Accelerating Ray-Scene Intersection Calculations

Transcription

1 ccelerating Ray-Scene Intersection alculations onnelly arnes S 80: Graphics cknowledgment: slides by Jason Lawrence, Misha Kazhdan, llison Klein, Tom unkhouser, dam inkelstein and avid obkin

2 Overview cceleration techniques oounding volume hierarchies ospatial partitions»uniform grids»octrees»sp trees

3 Goal ind intersection with front-most primitive in group Intersection indintersection(ray ray, Scene scene) { min_t = min_shape = NULL or each primitive in scene { } t = Intersect(ray, primitive); if (t > 0 and t < min_t) then min_shape = primitive min_t = t } } return Intersection(min_t, min_shape)

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5 cceleration Techniques direct approach tests for an intersection of every ray with every primitive in the scene. cceleration techniques: ogrouping: Group primitives together and test if the ray intersects the group. If it doesn t, don t test individual primitives. oordering: Test primitives/groups based on their distance along the ray. If you find a close hit, don t test distant primitives/groups.

6 ounding Volumes heck for intersection with the bounding volume: oounding cubes oounding boxes oounding spheres otc. Stuff that s easy to intersect

7 ounding Volumes heck for intersection with the bounding volume

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

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

10 ounding Volume Hierarchies uild hierarchy of bounding volumes oounding volume of interior node contains all children

11 ounding Volume Hierarchies Grouping acceleration indintersection(ray ray, Node node) { min_t = min_shape = NULL // Test if you intersect the bounding volume if(!intersect ( node.boundingvolume ) ) { return (min_t,min_shape); } } // Test the children for each child { (t, shape) = indintersection(ray, child) if (t < min_t) {min_shape=shape} } return (min_t, min_shape);

12 ounding Volume Hierarchies Use hierarchy to accelerate ray intersections ointersect node contents only if hit bounding volume

13 ounding Volume Hierarchies Use hierarchy to accelerate ray intersections ointersect node contents only if hit bounding volume on t need to test shapes or Need to test groups,, and Need to test shapes,,, and

14 ounding Volume Hierarchies Grouping + Ordering acceleration indintersection(ray ray, Node node) { // ind intersections with child node bounding volumes... // Sort intersections front to back... // Process intersections (checking for early termination) min_t = min_shape = NULL for each intersected child { if (min_t < bv_t[child]) break; (t, shape) = indintersection(ray, child); if (t < min_t) { min_t = t min_shape = shape } } return (min_t, min_shape); }

15 ounding Volume Hierarchies Use hierarchy to accelerate ray intersections ointersect nodes only if you haven t hit anything closer

16 ounding Volume Hierarchies Use hierarchy to accelerate ray intersections ointersect nodes only if you haven t hit anything closer on t need to test shapes,,,, or Need to test groups,, and Need to test shape

17 Overview cceleration techniques oounding volume hierarchies ospatial partitions»uniform grids»octrees»sp trees

18 Uniform (Voxel) Grid onstruct uniform grid over scene oindex primitives according to overlaps with grid cells primitive may belong to multiple cells cell may have multiple primitives

19 Uniform (Voxel) Grid Trace rays through grid cells oast oincremental Only check primitives in intersected grid cells

20 Uniform (Voxel) Grid Potential problem: ohow choose suitable grid resolution? Too little benefit if grid is too coarse Too much cost if grid is too fine

21 Teapot in a Stadium Problem ould have much complicated geometry (e.g. a teapot) inside a single cell of the voxel grid. Why is this problematic?

