1. Visibility Culling Markus Hadwiger & Andreas Varga

2. Basics Hierarchical Subdivision –Hierarchical Bounding Boxes –Octrees –K-D Trees ( K-Dimensional Space) –BSP Trees ( Binary Space Partition ) Potentially Visible Sets (PVS)

3. Hierarchical Bounding Box (HS) Construct a bounding box for each object Merge nearby bounding box into bigger ones Not very structured and systematic Perform well for certain viewpoint Shortcomings: –Highly dependent on the given scene (worse: on the actual viewpoint) –Unpredictable not very useful !

4. Hierarchical Bounding Box Example (HS) WORLD ROLLERCOASTER CAR #2CAR #1 GUY_BAD GUNGUY_BAD

5. Octrees (HS) Each node of and octree has form one to eight children if it is an internal node; otherwise it is a leaf node Culling against the viewing frustum Shortcomings of regular subdivision –Efficiently problem (inflexible) –Depend on the location of each polygon The two dimensional version of an octree is called quadtree

6. Octrees Example (HS)

7. K-D Trees 2/2 (HS) Hierarchically subdivide n-dimensional space A binary tree –partitioning space into two halfspaces at each level –two equal-sized partitions is not necessary (Octrees) Always done axial A separating hyperplane can depend on actual data Balance of binary tree –One halfspace contains the same number of objects as the other halfspace

8. K-D Trees Example 1/2 (HS) 1 1 23 2 3 4567 4 5 6 7 8910111213 8 9 10 11 12 13

9. K-D Trees Example 2/2 (HS)

10. BSP Trees 6 (HS) Generalization of k-D trees –Space is subdivided along arbitrarily oriented hyperlpanes –Subdivision of space into two halfspace at each step Produces a binary tree Internal node corresponds to the partitioning hyperplane Leaf nodes are empty halfspaces Exact visibility determination for arbitrary viewpoint –For entirely static polygonal scenes Can be precalculated once and traversal at run time with arbitrary viewpoint

11. BSP Trees Example 1 (HS) 1 2 3 4 5 6 1

12. BSP Trees Example 2 (HS) 1 2 3 4a 5 6 4b front 1 2

13. BSP Trees Example 3 (HS) 1 2 3 4a 5 6 4b 1 32 frontback

14. BSP Trees Example 4 (HS) 1 2 3 4a 5 6 4b 1 32 4a frontback front 4b back

15. BSP Trees Example 5 (HS) 1 32 4a 4b 6 5 1 2 3 4a 5 6 4b frontback frontbackfront

16. BSP Trees Example 6 (HS) 1 2 3 4 5 6 V1 V2 1 32 4a 4b 6 5 frontback frontbackfront The painting order from V1: 3, 5, 1, 4b, 2, 6, 4a The painting order from V2: 3, 5, 1, 4b, 2, 4a, 6 We got correct picture of who is behind whom no matter where we were looking from.

17. BSP Trees Example 6 (HS)

18. Cell-Portals Assume the world can be broken into cells –Simple shapes –Rooms in a building, for instance Define portals to be the transparent boundaries between cells –Doorways between rooms, windows, etc In a world like this, can determine exactly which parts of which rooms are visible –Then render visible rooms plus contents

19. Cell-Portals Example AB CD EF AB CD EF － Node are cells, edges are portals － K-D trees and BSP trees are used to generate the cell structure and find neighbors and portals － Portals can be one way (directed edges) － Graph is normally stored in adjacency list format － Each cell stores the edges (portals) out of it

20. Cell and Portal Visibility Keep track of which cell the viewer is in Somehow walk the graph to enumerate all the visible regions –Can be done as a preprocess to identify the potentially visible set (PVS) for each cell Cell-to-region visibility, or cell-to-object visibility –Can be done at run-time for a more accurate visible set Start at the known viewer location Eye-to-region or Eye-to-cell visibility –Trade-off is between time spent rendering more than is necessary vs. time spent computing a smaller set Depends on the environment, such as the size of cells, density of objects, …

21. Potentially Visible Sets (PVS) PVS: The set of cells/regions/objects/polygons that can be seen from a particular cell –Generally, choose to identify objects that can be seen –Trade-off is memory consumption vs. accurate visibility Computed as a pre-process –Have to have a strategy to manage dynamic objects Used in various ways: –As the only visibility computation - render everything in the PVS for the viewer’s current cell –As a first step - identify regions that are of interest for more accurate run-time algorithms

22. Cell-to-Cell PVS Cell A is in cell B ’ s PVS if there exist a stabbing line that originates on a portal of B and reaches a portal of A –A stabbing line is a line segment intersecting only portals –Neighbor cells are trivially in the PVS I J H G A C BE F D PVS for I contains: B, C, E, F, H, J

23. Finding Stabbing Lines In 2D, have to find a line that separates the left edges of the portals from the right edges In 3D, more complex because portals are now a sequence of arbitrarily aligned polygons –Put rectangular bounding boxes around each portal and stab those L L LLR R R R

24. Stab Trees A stab tree indicates: –The PVS for a cell –The portal sequences to get from one to the other Used in further visibility processing –Restricts number of cells/portals that must be looked at A C DE A/C C/D 1 C/D 2 C/E AB CD EF D F D/F

