1. 1 From-Point Occlusion Culling From-Point Occlusion Culling Chapter 23

2. 2 Talk Outline Image space methods –Hierarchical Z-Buffer –Hierarchical occlusion maps –Some other methods Object space methods –General methods Shadow frusta, BSP trees, temporal coherent visibility –Cells and portals

3. 3 What Methods are Called Image-Space? Those where the decision to cull or render is done after projection (in image space) View volume Object space hierarchy Decision to cull

4. 4 Ingredients of an Image Space Method An object space data structure that allows fast queries to the complex geometry Space partitioningHierarchical bounding volumes Regular grid

5. 5 An Image Space Representation of the Occlusion Information Discrete –Z-hierarchy –Occlusion map hierarchy Continuous –BSP tree –Image space extends

6. 6 General Outline of Image Space Methods During the in-order traversal of the scene hierarchy do: –compare each node against the view volume –if not culled, test node for occlusion –if still not culled, render objects/occluders augmenting the image space occlusion Most often done in 2 passes –render occluders – create occlusion structure –traverse hierarchy and classify/render

7. 7 Testing a Node for Occlusion If the box representing a node is not visible then nothing in it is either The faces of the box are projected onto the image plane and tested for occlusion occluder hierarchical representation

8. 8 Testing a Node for Occlusion If the box representing a node is not visible then nothing in it is either The faces of the box are projected onto the image plane and tested for occlusion occluder hierarchical representation

9. 9 Hierarchical Test

10. 10 Differences of Algorithms The most important differences between the various approaches are: –the representation of the (augmented) occlusion in image space and, –the method of testing the hierarchy for occlusion

11. 11 Hierarchical Z-Buffer (HZB) (Greene and Kass, SIG 93) An extension of the Z-buffer VSD algorithm It follows the outline described above Scene is arranged into an octree which is traversed top-to-bottom and front-to-back During rendering the Z-pyramid (the occlusion representation) is incrementally built Octree nodes are compared against the Z- pyramid for occlusion

12. 12 The Z-Pyramid The content of the Z-buffer is the finest level in the pyramid Coarser levels are created by grouping together four neighbouring pixels and keeping the largest z-value The coarsest level is just one value corresponding to overall max z

13. 13 The Z-Pyramid Objects are rendered Depth taken from the z-buffer Construct pyramid by taking max of each 4 = furthest = closer = closest

14. 14 Using The Z-Pyramid = furthest = closer = closest

15. 15 Maintaining the Z-Pyramid Ideally every time an object is rendered causing a change in the Z-buffer, this change is propagated through the pyramid However this is not a practical approach

16. 16 More Realistic Implementation Make use of frame to frame coherence –at start of each frame render the nodes that were visible in previous frame –read the z-buffer and construct the z- pyramid –now traverse the octree using the z-pyramid for occlusion but without updating it

17. 17 HZB: Discussion It provides good acceleration in very dense scenes Getting the necessary information from the Z-buffer is costly A hardware modification was proposed for making it real-time

18. 18 Hierarchical Occlusion Maps (Zhang et al, SIG 97) Similar idea to HZB but –they separate the coverage information from the depth information, two data structures hierarchical occlusion maps depth (several proposals for this) Two passes –render occluders and build HOM –render scene hierarchy using HOM to cull

19. 19 What is the Occlusion Map Pyramid? A hierarchy of occlusion maps (HOM) At the finest level it’s just a bit map with –1 where it is transparent and –0 where it is opaque (ie occluded) Higher levels are half the size in each dimension and store gray-scale values Records average opacities for blocks of pixels Represents occlusion at multiple resolutions

20. 20 Occlusion Map Pyramid 64 x 6432 x 3216 x 16

21. 21 How is the HOM Computed? Clear the buffer to black Render the occluders in pure white (no lighting, textures etc) The contents of the buffer form the finest level of the HOM Higher levels are created by recursive averaging (low-pass filtering) Construction accelerated by hardware - bilinear interpolation or texture maps / mipmaps

22. 22 Occlusion Map Pyramid

23. 23 Overlap Tests To test if the projection of a polygon is occluded –find the finest-level of the pyramid whose pixel covers the image-space box of the polygon –if fully covered then continue with depth test –else descend down the pyramid until a decision can be made

24. 24 Resolving Depth The point with nearest depth Occluders Viewing direction This object passes the depth test The plane A Image plane Bounding rectangle at nearest depth D. E. B. Occluders A Viewing direction Transformed view-frustum Bounding rectangle at farthest depth B Imageplane Either: a single plane at furthest point of occluders Or: uniform subdivision of image with separate depth at each partition Or even: just the Z-buffer content

25. 25 Aggressive Approximate Culling 0 1 234

26. 26 HP Hardware implementation Before rendering an object, scan- convert its bounding box Special purpose hardware are used to determine if any of the covered pixels passed the z-test If not the object is occluded