22 Ray-Scene Intersection» cceleration techniques oounding volume hierarchies ospatial partitions»uniform grids»octrees»sp trees

23 Octrees We can think of a voxel grid as a tree. othe root node is the entire region oach node has eight children obtained by subdividing the parent into eight equal regions

24 Octrees We can think of a voxel grid as a tree. othe root node is the entire region oach node has eight children obtained by subdividing the parent into eight equal regions

25 Octrees We can think of a voxel grid as a tree. othe root node is the entire region oach node has eight children obtained by subdividing the parent into eight equal regions

26 Octrees We can think of a voxel grid as a tree. othe root node is the entire region oach node has eight children obtained by subdividing the parent into eight equal regions

27 Octrees In an octree, we only subdivide regions that contain more than one shape.

28 Octrees In an octree, we only subdivide regions that contain more than one shape.

29 Octrees In an octree, we only subdivide regions that contain more than one shape.

30 Octrees In an octree, we only subdivide regions that contain more than one shape.

31 Octrees In an octree, we only subdivide regions that contain more than one shape.

32 Octrees In an octree, we only subdivide regions that contain more than one shape. daptively determines grid resolution.

33 Ray-Scene Intersection Intersections with geometric primitives osphere otriangle» cceleration techniques oounding volume hierarchies ospatial partitions»uniform (Voxel) grids»octrees»sp trees

34 inary Space Partition (SP) Tree Recursively partition space by planes

35 inary Space Partition (SP) Tree Recursively partition space by planes ogenerate a tree structure where the leaves store the shapes.

36 inary Space Partition (SP) Tree Recursively partition space by planes ogenerate a tree structure where the leaves store the shapes.

37 inary Space Partition (SP) Tree Recursively partition space by planes ogenerate a tree structure where the leaves store the shapes.

38 inary Space Partition (SP) Tree Recursively partition space by planes ogenerate a tree structure where the leaves store the shapes.

39 inary Space Partition (SP) Tree Recursively partition space by planes ogenerate a tree structure where the leaves store the shapes.

40 inary Space Partition (SP) Tree Recursively partition space by planes overy cell is a convex polyhedron

41 inary Space Partition (SP) Tree xample: Point Intersection P

42 inary Space Partition (SP) Tree xample: Point Intersection orecursively test what side we are on P

43 inary Space Partition (SP) Tree xample: Point Intersection orecursively test what side we are on»left of (root) P

44 inary Space Partition (SP) Tree xample: Point Intersection orecursively test what side we are on»left of P

45 inary Space Partition (SP) Tree xample: Point Intersection orecursively test what side we are on»right of Test P

46 inary Space Partition (SP) Tree xample: Point Intersection orecursively test what side we are on»missed. No intersection! P

47 inary Space Partition (SP) Tree xample: Ray Intersection o???

48 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»test half to the left of

49 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»test half to the right of

50 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»intersection with. one!

51 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»test half to the left of

52 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»test half to the right of

53 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»missed. Recurse!

54 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»test half to left of

55 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»test half to left of

56 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»missed. Recurse!

57 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»no half to right of.

58 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»test half to right of

59 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»test half to left of

60 inary Space Partition (SP) Tree xample: Ray Intersection orecursively split the ray and test nearer and farther halves, nearest first. Stop once you hit something:»intersection with. one!

61 inary Space Partition (SP) Tree RayTreeIntersect(Ray ray, Node node, double min, double max) { if (Node is a leaf) return intersection of closest primitive in cell, or NULL if none else // ind splitting point dist = distance along the ray point to split plane of node // ind near and far children near_child = child of node that contains the origin of Ray far_child = other child of node // Recurse down near child first if the interval to look is on near side { isect = RayTreeIntersect(ray, near_child, min, max) if( isect ) return isect // If there s a hit, we are done } } // If there s no hit, test the far child if the interval to look is on far side return RayTreeIntersect(ray, far_child, min, max)

62 cceleration Intersection acceleration techniques are important oounding volume hierarchies ospatial partitions General concepts osort objects spatially omake trivial rejections quick xpected time is sub-linear in number of primitives

63 Summary Writing a simple ray casting renderer is easy ogenerate rays ointersection tests olighting calculations Image Rayast(amera camera, Scene scene, int width, int height) { Image image = new Image(width, height); for (int i = 0; i < width; i++) { for (int j = 0; j < height; j++) { Ray ray = onstructraythroughpixel(camera, i, j); Intersection hit = indintersection(ray, scene); image[i][j] = Getolor(hit); } } return image; }

64 Next Time is Illumination! Without Illumination With Illumination