25. Run-Time Visibility PVS approaches are entirely pre-processing –At run time, just render PVS Better results can be obtained with a little run-time processing –Sometimes guided by PVS –It appears that most games don’t bother, the trade-off favors pre-processed visibility and over-rendering At run time the viewer’s location is known, hence Eye-to-Region visibility

26. Eye-to-Cell Recall that finding stabbing lines involved finding a line that passed through all the portals The viewer adds some constraints: –The stabbing line must pass through the eye –It must be inside the view frustum The resulting problem is still reasonably fast to solve –Results in knowledge of which cells are visible from the eye –Use the stab tree from the PVS computation to avoid wasting effort –Further optimization is to keep reducing the view frustum as it passes through each portal, which leads us to…

27. Eye-to-Region Visibility Define a procedure : –Takes a view frustum and a cell Viewer not necessarily in the cell –Draws the contents of the cell that are in the frustum –For each portal out of the cell, clips the frustum to that portal and recurs with the new frustum and the cell beyond the portal Make sure not to go to the cell you entered Start in the cell containing the viewer, with the full viewing frustum Stop when no more portals intersect the view frustum

28. Eye-to-Region Example View

29. Eye-to-Region Example View

30. Eye-to-Region Example View

31. Eye-to-Region Example View

32. Eye-to-Region Example View

33. Eye-to-Region Example View

34. Eye-to-Region Example View

35. Non-Invasive Interactive Visualization of Architectural Environments Christopher NiederauerU.C. Santa Barbara Mike HoustonStanford University Maneesh AgrawalaMicrosoft Research Greg HumphreysUniversity of Virginia

36. Problem Environments of video game are vast and tend to be densely occluded. Most 3D model viewing application lack the ability to simultaneously display the interior spaces and the external structure of the environment.

37. Motivation Arcball style manipulator Walkthrough Can ’ t see overall interior/exterior structure! ArcBall [Shoemake 1992][Teller 1992]

38. Motivation The occlusions make it impossible to see all the action at once! Quake III [Id Software c. 2002]

39. The Idea Exploded view –just below the ceilings Non-Invasive [Mohr 2001] –without modification –use Chromium [Humphreys et al. 2002] Overall structure is visible!

40. How It ’ s Done Example Architecture: Soda Hall –Geometric Analysis (once) –Rendering (every frame) OpenGL Stream Geometric Analysis Gather Data Find Splits Rendering … Floor Composite

41. Gather Architectural Data Intercept the OpenGL stream –Find downward facing polygons Requires up-vector up 1 23 –Compute the height of downward facing polygon 1 height = v1 ‧ upVector polygon normal = (v2-v1) x (v3-v2)

42. 446 Gather Architectural Data Create Histogram 286 126 Height Ceiling Area Geometric AnalysisRendering OpenGL Stream … Floor Composite Soda Hall Side Profile 606 766 942 Find Splits Gather Data

43. Find Splits Find Splitting Heights Geometric AnalysisRendering Gather Data OpenGL Stream … Floor Composite

44. Offset Ceiling Heights

46. Geometric Analysis Find Splits Geometric Analysis Rendering Gather Data OpenGL Stream … Floor Composite Find Downward Facing Polygons Up Vector Find Split Heights Player Height NumSplits Table Mapping Height to Surface Area List of Split Height

47. Rendering Multiple Playback (Once per Floor) –Viewpoint Control –Clipping Planes –Translate along Up Vector Geometric AnalysisRendering Gather Data Find Splits OpenGL Stream … Floor Composite

48. Rendering Multiple Playback Set Viewpoint Clip Plans & Translation Viewpoint NumSplits Multipass Composite Set Viewpoint Clip Plans & Translation … NumSplits Passes of Original OpenGL NumSplits Passes of Modified OpenGL Separation Distance Exploded view visualization Geometric Analysis List of Split Heights Original Application OpenGL

49. Cluster Speedup Composite Floor 1 Floor 2Floor 3 Complete Model 800 MHz Pentium III Xeon processor NVIDIA GeForce4 graphics accelerator

50. Soda Hall Trackball Walkthrough

51. Results with Soda Hall (Single Floor)

52. Quake III: Arena Trackball Walkthrough

53. Results with Quake III: Arena (Single Floor) Item

54. Video

55. Transparent Back-Faces

56. Future Directions Make fully automated: –Semantic inputs Up vector Number of stories to split into

57. Future Directions [Salomon et al, 2003]

58. Future Directions (Hand Designed Mock-up)

59. Summary and Conclusions Can improve viewer comprehension

60. Resource Visibility Culling http://www.cg.tuwien.ac.at/~msh/ http://www.cg.tuwien.ac.at/~msh/ Stephen Chenney http://www.cs.wisc.edu/~schenney/ http://www.cs.wisc.edu/~schenney/ Non-Invasive Interactive Visualization of Dynamic Architectural Environments http://graphics.stanford.edu/papers/archsplit/ http://graphics.stanford.edu/papers/archsplit/ Chromium Homepage http://chromium.sourceforge.net/ http://chromium.sourceforge.net/