1. CS-321 Dr. Mark L. Hornick 1 Three-Dimensional Graphics Problem How can you effectively display 3-D information on a 2-D display?

2. CS-321 Dr. Mark L. Hornick 2 Ambiguous images – which one is it? ? ?

3. CS-321 Dr. Mark L. Hornick 3 Using dashed lines or removing hidden lines helps

4. CS-321 Dr. Mark L. Hornick 4 Stereo views Stereo pairs

5. CS-321 Dr. Mark L. Hornick 5 Depth Cueing

6. CS-321 Dr. Mark L. Hornick 6 3-D to 2-D Projection Parallel projection Points projected along parallel lines Parallel lines remain parallel Preserves relative proportions Objects retain original size Unrealistic appearance Perspective projection Project along converging paths Distant objects appear smaller Does not preserve proportions Realistic view

7. CS-321 Dr. Mark L. Hornick 7 Orthographic Parallel Projection Projection vector perpendicular to view plane

8. CS-321 Dr. Mark L. Hornick 8 Orthographic Transform Transform world to view coordinates So direction vector aligned to +z Keep x d and y d coordinates “Flatten” z d coordinate Ignore? Set to zero? Use for depth cueing?

9. CS-321 Dr. Mark L. Hornick 9 Perspective Projections Closer objects have larger projections Projection reference point

10. CS-321 Dr. Mark L. Hornick 10 Perspective Projection Details Projection reference point (view from +z) P=(x,y,z) (x p,y p,z p ) (0,0,0) (0,0,z f ) Z p = 0

11. CS-321 Dr. Mark L. Hornick 11 Perspective Projection Details Z p = 0

12. CS-321 Dr. Mark L. Hornick 12 Perspective Matrix

13. CS-321 Dr. Mark L. Hornick 13 Perspective Transformation

14. CS-321 Dr. Mark L. Hornick 14 Model Coordinates to Device Coordinates Including scaling and perspective matrices M and S Computes the non-normalized homogeneous transformed vector v h The normalized homogeneous transformed vector v d :