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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

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