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Tong-Yee Lee

Tong-Yee Lee. A view frustum, with near- and far- clip planes. Only the shaded volume is rendered. Bounding Volume. Simple shape that completely encloses an object Generally a box or sphere We’ll use spheres: Easiest to work with Though hard to get tight fits.

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Tong-Yee Lee

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  1. Tong-Yee Lee

  2. A view frustum, with near- and far- clip planes. Only the shaded volume is rendered.

  3. Bounding Volume • Simple shape that completelyencloses an object • Generally a box or sphere • We’ll use spheres: • Easiest to work with • Though hard to gettight fits

  4. Hierarchical bounding volumes Recall class about projection example

  5. 2D Clipping but waste division for outside viewing window

  6. This manner is OK. But, it needs “Division” before clipping. Sometimes, it is kind of waste. For example, red color shapes below. Z=-f Z=0 Z = -n

  7. Another Trivial Rejection Clipping w = -z What does it imply? Remember if a point is behind eye, we can not see it!!. i.e., z > 0, means it is behind eye. So, we can check the fourth item(before division). If the fourth item is negative, this point is behind the eye point.

  8. Removing Back-Faces • Idea: Compare the normal of each face with the viewing direction Given n, the outward-pointing normal of F for each face F of object     if (n.v > 0)         throw away the faceDoes it work? It always culls half number of input polygons

  9. Inside Outside Outside Inside A Case 2 Case 1 P’: output B A B P: output P: output second A B B P’: output first No output Case 4 Case 3 A Outside Inside Inside Outside

  10. B A

  11. B P: output second P’: output first A

  12. B A P: output

  13. A P’: output B

  14. A No output B

  15. B No output A

  16. Polygon Clipping in Homogeneous Coordinates (Clipping Space Coordinates

  17. C’ color is also linearly interpolated such as C’(r) = A’ (r)+(B’ (r)-A’(r))*t C’(g) = A’(g)+(B’(g)-A’(g))*t ……………. Or even for original 3D position (x,y,z) or texture space (u,v) or normal vector (Nx,Ny,Nz) Aout != Bout

  18. Case 2 Case 4 Ex: left: C0=-C3 C0=A0+t(B0-A0) C3=A3+t(B3-A3) A0+t(B0-A0) = -A3-t(B3-A3) =>> (-A3-A0)=t(B0-A0+B3-A3) Case 4 Case 1 Ex: left side B0,B1,B2,B3 A0,A1,A2,A3 Return #num of vertex

  19. P: output second A B P’: output first Case 4 Outside Inside C C Ex: left boundary: C0=-C3 C0=A0+t(B0-A0) C3=A3+t(B3-A3) A0+t(B0-A0) = -A3-t(B3-A3) =>> (-A3-A0)=t(B0-A0+B3-A3) Left boundary C0=-C3 Right boundary C0=+C3 bottom boundary X : A0, B0 Y : A1, B1 Z : A2, B2 W: A3, B3 C1=-C3 ……….. ………..

  20. Outside Inside A Case 1 B P: output !Aout = !Bout Aout=!Bout Then, Bout is also input into the polygon!

  21. At most,it will have 6 extra vertex after clipping with six planes Circulate each Input polygon Vertex according To Sutherland- Hodgman polygon clipping

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