The document discusses viewport transformations which map objects from one coordinate system to another, such as mapping from world coordinates to screen coordinates. It explains that viewport transformations are used for viewing transformations like zooming and moving drawings. The document also describes how a matrix M can be determined to map a window defined in world coordinates to a viewport defined in screen pixel coordinates.

1. Viewing Transformations 5/18/2010

2. Good for mapping objects from one coordinate system to another This is what we do with windows and viewports 5/18/2010 This isViewport Transformation 2

3. Model of objects world coordinates: km, mm, etc. hierarchical models: human = torso + arm + arm + head + leg + leg arm = upperarm + lowerarm + hand … Viewing zoom in, move drawing, etc. 5/18/2010 Why transformations?

4. 5/18/2010 Window and viewport Viewport: Area on screen to be used for drawing. Unit: pixels (screen coordinates) Note: y-axis often points down Window: Virtual area to be used by application Unit: km, mm,… (world coordinates) (800,600) (600,400) (200,200) (0,0) (2,1) (-2,-1)

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8. Determine a matrix M, such that the window (wx1, wx2, wy1, wy2) is mapped on the viewport (vx1, vx2, vy1, vy2): A = T(-wx1, -wy1) B = S(1/(wx2-wx1), 1/(wy2-wy1)) A C = S(vx2-vx1 ,vy2-vy1)B M = T(vx1, vy1) C 5/18/2010 Window/viewport transform

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12. 5/18/2010 Now Map Rectangles

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14. 5/18/2010 Transformation in x and y

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