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Unit3 3d

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  • 1. Supriya H. Madane
  • 2. 3D Transformation Supriya H. Madane Slide 2
  • 3. Types of 3D reference system according to co-ordiante axes. Left handed System Right handed System 3D Transformation Supriya H. Madane Slide 3
  • 4. 1) Left handed System3D Transformation Supriya H. Madane Slide 4
  • 5. 2) Right handed System3D Transformation Supriya H. Madane Slide 5
  • 6. 3D Transformation Supriya H. Madane Slide 6
  • 7. Translation 3D Transformation Rotation3D Transformation Supriya H. Madane Slide 7
  • 8. Translation in 3D! Remembering 2D transformations -> 3x3 matrices, take a wild guess what happens to 3D transformations. 1 0 tx x tx T tx , t y 0 1 ty T=(tx, ty, tz) y ty 0 0 1 1 0 0 tx x tx 0 1 0 ty T tx , t y , tz y ty 0 0 1 tz z tz 0 0 0 1 3D Transformation Supriya H. Madane Slide 8
  • 9. Scaling, 3D Style sx 0 0 S=(sx, sy, sz) sx 0 xS sx , s y * 0 sy 0 0 sy y 0 0 1 sx 0 0 0 sx 0 0 x 0 sy 0 0S sx , s y , sz 0 sy 0 * y 0 0 sz 0 0 0 sz z 0 0 0 1 3D Transformation Supriya H. Madane 9
  • 10. Rotations about the Z axis R=(0,0,1, ) cos sin 0 cos sin R sin cos 0 sin cos 0 0 1 cos sin 0 0 sin cos 0 0 R (0,0,1, ) 0 0 1 0 0 0 0 13D Transformation Supriya H. Madane 10
  • 11. Rotations about the X axisLet’s look at the other axis rotations R=(1,0,0, ) 1 0 0 0 0 cos sin 0 R (1,0,0, ) 0 sin cos 0 0 0 0 1 3D Transformation Supriya H. Madane 11
  • 12. Rotations about the Y axis R=(0,1,0, ) cos 0 sin 0 0 1 0 0 R (0,1,0, ) sin 0 cos 0 0 0 0 13D Transformation Supriya H. Madane 12
  • 13. Viewing in 3D 3D Transformation Supriya H. Madane Slide 13
  • 14.  Man-made objects often have “cube-like” shape. These objects have 3 principal axes. From www.loc.gov/ jefftour/cutaway.html 3D Transformation Supriya H. Madane Slide 14
  • 15. Display device (a screen) is • How do we map 3D objects to 2D space? 2D… 2D to 2D is • 2D window to world.. and a viewport on the 2D surface. straight • Clip what wont be shown in the 2D window, and forward… map the remainder to the viewport. 3D to 2D is • Solution : Transform 3D objects on more to a 2D plane using projectionscomplicated… 3D Transformation Supriya H. Madane Slide 15
  • 16. Rays converge on eye position Rays parallel to view plane Perspective Parallel Orthographic Oblique Elevations Axonometric Cavalier Cabinet Top Left Right Isometric Dimetric Trimetric
  • 17.  In 3D…  View volume in the world  Projection onto the 2D projection plane  A viewport to the view surface Process…  1… clip against the view volume,  2… project to 2D plane, or window,  3… map to viewport. 3D Transformation Supriya H. Madane Slide 17
  • 18.  Conceptual Model of the 3D viewing process3D Transformation Supriya H. Madane 18
  • 19.  2 types of projections  perspective and parallel. Key factor is the center of projection.  if distance to center of projection is finite : perspective  if infinite : parallel 3D Transformation Supriya H. Madane Slide 19
  • 20.  Perspective:  visual effect is similar to human visual system...  has perspective foreshortening  size of object varies inversely with distance from the center of projection.  angles only remain intact for faces parallel to projection plane. Parallel:  less realistic view because of no foreshortening  however, parallel lines remain parallel.  angles only remain intact for faces parallel to projection plane. 3D Transformation Supriya H. Madane Slide
  • 21.  Any parallel lines not parallel to the projection plane, converge at a vanishing point.  There are an infinite number of these, 1 for each of the infinite amount of directions line can be oriented. If a set of lines are parallel to one of the three principle axes, the vanishing point is called an axis vanishing point.  There are at most 3 such points, corresponding to the number of axes cut by the projection plane. 3D Transformation Supriya H. Madane Slide 21
  • 22. One point, two point, three point perspective One point perspective: One principal axis intersects view plane 3D Transformation Supriya H. Madane Slide
  • 23. One point, two point, three point perspective Two point perspective: two principal axes intersect view plane 3D Transformation Supriya H. Madane 23
  • 24. One point, two point, three point perspective 3D Transformation Supriya Three principal axes intersect view plane Three point perspective: H. Madane 24
  • 25. View Plane Three point Two point3D Transformation Supriya H. Madane One point 25
  • 26.  2 principle types:  orthographic and oblique. Orthographic :  direction of projection = normal to the projection plane. Oblique :  direction of projection != normal to the projection plane. 3D Transformation Supriya H. Madane Slide
  • 27.  Orthographic (or orthogonal) projections:  front elevation, top-elevation and side-elevation.  all have projection plane perpendicular to a principle axes. Useful because angle and distance measurements can be made... However, As only one face of an object is shown, it can be hard to create a mental image of the object, even when several view are available. 3D Transformation Supriya H. Madane Slide
  • 28.  Orthogonal projections:3D Transformation Supriya H. Madane 28
  • 29. 3D Transformation Supriya H. Madane Slide
  • 30. 3D Transformation Supriya H. Madane 30
  • 31. 3D Transformation Supriya H. Madane 31