1. Estruturas de Dados Espaciais MC-930 MO-603

2. Speeding Up Ray Tracing

3. Estruturas de Dados Espaciais

4. Bounding Volumes

5. Hierarquical Bounding Volume

6. Grids Data structure: a 3-D array of cells (voxels) that tile space –Each cell points to list of all surfaces intersecting that cell

7. Mais sobre Grids Be Careful! The fact that a ray passes through a cell and hits na object doesn’t mean the ray hit that object in that cell Optimization: cache intersection point and ray id in “mailbox” associated with each object Grids are a poor choice when the world is nonhomogeneous (clumpy) –e.g. a teapot in a stadium: many polygons clustered in a small space How many cells to use? –too few Þ many objects per cell Þ slow –too many Þ many empty cells to step through Þ slow Grids work well when you can arrange that each cell lists a few (ten, say) objects Better strategy for some scenes: nested grids

8. Octrees

9. Which Structure is Best for Ray Tracing?

10. K-d Trees and BSP Trees

11. Building a BSP Tree the subdivision of space it implies a BSP tree using 2 as root 2 31 1 2 3 abcd a b c d viewpoint

12. Building the Tree 2 1 2a 2b 3 3 2a 2b 1 viewpoint Using line 3 for the root requires a split

13. Building a Good Tree - the tricky part

14. Uses for Binary Space Partitioning (BSP) Trees

15. Painter’s Algorithm with BSP trees

16. Drawing a BSP Tree front_to_back(tree, viewpt) { if (tree == null) return; if (positive_side_of(root(tree), viewpt)) { front_to_back(positive_branch(tree, viewpt); display_polygon(root(tree)); front_to_back(negative_branch(tree, viewpt); } else { …draw negative branch first…} }

17. Drawing Back to Front 1 2a 2b 3 3 2a 2b 1 viewpoint Hidden surface removal

18. Clipping BSP Trees

20. Clipping Using Spatial Data Structures