Physically Based Rendering ( ) Intersection Acceleration

Transcription

1 Physically ased Rendering ( ) Intersection cceleration

2 Intersection Testing ccelerated techniques try to leverage: Grouing: To efficiently discard grous of rimitives that are guaranteed to be missed by the ray. Ordering: To test nearer intersections first and allow for early termination if there is a hit.

3 Intersection Testing Two roaches: 1. Sace artitions: ecomose sace into cells and assign rimitives to the cells in which they fall. rimitive may aear in multile cells 2. Object artitions: Grou objects into clusters luster volumes may overla

4 Uniform (Voxel) Grid cceleration onstruct uniform grid over scene Index rimitives according to overlas with grid cells rimitive may belong to multile cells cell may have multile rimitives

5 Uniform (Voxel) Grid cceleration Trace rays through grid cells ast Incremental Only check rimitives in intersected grid cells

6 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values

7 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside:

8 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir.

9 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel

10 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one!

11 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one! 4. Udate current t

12 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one! 4. Udate current t

13 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one! 4. Udate current t

14 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one! 4. Udate current t

15 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one! 4. Udate current t ouldn t we just sto the first time we hit?

16 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one! 4. Udate current t

17 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one! 4. Udate current t

18 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one! 4. Udate current t

19 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one! 4. Udate current t

20 Uniform (Voxel) Grid cceleration Traversal: 1. ind initial x, y intersections and t values 2. While inside: 1. ind closer hit dir. 2. Test rims. in voxel 3. If hit inside voxel: one! 4. Udate current t

21 Uniform (Voxel) Grid cceleration Potential roblem: How choose suitable grid resolution? Too little benefit if grid is too coarse Too much cost if grid is too fine

22 ounding Volumes heck for intersection with the bounding volume: ounding cubes ounding boxes ounding sheres tc. Stuff that s easy to intersect

23 ounding Volumes heck for intersection with the bounding volume

24 ounding Volumes heck for intersection with the bounding volume If ray doesn t intersect bounding volume, then it doesn t intersect its contents

25 ounding Volumes heck for intersection with the bounding volume If ray doesn t intersect bounding volume, then it doesn t intersect its contents Still need to check for intersections with shae.

26 ounding Volume Hierarchies uild (binary) hierarchy of bounding volumes ounding volume of interior node contains all children

27 ounding Volume Hierarchies Grouing acceleration loat indintersection( Ray ray, ode node) { min_t = -1 if(!intersect ( node.boundingvolume ) ) return min_t // Test ounding box foreach shae { // Test node s shae t = Intersect( shae ) if( t>0 && (t<min_t min_t<0) ) min_t = t } } for each child { // Test node s children t = indintersection(ray, child) if (t>0 && (t < min_t min_t<0) ) min_t = t } return min_t;

28 ounding Volume Hierarchies uild (binary) hierarchy of bounding volumes ounding volume of interior node contains all children v 2 v 4 1 5

29 ounding Volume Hierarchies uild (binary) hierarchy of bounding volumes ounding volume of interior node contains all children 1 on t need to test shaes or eed to test 2 grous 1, 32, 3, 4, and 5 eed to test shaes,,, and v 2 v 4 1 5

30 ounding Volume Hierarchies Grouing + Ordering acceleration loat indintersection(ray ray, ode node) { // ind intersections with the shaes of the node // ind intersections with child node bounding volumes... // Sort child intersections front to back... } // Process intersections (checking for early termination) for each intersected child { if (min_t < bv_t[child]) break; t = indintersection(ray, child); if (t>0 && (t < min_t min_t<0) ) min_t = t } return min_t

31 ounding Volume Hierarchies uild (binary) hierarchy of bounding volumes ounding volume of interior node contains all children on t need to test shaes,,,, or 3 1 eed to test grous 1, 2, 3, 4, and 5 eed to 2 test shae v 4 1 5

32 ounding Volume Hierarchies How do we build u the bounding volume hierarchy?

33 ounding Volume Hierarchies How do we build u the bounding volume hierarchy? hoose an axis: 1. venly slit rimitives based on centroids.

34 ounding Volume Hierarchies How do we build u the bounding volume hierarchy? hoose an axis: 1. venly slit rimitives based on centroids.

