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CSC418 Computer Graphics

CSC418 Computer Graphics. Polygon normals Back Faces Visibility Algorithms. Polygon Normal. Triangle normal calculation Polygon normal calculation Polymeshes (vertex normals). Polygon Normal. Triangle normal calculation N=(P2-P1)X(P3-P2). P1. P3. P2. Polygon Normal.

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CSC418 Computer Graphics

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  1. CSC418 Computer Graphics • Polygon normals • Back Faces • Visibility Algorithms

  2. Polygon Normal • Triangle normal calculation • Polygon normal calculation • Polymeshes (vertex normals)

  3. Polygon Normal • Triangle normal calculation N=(P2-P1)X(P3-P2) P1 P3 P2

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

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

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

  7. Polymesh Normal • Face normals

  8. Polymesh Normal • Vertex normals

  9. Polymesh Normal • Vertex normals average the face normals

  10. Bilinear Interpolation Puv = (1-u)(1-v)P0 + ( u )(1-v)P1 + ( u )( v )P2 + (1-u)( v )P3 P3 P2 Puv v P0 u P1

  11. Bilinear Interpolation Puv = (1-u)(1-v)P0 + ( u )(1-v)P1 + ( u )( v )P2 + (1-u)( v )P3 Gourard shading (color interpolation) P3 P2 Puv v P0 u P1

  12. Visibility Problem • What is NOT visible?

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

  14. Backface culling

  15. Backface culling

  16. Backface culling N V E

  17. Backface culling • N.V > 0 is a back face?

  18. Backface culling • N.(P-E) >0 P N V E

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

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

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

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

  23. Painters Algorithm • Problems • Large faces • Intersecting faces • Cycles

  24. Visibility Problem • Image space algorithms • Operate in display terms pixels, scanlines • Visibility resolved to display resolution • Examples: Z-buffer, ray-tracing • O(n*resolution) • Object Space algorithms • Analytically compute visible fragments • Examples: painters algorithm, BSP • O(n2 )

  25. CSC418 Computer Graphics • Next Lecture • BSP trees • Depth sorting • Z-buffer A-buffer

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