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Shear & Perspective

Shear & Perspective. CS5600 Computer Graphics Rich Riesenfeld Spring 2006 (Sp2014 edits by T. J. Peters). Lecture Set 7. 3D Shear in x -direction. 3D Shear in x -direction. 3D Shears : Clamp a Principal Plane , shear in other 2 DoFs. Shear in x . . then , y :.

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Shear & Perspective

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  1. Shear & Perspective CS5600Computer Graphics Rich Riesenfeld Spring 2006 (Sp2014 edits by T. J. Peters) Lecture Set 7

  2. 3DShear in x -direction Utah School of Computing

  3. 3DShear in x -direction Utah School of Computing

  4. 3D Shears: Clamp aPrincipal Plane, shear in other2DoFs Utah School of Computing

  5. Shearinx..then, y: Utah School of Computing

  6. 3D Shear iny -direction Utah School of Computing

  7. 3DShear iny -direction Utah School of Computing

  8. 3DShear inz-direction Utah School of Computing

  9. 3DShear inz Utah School of Computing

  10. 3DShear inz Utah School of Computing

  11. ShearInverse Utah School of Computing

  12. ShearInverse Utah School of Computing

  13. Double Shear in x and y Utah School of Computing

  14. Ex: a=0.5and b=1.0 Utah School of Computing

  15. Shearinx..then, y: Utah School of Computing

  16. Shearinx .then, y: Utah School of Computing

  17. Shears in x and y donotCommute Sh in x(a=½) , then Shy(b=1) Sh iny(b=1) , then Sh inx(a=½) Utah School of Computing

  18. Shearin x then in y Utah School of Computing

  19. Shearin y then in x Utah School of Computing

  20. Results Are Different y then x: x then y: Utah School of Computing

  21. What is “Perspective?” • A mechanism for portraying 3D in 2D • “True Perspective” corresponds to projection onto a plane • “True Perspective” corresponds to an ideal camera image Utah School of Computing

  22. “True” Perspective in 2D (x,y) h p Utah School of Computing

  23. “True” Perspective in 2D Utah School of Computing

  24. “True” Perspective in 2D (x,y) h p Utah School of Computing

  25. “True” Perspective in 2D Utah School of Computing

  26. “True” Perspective in 2D Utah School of Computing

  27. Geometry Same for Eye at Origin Screen Plane (x,y) h Utah School of Computing

  28. Values below 0? (x,y) h p Utah School of Computing

  29. “True” Perspective in 2D Utah School of Computing

  30. “True” Perspective in 2D Utah School of Computing

  31. “True” Perspective in 2D Utah School of Computing

  32. Viewing Frustum Utah School of Computing

  33. What happens for large p?” Utah School of Computing

  34. Projection Becomes Orthogonal: “Right Thing Happens” (x,y) h=y Utah School of Computing

  35. The End (Modified) Transformations II Lecture Set 7x

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