Hidden Surface Removal

1. Hidden Surface Removal Fall, 2011

2. Visibility • Surface may be back-facing • Surface may be occluded • Surface may overlap in the image plane • Surface may intersect

3. Visibility Culling & Hidden Surface Removal • Determine which parts of which surfaces should be scan converted

4. Visibility Culling & Hidden Surface Removal • Visibility Culling • Back Face Culling • View Frustum Culling • Occlusion Culling • Hidden Surface Removal • Object space • Polygon Clipping • Depth sort • Screen space • Ray casting • Scan-line • Z-buffer • Area subdivision

5. 3D Rendering Pipeline Somewhere in here we have to decide which objects are visible, and which objects are hidden

6. Back-Face Culling Q: How do we test for back-facing polygons? A: Dot product of the normal and viewing direction

7. 3D Rendering Pipeline

8. View Frustum Culling • Do not draw polygons outside the view frustum • Accelerate checks with bounding volume hierarchies or spatial data structures (e.g., octree)

9. Occlusion Culling • Cell & Portal

10. Hidden Surface Removal Algorithm • Object space • Polygon Clipping • Depth sort • Screen space • Ray casting • Scan-line • Z-buffer • Area subdivision

11. Weiler-Atherton Polygon Clipping • Clip to polygons overlapping and in front of them • Computes exact visible areas of every polygon • Way slow!

12. Depth sort • “Painter’s algorithm” • Sort surface in order of decreasing maximum depth • Scan convert surfaces in back-to-front order

13. 3D Rendering Pipeline

14. BSP Tree • Binary space partition with solid cells labeled • Constructed from polygonal representations • Provides linear-time depth sort for arbitrary view

15. Hidden Surface Removal Algorithm • Object space • Polygon Clipping • Depth sort • Screen space • Ray casting • Scan-line • Z-buffer • Area subdivision

16. Ray Casting • Fire a ray for every pixel • If ray intersects multiple objects, take the closest

17. Ray Casting Pipeline

18. Z-Buffer • Color & depth of closest object for every pixel • Update only pixels whose depth is closer than in buffer • Depths are interpolated from vertices, just like colors

19. 3D Rendering Pipeline

20. Scan-line Algorithm • For each scan line, construct spans • Sort by depth

21. 3D Rendering Pipeline

22. Area Subdivision • Warnock’s algorithm • Fill area if: • All surfaces are outside area, or • Only one surface intersects area, or • One surface occludes other surfaces in area • Otherwise, subdivide

23. 3D Rendering Pipeline

24. Summary • Find visible surfaces • Visibility Culling • Back Face Culling • View Frustum Culling • Occlusion Culling • Hidden Surface Removal • Object space • Polygon Clipping • Depth sort • Screen space • Ray casting • Scan-line • Z-buffer • Area subdivision