35 ounding Volume Hierarchies How do we build u the bounding volume hierarchy? hoose an axis: 1. venly slit rimitives based on centroids. 2. ind the center and slit left/right.

36 ounding Volume Hierarchies How do we build u the bounding volume hierarchy? hoose an axis: 1. venly slit rimitives based on centroids. 2. ind the center and slit left/right.

37 ounding Volume Hierarchies How do we build u the bounding volume hierarchy? 3. Surface area heuristic: min c c c isect, ost of leaf node trav isect c isect : ost of testing for intersection c trav : ost of traversing a bounding volume : number of rimitives in bounding volume / : number of rimitives in child / / : robability that a ray isect the bounding volume will isect the child volume / ost of child nodes /

38 Minimum rea Heuristic min hallenge 1: How do you assign robabilities? hallenge 2: c isect, c trav c isect How do you choose the one out of different (non-trivial) ways to artition?

39 min hallenge 1: Minimum rea Heuristic c isect, c trav c isect How do you assign robabilities? or two convex shaes, the robability that a ray entering will also enter is: rea( ) / rea( )

40 Minimum rea Heuristic min hallenge 2: c isect, c trav c isect How do you choose the one out of different (non-trivial) ways to artition? Slitting by looking at centroids relative to a slit osition, there are only -1 slit ositions to consider.

41 Minimum rea Heuristic min hallenge 2: c isect, c trav c isect How do you choose the one out of different (non-trivial) ways to artition? Slitting by looking at centroids relative to a slit osition, there are only -1 slit ositions to consider. hoose the cost minimizer

42 min hallenge 2: Minimum rea Heuristic c isect, c trav c isect How do you choose the one out of different (non-trivial) ways to artition? Slitting by looking at centroids relative to a slit osition, there are only -1 slit ositions to consider. ll slits between successive centers give hoose the cost the minimizer same artition

43 Kd Trees Slit along the coordinate axes

44 Kd Trees Slit along the coordinate axes 1 1

45 Kd Trees Slit along the coordinate axes

46 Kd Trees Slit along the coordinate axes

47 Kd Trees Slit along the coordinate axes

48 Kd Trees Slit along the coordinate axes

49 Kd Trees Slit along the coordinate axes ote: 7 5 Primitives may belong to multile nodes

50 Minimum rea Heuristic min c isect, c trav c isect hallenge 2: How do you choose a artition location?

51 Minimum rea Heuristic min hallenge 2: c isect, c trav c isect How do you choose a artition location? Look at the end-oints of the rojection of the bounding boxes on the axes.

52 Minimum rea Heuristic min hallenge 2: c isect, c trav c isect How do you choose a artition location? Look at the end-oints of the rojection of the bounding boxes on the axes. hoose the artition that minimizes the cost.

53 min hallenge 2: Minimum rea Heuristic c isect, c trav c isect How do you choose a artition location? Look at the end-oints of the rojection of the bounding boxes on the axes. hoose the artition that minimizes ll slits the between cost. successive end-oints give the same artition

54 Minimum rea Heuristic min hallenge 2: c isect, c trav c isect How do you choose a artition location? or efficiency, generate k buckets and only consider artitioning on bucket boundaries. hoose the artition that minimizes the cost.

55 Minimum rea Heuristic min hallenge 2: c isect, c trav c isect How do you choose a artition location? or efficiency, generate k buckets and only consider artitioning on bucket boundaries. hoose the artition that minimizes the cost. v v

56 Minimum rea Heuristic min hallenge 2: c isect, c trav c isect How do you choose a artition location? or efficiency, generate k buckets and only consider artitioning on bucket boundaries. hoose the artition that minimizes the cost. v v

57 Minimum rea Heuristic min hallenge 2: c isect, c trav c isect How do you choose a artition location? or efficiency, generate k buckets and only consider artitioning on bucket boundaries. hoose the artition that minimizes the cost. v v

58 Minimum rea Heuristic ote: In contrast to bounding volumes, it may make sense to create kd-tree nodes with no rimitives (to cull out large emty sace): min c c c isect, trav isect min c isect, c trav c (1 ) isect with 01 and =0 if,