2. CSC418 Computer Graphics n Polygon normals n Back Faces n Visibility Algorithms

3. Polygon Normal n Triangle normal calculation n Polygon normal calculation n Polymeshes (vertex normals)

4. Polygon Normal n Triangle normal calculation N=(P2-P1)X(P3-P2) P2 P3 P1

5. Polygon Normal n Polygon normal calculation N=(P2-P1)X(P3-P2) P2 P3 P1 P4 P5 Pn

6. Polygon Normal n Polygon normal calculation N=(P2-P1)X(P3-P2) Problems n Sliver triangles n Non-planar polygons P2 P3 P1 P4 P5 Pn

7. Polygon Normal n Polygon normal calculation Nx =  yj – yi)(zj + zi) Ny =  zj – zi)(xj + xi) Nz =  xj – xi)(yj + yi) j= (i+1) mod n P2 P3 P1 P4 P5 Pn

8. Polymesh Normal n Face normals

9. Polymesh Normal n Vertex normals

10. Polymesh Normal n Vertex normals average the face normals

11. Bilinear Interpolation P uv = (1-u)(1-v)P0 + ( u )(1-v)P1 + ( u )( v )P2 + (1-u)( v )P3 P0 P1 P2 P3 u v P uv

12. Bilinear Interpolation P uv = (1-u)(1-v)P0 + ( u )(1-v)P1 + ( u )( v )P2 + (1-u)( v )P3 P0 P1 P2 P3 u v P uv Gourard shading (color interpolation)

13. Visibility Problem n What is NOT visible?

14. Visibility Problem n What is NOT visible? primitives outside of the field of view back-facing primitives primitives occluded by other objects closer to the camera

15. Backface culling

17. V N E

18. n N.V > 0 is a back face?

19. Backface culling n N.(P-E) >0 V N E P

20. Backface culling Where in the graphics pipeline can we do backface culling? canonical projection

21. Occluded faces Does backface culling always determine visibility completely for a single object?

22. Occluded faces n In typical scenes some polygons will overlap, we must determine which portion of each polygon is visible to eye!

23. Painters Algorithm n Sort primitives in Z. n Draw primitives back to front (CBA). A B C

24. Painters Algorithm n Problems –Large faces –Intersecting faces –Cycles

25. Visibility Problem n Image space algorithms –Operate in display terms pixels, scanlines –Visibility resolved to display resolution –Examples: Z-buffer, ray-tracing –O(n*resolution) n Object Space algorithms –Analytically compute visible fragments –Examples: painters algorithm, BSP –O(n 2 )

26. CSC418 Computer Graphics n Next Lecture –BSP trees –Depth sorting –Z-buffer A-buffer