Frustum Culling in OpenGL

1. Frustum Culling in OpenGL Ref: MarkMoley.com Fall 2006 revised

2. Culling Techniques Fall 2006 revised

3. Outline • Introduction • View Frustum • Plane Equation • Frustum Plane Extraction • Frustum/Point/Sphere Inclusion Tests Fall 2006 revised

4. Definition (View Frustum) • the volume of space that includes everything visible from a given viewpoint • defined by six planes arranged in the shape of a pyramid with the top chopped off • If a point is inside this volume then it's in the frustum and it's visible, and vice versa • Visible here mean potentially visible. It might be behind another point that obscures it, but it's still in the frustum. … the scope of occlusion culling Fall 2006 revised

5. View Frustum (cont) Fall 2006 revised

6. Definition (Plane) • Divide the space into two halves; extends to infinity • any given point is (in front of | behind | on) the plane. • In R3, a plane is defined by four numbers: • A plane equation: Ax + By + Cz +D = 0 Fall 2006 revised

7. Plane Equation Fall 2006 revised

8. Normalized Plane Equation Fall 2006 revised

9. Frustum Culling • Idea: • If object is not in frustum, do not send it through pipeline (it is not visible) • Wrap the object in a bounding volume; test the bounding volume against frustum (in world coordinate system) • Sphere, bounding boxes, … • Tasks: • Frustum plane extraction • Inclusion tests for different bounding volumes Fall 2006 revised

10. u s t M P Frustum Plane Extraction • The rendering pipeline: In frustum culling, s is usually a point on BV, in world coordinate Fall 2006 revised

11. u s t M P Rendering Pipeline (cont) c : product of PM In OpenGL,clip volume is [-1,1]3 Fall 2006 revised

12. uy ux -1 1 Left Frustum Plane Extraction (Left) Fall 2006 revised

13. The left plane in clip coordinate: The corresponding equation in world coordinate: uy ux -1 1 Left Left Plane (cont) Fall 2006 revised

14. uy ux -1 1 Right Frustum Plane Extraction (Right) Fall 2006 revised

15. The right plane in clip coordinate: The corresponding equation in world coordinate: Right uy ux -1 1 Right Plane (cont) Fall 2006 revised

16. Summary Fall 2006 revised

17. PointInFrustum Test • A point in frustumin all 6 halfspaces The valid sides of all halfspaces are > 0 Fall 2006 revised

18. SphereInFrustum Test p p PointInOffsetFrustum Test Minkowski sum of sphere and frustum Fall 2006 revised

19. Minkowski Sum Coordinate dependent! Fall 2006 revised

20. uy ux -1 1 Left Signed Distance to Left Plane • Plane equations are further normalized to facilitate distance computation d<0 Fall 2006 revised

21. Remarks • Use bounding spheres • Can be conservative if the object is slender • Use hierarchical bounding volume where appropriate (see next page) • BoxInFrustum: • complicated and expensive • AABB: already so • OBB: more so Fall 2006 revised

22. How can bounding volume hierarchies help? View-frustum culling Ray-tracing Collision detection Fall 2006 revised

23. How can bounding volume hierarchies help? View-frustum culling Ray-tracing Collision detection Fall 2006 revised

24. How can bounding volume hierarchies help? View-frustum culling Ray-tracing Collision detection Fall 2006 revised

25. How can bounding volume hierarchies help? View-frustum culling Ray-tracing Collision detection Fall 2006 revised

26. Example (Culling Off: FPS 15.5) Fall 2006 revised

27. Example (Culling On: FPS 31.0) Fall 2006 revised

28. Epilogue Portal rendering World coordinates?! Plane representation in R3 Fall 2006 revised

29. Similar to building walkthrough Occlusions in scene are common (culling important) Geometric database can be huge; preprocessing is required to facilitate smooth viewing Indoor Scenes Fall 2006 revised

30. Potential visible set (PVS) only load the rooms that are visible from the current room Preprocessing for Indoor Scenes Fall 2006 revised

31. 1 7 2 4 3 6 5 E M B 8 L C R Ki K M Portal Rendering B 1 4 E 2 C 7 3 6 5 L 8 R K Fall 2006 revised Ki

32. Portal Rendering • only render the other rooms in PVS if the “portal surfaces” are in sight Fall 2006 revised

33. u s t M P Earlier, we said… But aren’t slocal coordinates? Fall 2006 revised

34. Modelview Matrix Viewing Transform Model Transform world coordinates Recall Pipeline… Fall 2006 revised

35. the scene is (mostly) static and specified in their world coordinate (the modeling transform is identity) the viewer navigates around them, changing the viewing transform only Frustum Culling Scenario Fall 2006 revised

36. Modelview Matrix Viewing Transform Model Transform world coordinates Therefore … I t u s t = PMs M : viewing transform s : world coordinate Fall 2006 revised

37. x–z+10 L R –x–z+10 X Z Verification Fall 2006 revised

38. Supplement: Representing a Plane in R3 x: pivot variable Fall 2006 revised

39. Plane in R3 (cont) n x p Fall 2006 revised

40. Summary • Algebraic equation • Parametric equation • Vector equation • Depending on the application, select the most suitable equation • In/out test • Projection • … Fall 2006 revised

41. Compute and display the screen-space bounding box of an AABB (axis-aligned bounding box) Convert world coordinates to clip coordinates, perspective-divide to get normalized device coordinate (and then window coordinates) Useful in GPU-assisted collision detection applications Screen-Space Bounding Box (SSBB) Fall 2006 revised

42. Useful for projective texturing (showing where the projector is) Useful for illustrating frustum culling Given [-1,1]3 clip coordinates, determine their corresponding world coordinates to render Display Viewing Frustum Fall 2006 revised