − 0)/(5 − 1) = 1/4. N = T(xvmin, yvmin) · S(sx, sy) · T(−xwmin, −ywmin), which gives the matrix [1/2 0 −1/2], [0 1/4 −1/4], [0 0 1].