27. 27 Occluder Shadows (Wonka et al, EG 99)

28. 28 Occluder Shadows

29. 29 Simplified Occlusion Map Read top half of the buffer to use as an occlusion map Project top of cell to image space Simplify projection to a line Test if any pixel along line is visible

30. 30 Discussion on Image Space Advantages (not for all methods) –hardware acceleration –generality (anything that can be rendered can be used as an occluder) –robustness, ease of programming –option of approximate culling Disadvantages –hardware requirements –overheads

31. 31 Object Space Methods Visibility culling with large occluders –Hudson et al, SoCG 97 –Bittner et al, CGI 98 –Coorg and Teller, SoCG 96 and I3D 97 Cells and portals –Teller and Sequin, Siggraph 91 –Luebke and Georges, I3D 95

32. 32 Occlusion Using Shadow Frusta (Hudson et al, SoCG 97) C B A Viewpoint Occluder

33. 33 Assuming we can Find Good Occluders For each frame –form shadow volumes from likely occluders –do view-volume cull and shadow-volume occlusion test in one pass across the spatial sub-division of the scene –each cell of the sub-division is tested for inclusion in view-volume and non-inclusion in each shadow volume

34. 34 Occluder Test Traverse the scene hierarchy top down Overlap test (cell to shadow volume) is performed in 2D –when the hierarchy uses an axis-aligned scheme (eg kd-trees, bounding boxes etc) then a very efficient overlap test is presented

35. 35 Occlusion Trees (Bittner et al, CGI 98) Just as before –scene represented by a hierarchy (kd-tree) –for each viewpoint select a set of potential occluders compare the scene hierarchy for occlusion However, unlike the previous method –the occlusion is accumulated into a binary tree –the scene hierarchy is compared for occlusion against the tree

36. 36 Create shadow volume of occluder 1 View point O1O1 O3O3 O2O2 Tree 1 2 O1O1 IN out 1 2

37. 37 Insert occluder 2 and augment tree with its shadow volume View point O1O1 O3O3 O2O2 Tree 1 2 O1O1 IN out 3 4 O2O2 IN out 1 2 3 4

38. 38 And so on until all occluders are added View point O1O1 O3O3 O2O2 Tree 1 2 O1O1 IN out 3 4 O2O2 IN out 1 2 3 4 5 6 O3O3 IN out O4O4

39. 39 Check occlusion of objects T 1 and T 2 by inserting them in tree View point O1O1 O3O3 O2O2 Tree 1 2 O1O1 IN out 3 4 O2O2 IN out 1 2 3 4 5 6 O3O3 IN out T1T1 T2T2

40. 40 Occluder selection This is a big issue relevant to most occlusion culling algorithms but particularly to the last two At pre-processing –Identify likely occluders for a cell they subtend a large solid-angle –Test likely occluders use a sample of viewpoints and compute actual shadow volumes resulting At run time –locate the viewpoint in the hierarchy and use the occluders associated with that node

41. 41 Metric for Comparing Occluder Quality Occluder quality: (-A *(N V)) / ||D|| 2 A : the occluder’s area N : normal V : viewing direction D : the distance between the viewpoint and the occluder center

42. 42 Cells and Portals (Teller and Sequin, SIG 91) Decompose space into convex cells For each cell, identify its boundary edges into two sets: opaque or portal Precompute visibility among cells During viewing (eg, walkthrough phase), use the precomputed potentially visible polygon set (PVS) of each cell to speed-up rendering

43. 43 Determining Adjacent Information

44. 44 For Each Cell Find Stabbing Tree

45. 45 Compute Cell Visible From Each Cell SL  0,  L  L SR  0,  R  R Linear programming problem: Find_Visible_Cells(cell C, portal sequence P, visible cell set V) V=V  C for each neighbor N of C for each portal p connecting C and N orient p from C to N P’ = P concatenate p if Stabbing_Line(P’) exists then Find_Visible_Cells (N, P’, V)

46. 46 Eye-to-Cell Visibility A cell is visible if –cell is in VV –all cells along stab tree are in VV –all portals along stab tree are in VV –sightline within VV exists through portals The eye-to-cell visibility of any observer is a subset of the cell-to-cell visibility for the cell containing the observer

47. 47 Image Space Cells and Portals (Luebke and Georges, I3D 95) Instead of pre-processing all the PVS calculation, it is possible to use image-space portals to make the computation easier Can be used in a dynamic setting

48. 48 Top View Showing the Recursive Clipping of the View Volume

49. 49 Discussion on Object Space Visibility culling with large occluders –good for outdoor urban scenes where occluders are large and depth complexity can be very high –not good for general scenes with small occluders Cells and portals –gives excellent results IF you can find the cells and portals –good for interior scenes –identifying cells and portals is often done by hand General polygons models “leak”

50. 50 Conclusion There is a very large number of point- visibility algorithms Image space are becoming more and more attractive Specialised algorithms should be preferred if speed is most important factor