Viewing transformation
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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.
Viewing transformation
- 2. Good for mapping objects from one coordinate system to anotherThis is what we do with windows and viewports5/18/2010This isViewport Transformation2
- 3. Model of objectsworld coordinates: km, mm, etc.hierarchical models:human = torso + arm + arm + head + leg + legarm = upperarm + lowerarm + hand …Viewingzoom in, move drawing, etc.5/18/2010Why transformations?
- 4. 5/18/2010Window and viewportViewport: Area on screen to be used for drawing. Unit: pixels (screen coordinates) Note: y-axis often points downWindow: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)) AC = S(vx2-vx1 ,vy2-vy1)BM = T(vx1, vy1) C5/18/2010Window/viewport transform
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- 14. 5/18/2010Transformation in x and y
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