ray tracing 2: acceleration

CS 445Greg Humphreys, Spring 2003

Ray Tracing 2:Acceleration

Greg Humphreys, Spring 2003Intro Graphics Raytracing Stuff

Ray Tracing Acceleration Techniques

Too Slow!

Uniform gridsSpatial hierarchies•K-D•Octtree•BSPHierarchical gridsHierarchical bounding volumes (HBV)

Tighter boundsFaster intersector

Early ray terminationAdaptive sampling

Beam tracingCone tracingPencil tracing

Faster intersection

N 1

Fewer rays Generalized rays


Uniform GridsPreprocess scene1. Find bounding box


Uniform GridsPreprocess scene1. Find bounding box2. Determine grid

resolution3 | |n d O



resolution

3. Place object in cell if its bounding box overlaps the cell

3 | |n d O



resolution

3. Place object in cell if its bounding box overlaps the cell

4. Check that object overlaps cell (expensive!)

3 | |n d O


Uniform GridsPreprocess sceneTraverse grid

3D line = 3D-DDA6-connected line


Caveat: OverlapOptimize objects that overlap multiple cellsCaveat 1 (correctness):

Intersection must lie within current cell

Caveat 2 (efficiency):Redundant intersection tests“Mailboxes” Assign each ray a number Object intersection cache (“mailbox”)

• Store ray number, intersection information


Spatial Hierarchies

A

B C

D

A

B

C

D

Leaf nodes correspond to unique regions in space


Spatial Hierarchies

A

B C

D

A

B

C

D

Point location by recursive search


Variations

KD tree octtree BSP tree


Creating Spatial Hierarchiesinsert(node,prim) {

if( overlap(node->bound,prim) )if( leaf(node) ) {

if( node->nprims > MAXPRIMS && node->depth < MAXDEPTH ) {

subdivide(node);foreach child in node

insert(child,prim)}else list_insert(node->prims,prim);

}else

foreach child in nodeinsert(child,prim)

}// Typically MAXDEPTH=16, MAXPRIMS=2-8


Median-Cut

Build hierarchy bottom-upChose direction and position carefullySurface-area heuristic


Surface Area and RaysNumber of rays in a given direction that hit an

object is proportional to its projected area

The total number of rays hitting an object is

Crofton’s theorem:For a convex body:

Example: Sphere

projA

4 A

4

SA

2 24 S r A r


Surface Area and RaysProbability of a ray hitting an object that

is completely inside a cell is:

cS

oS

Pr o

c

Sr O

S


Ray Traversal AlgorithmsRecursive inorder traversal

Kaplan, Arvo, Jansen

mint

maxt*t

*maxt t

Intersect(L,tmin,tmax)

mint

maxt

*t

*min maxt t t

Intersect(L,tmin,t*)Intersect(R,t*,tmax)

maxt

mint*t*

mint tIntersect(R,tmin,tmax)


Hierarchical GridsGood compromise preferred by many

practitioners

IMAGE

IMAGE

IMAGE


Hierarchical Bounding VolumesCreate tree of bounding volumesChildren are contained within parentCreation preprocess

From model hierarchy Automatic clustering

Searchintersect(node,ray,hits) {

if( intersectp(node->bound,ray)if( leaf(node) )

intersect(node->prims,ray,hits)

elsefor each child

intersect(child,ray,hits)}


Comparison

Scheme Spheres

Rings

Tree

Uniform grid D=1 244 129 1517

D=20

38 83 781

Hierarchical grid

34 116 34Vlastimil Havran, Best Efficiency Scheme Projecthttp://sgi.felk.cvut.cz/BES/

ray tracing 2: acceleration

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