University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell

Anti-aliased and acceleratedray tracing

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 2

ReadingRequired:

Watt, sections 12.5.3 – 12.5.4, 14.7Further reading:

A. Glassner. An Introduction to Ray Tracing. AcademicPress, 1989. [In the lab.]

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 3

Aliasing in renderingOne of the most common rendering artifacts is the“jaggies”. Consider rendering a white polygonagainst a black background:

We would instead like to get a smoother transition:

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 4

Anti-aliasingQ: How do we avoid aliasing artifacts?

1. Sampling:2. Pre-filtering:3. Combination:

Example - polygon:

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 5

Polygon anti-aliasing

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 6

Antialiasing in a ray tracerWe would like to compute the average intensity in the neighborhood ofeach pixel.

When casting one ray per pixel, we are likely to have aliasing artifacts.To improve matters, we can cast more than one ray per pixel andaverage the result.A.k.a., super-sampling and averaging down.

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 7

Speeding it upVanilla ray tracing is really slow!Consider: m x m pixels, k x k supersampling, and nprimitives, average ray path length of d, with 2 rays castrecursively per intersection.Complexity =For m=1,000,000, k = 5, n = 100,000, d=8…veryexpensive!!In practice, some acceleration technique is almost alwaysused.We’ve already looked at reducing d with adaptive raytermination.Now we look at reducing the effect of the k and n terms.

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 8

Antialiasing by adaptive samplingCasting many rays per pixel can be unnecessarily costly.For example, if there are no rapid changes in intensity atthe pixel, maybe only a few samples are needed.Solution: adaptive sampling.

Q: When do we decide to cast more rays in a particulararea?

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 9

Let’s say you were intersecting a ray with a polyhedron:

Straightforward methodintersect the ray with each trianglereturn the intersection with the smallest t-value.

Q: How might you speed this up?

Faster ray-polyhedron intersection

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 10

Ray Tracing Acceleration Techniques

1N

Faster Intersection

Fewer Rays

Generalized Rays

Approaches

Tighter boundsFaster intersector

Uniform gridsSpatial hierarchies k-d, oct-tree, bsp hierarchical gridsHierarchical bounding volumes (HBV)

Early ray terminationAdaptive sampling

Beam tracingCone tracingPencil tracing

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 11

Uniform spatial subdivisionAnother approach is uniform spatial subdivision.

Idea:Partition space into cells (voxels)Associate each primitive with the cells it overlapsTrace ray through voxel array using fast incremental arithmetic tostep from cell to cell

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 12

Uniform Grids

Preprocess sceneFind bounding box

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 13

Uniform Grids

Preprocess sceneFind bounding box

Determine resolutionv x y z on n n n n= !

3max( , , )x y z on n n d n=

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 14

Uniform Grids

Preprocess sceneFind bounding boxDetermine resolution

Place object in cell, ifobject overlaps cell

3max( , , )x y z on n n d n=

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 15

Uniform Grids

Preprocess sceneFind bounding boxDetermine resolution

Place object in cell, ifobject overlaps cellCheck that objectintersects cell

3max( , , )x y z on n n d n=

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 16

Uniform Grids

Preprocess sceneTraverse grid3D line – 3D-DDA6-connected line

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Caveat: Overlap

Optimize for objects that overlap multiple cells

Traverse until tmin(cell) > tmax(ray)Problem: Redundant intersection tests:Solution: Mailboxes

Assign each ray an increasing numberPrimitive intersection cache (mailbox)

Store last ray number tested in mailboxOnly intersect if ray number is greater

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 18

Non-uniform spatial subdivisionStill another approach is non-uniform spatial subdivision.

Other variants include k-d trees and BSP trees.

Various combinations of these ray intersections techniques are alsopossible. See Glassner and pointers at bottom of project web page formore.

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 19

Non-uniform spatial subdivisionBest approach - k-d trees or perhaps BSP trees

More adaptive to actual scene structureBSP vs. k-d tradeoff between speed from simplicity and better adaptability

0

1

2

4

7 8

5 6

3

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 20

Spatial Hierarchies

A

A

Letters correspond to planes (A)Point Location by recursive search

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 21

Spatial Hierarchies

B

A

B

A

Letters correspond to planes (A, B)Point Location by recursive search

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 22

Spatial Hierarchies

CB

D

C

D

A

B

A

Letters correspond to planes (A, B, C, D)Point Location by recursive search

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 23

Variations

oct-treekd-tree bsp-tree

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Ray Traversal Algorithms

Recursive inorder traversal[Kaplan, Arvo, Jansen]

mint

maxt *t

max*t t<

*t

min max*t t t< <

*t

min*t t<

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

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 25

Build Hierarchy Top-Down

Choose splitting plane• Midpoint• Median cut• Surface area heuristic

?

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 26

Surface Area and RaysNumber of rays in a given direction that hit anobject is proportional to its projected area

The total number of rays hitting an object isCrofton’s Theorem:

For a convex body

For example: sphere 4

SA =

4 A!

24S r!=

A

2A A r!= =

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 27

Surface Area and Rays

The probability of a ray hitting a convex shapethat is completely inside a convex cell equals

Pr[ ] o

o c

c

Sr S r S

S! ! =

oSc

S

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 28

Surface Area Heuristic

t a a i b b iC t p N t p N t= + +

80i tt t=a b

it

tt

Intersection time

Traversal time

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 29

Surface Area Heuristic

aa

Sp

S= b

b

Sp

S=

2n splits

a b

University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 30

Hierarchical bounding volumesWe can generalize the idea of bounding volume acceleration withhierarchical bounding volumes.

Key: build balanced trees with tight bounding volumes.

Many different kinds of bounding volumes.Note that bounding volumes can overlap.