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Viewing Transformations<br />5/18/2010<br />
Good for mapping objects from one coordinate system to another<br />This is what we do with windows and viewports<br />5/1...
Model of objects<br />world coordinates: km, mm, etc.<br />hierarchical models:<br />human = torso + arm + arm + head + le...
5/18/2010<br />Window and viewport<br />Viewport: <br />Area on screen to be used for drawing.<br />   Unit: pixels (scree...
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Determine a matrix M, such that the window (wx1, wx2, wy1, wy2) is mapped on the viewport (vx1, vx2, vy1, vy2):<br />A = T...
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5/18/2010<br />Now Map Rectangles<br />
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5/18/2010<br />Transformation in x and y <br />
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Viewing transformation

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Viewing transformation

  1. 1. Viewing Transformations<br />5/18/2010<br />
  2. 2. Good for mapping objects from one coordinate system to another<br />This is what we do with windows and viewports<br />5/18/2010<br />This isViewport Transformation<br />2<br />
  3. 3. Model of objects<br />world coordinates: km, mm, etc.<br />hierarchical models:<br />human = torso + arm + arm + head + leg + leg<br />arm = upperarm + lowerarm + hand …<br />Viewing<br />zoom in, move drawing, etc.<br />5/18/2010<br />Why transformations?<br />
  4. 4. 5/18/2010<br />Window and viewport<br />Viewport: <br />Area on screen to be used for drawing.<br /> Unit: pixels (screen coordinates)<br /> Note: y-axis often points down<br />Window:<br />Virtual area to be used by application<br /> Unit: km, mm,… (world coordinates) <br />(800,600)<br />(600,400)<br />(200,200)<br />(0,0)<br />(2,1)<br />(-2,-1)<br />
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  8. 8. Determine a matrix M, such that the window (wx1, wx2, wy1, wy2) is mapped on the viewport (vx1, vx2, vy1, vy2):<br />A = T(-wx1, -wy1)<br />B = S(1/(wx2-wx1), 1/(wy2-wy1)) A<br />C = S(vx2-vx1 ,vy2-vy1)B<br />M = T(vx1, vy1) C<br />5/18/2010<br />Window/viewport transform<br />
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  12. 12. 5/18/2010<br />Now Map Rectangles<br />
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  14. 14. 5/18/2010<br />Transformation in x and y <br />
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