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Viewing

Viewing. The Camera and Projection. Gail Carmichael (gail_c@scs.carleton.ca). The Goal. Understand the process of getting from 3D line segments to images of these lines on the screen. Canonical View Volume. Windowing transform brings points to pixels: M W. Canonical View Volume. =. M w.

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Viewing

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  1. Viewing The Camera and Projection Gail Carmichael (gail_c@scs.carleton.ca)

  2. The Goal Understand the process of getting from 3D line segments to images of these lines on the screen.

  3. Canonical View Volume Windowing transform brings points to pixels: MW

  4. Canonical View Volume = Mw

  5. Orthographic Projection Orthographic Perspective

  6. Orthographic Viewing Volume

  7. Orthographic View to Canonical View Move to Origin Scale World to Canonical Coordinates

  8. Orthographic View to Canonical View World to Canonical Coordinates

  9. Drawing Lines in Orthographic View Mo=Mw MscaleMmove_to_origin = Mo

  10. Arbitrary View Positions Top of cameragoes this way Camera is looking this way Camera is centered here

  11. Arbitrary View Positions w = - (g / ||g||) u = (t × w) / || t × w || v = w × u

  12. Arbitrary View Positions

  13. Coordinate Transformations

  14. Coordinate Transformations

  15. Coordinate Transformations

  16. Coordinate Transformations p = (xp,yp) ≡ o + xpx + ypy p = (up,vp) ≡ e + upu + vpv

  17. Coordinate Transformations p = (xp,yp) ≡ o + xpx + ypy p = (up,vp) ≡ e + upu + vpv

  18. Coordinate Transformations p = (xp,yp) ≡ o + xpx + ypy p = (up,vp) ≡ e + upu + vpv ? ? =

  19. Coordinate Transformations p = (xp,yp) ≡ o + xpx + ypy p = (up,vp) ≡ e + upu + vpv =

  20. Camera Coordinate Transform

  21. Camera Coordinate Transform Mv=

  22. Drawing with Arbitrary View and Orthographic Projection = Mo Mv

  23. Perspective Projection ys= y(d/z)

  24. Perspective Via Orthographic

  25. Perspective Via Orthographic

  26. Perspective Via Orthographic

  27. Perspective Transform Mp =

  28. Perspective Transform Mp =

  29. Perspective Transform Mp =

  30. Drawing with Arbitrary View and Perspective Projection = Mo Mp Mv

  31. CAUTION!! Everything up until now used the more common right-hand coordinate system. Direct3D uses the left-hand coordinate system. See:http://msdn.microsoft.com/en-us/library/windows/desktop/bb204853%28v=vs.85%29.aspx

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