Spatial Data Structures

1. Spatial Data Structures Jason Goffeney, 4/26/2006 from Real Time Rendering

2. Material Recipes • As previously mentioned there are several different components used in the creation of a material for an object • Ambient • Diffuse • Specular • Shininess • Emissive

3. Material Recipes Use Shininess value times 128

4. Spatial Data Structures • One of the important topics for performing real time graphics applications are data structures for efficient queries to do: • Graphics Culling • Intersection Testing

5. Spatial Data Structure • Spatial Data Structures organize geometry in some n - dimensional space (generally 2 or 3 but can work in higher dimensional space). • The list is the simplest data structure and fairly slow for large data sets but reasonable for smaller ones.

6. Spatial Data Structures • Most spatial data structures are hierarchical as a tree like structure nested and recursive. • Searching a list is O(n) while searching a tree is O(log n). • Usually constructing a spatial data structure is fairly slow and is done as preprocessing.

7. Spatial Data Structures • There are several types of spatial data structures: • Bounding Volume Hierarchies • BSP Trees • Octrees • Scene Graphs

8. Bounding Volume Hierarchies • The most common bounding volume is the bounding box. • Other common types are sphere and cylinders. • The idea is that the bounding volume is simpler than the more complex shapes it contains.

9. Bounding Volume Hierarchies • A Bounding Volume Hierarchy (BVH) is the most common kind of spatial data structure for rendering real-time 3-d scenes. • Each object in a scene is bound by a volume and then groups of objects are bounded and eventually the entire scene is bounded.

10. Bounding Volume Hierarchies Root Tree of Objects Simple Scene of Objects

11. Bounding Volume Hierarchies • For a tree where each node has k children then the height of the tree is logk n where n is the number of nodes in the tree. • A binary tree is the simplest choice but a higher number of children per node can give slightly better results.

12. Bounding Volume Hierarchies • In the example of ray casting you search each subtree recursively. If the ray hits the outer volume check each the children If a child node is not hit then skip the rest of its subtree

13. Bounding Volume Hierarchies • Speed up comes from simple intersection tests with bounding volumes and also from culling subtrees • If objects move around then first check is it still fits in its current bounding volume. Otherwise remove it and change the parent bounding volume and drop the node in the root of the tree and reinsert it.

14. Binary Space Partitioning Trees • These trees are created by using a plane to split space into two pieces and sorting the geometry into each side. • There are two flavors of BSP trees. • Axis-Aligned • Polygon-Aligned

15. Binary Space Partitioning Trees • Axis-Aligned BSP Tree • The whole scene is enclosed in an axis-aligned bounding box (AABB). • The idea is to subdivide that box into smaller and smaller boxes. • For each split an axis is chosen and a plane perpendicular to that axis is generated that divides the space into two boxes

16. Binary Space Partitioning Trees 0 0 1b 1a 2 0 1b 1a

17. Binary Space Partitioning Trees 0 2 1a 1b 0 1b 1a 2

18. Binary Space Partitioning Trees • Axis-Aligned BSP Tree • Space is usually split until some criteria has been reached (height of tree) • One of the strategies of splitting is to rotate through the axes each turn. • One of the benefits of the BSP tree is that it provides a rough front to back sorting based on the position of the viewer.

19. 2 0 1b 1a Binary Space Partitioning Trees x2 • Traverse the tree by first moving down the subtrees • defined by the side of the plane the user is one. • For plane 0 is the viewer’s x position > x0? • - Yes, so take right subtree. • For plane 1b is viewer’s y position > y1b? • - No, so take the left subtree. • Test against objects in that subtree and go back to • parent if no collision. y1b y1a x0

20. Binary Space Partitioning Trees • Polygon-Aligned BSP Trees • In this version a polygon from the scene is chosen and the plane it lies in becomes the splitting plane. • The other polygons in the scene are divided by the plane and any polygons the plane intersects are cut by the plane

21. Binary Space Partitioning Trees C A A B A B C F C G D E F G A B D E

22. Binary Space Partitioning Trees • Polygon-Aligned BSP Trees • Constructing this kind of tree is very expensive and is general done and then saved in a file. • Traversing this tree based on the position of the camera will provide a strict back to front (or front to back) sorting of the polygons

23. Binary Space Partitioning Trees F • Determine which side of the plane the • camera lies on by a point/plane comparison • The polygon set on the far side of the plane is • is beyond the near side set • From the far side set again do the comparison • and determine the far side of its splitting plane • Back to front order is for this example is: • F - G- A - D - B- E • This does not tell which polygon is closest but • which polygon occludes (hides) another polygon. C G A B D E A B C D E F G

24. Octrees • Similar to an AA-BSP tree a box is split simultaneously along all 3 axes and the split point is in the center of the box creating 8 new boxes. • Enclose the entire space in an AABB and split until you meet a stopping criteria. • The 2D version of the octree is the quadtree.

25. Octrees • Objects that cross boundaries are either: • Split • Stored in multiple nodes • Stored in the largest box that contains it

26. Scene Graphs • BVHs, BSP tree and Octrees all use some sort of tree to partition space and store geometry. • Scene graphs are higher level structures that that are augmented with textures, transforms, levels-of-detail, material properties, light sources, etc.

27. Scene Graphs • Every graphics application has some sort of scene graph even if it is a root node with a set of children to display. • A node in a scene graph often has a bounding volume while leaves store geometry. • A leaf may contain an entire spatial data structure (such as a BSP Tree) to encode the geometry.

28. Scene Graphs • Transformations can be placed in any internal node and effects the entire subtrees of that node. • Draw the star • Save the current matrix • Apply a rotation • Draw Planet One • Save the current matrix • Apply a second rotation • Draw Moon A • Draw Moon B • Reset the matrix we saved • Draw Planet two • Save the current matrix • Apply a rotation • Draw Moon C • Draw Moon D • Reset the matrix we saved • Reset the matrix we saved

29. Scene Graphs • A single leaf node can have multiple parents. Car Chassis Transform Transform Transform Transform Wheel

30. Scene Graph • Maintenance • The most intuitive method is to alter a scene graph through a GUI (Maya, 3DMax) • Otherwise design a scripting “language” to insert and delete nodes from the graph

31. Scene Graphs • Open Source Scene Graphs: • Open Scene Graph • Open SG • These are two semi-competing scene graphs which have somewhat specialized.

32. References • Tomas Akenine-Moller and Eric Haines. Real Time Rendering. 2nd Edition. A. K. Peters. 2002. • http://www.gamedev.net/reference/programming/features/scenegraph/