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Speeding Up Ray Tracing

Images from Virtual Light Field Projectwww.cs.ucl.ac.uk/vlf

©Slides Anthony Steed 1999 & Mel Slater 2004

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Optimisations

Limit the number of rays Make the ray test faster

• for shadow rays– the main drain on resources in there are

several lights

• for primary rays• for all rays

over 90% of the cost of raytracing is in ray-objectintersection tests

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Primary Rays

Use a z-buffer! Instead of writing colour write and object

identifier• Easy to support in OpenGL - turn off lighting,

do flat shading and encode object id within 24bit colour

Difficult technique to use elsewhere because rays are no longer spatially coherent and evenly spaced

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General Rays

Techniques to use• bounding volumes• hierarchical bounding volumes• space subdivision

– regular – adaptive

• ray coherence

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Bounding Volume

Find a tight bounding volume and use it for a first reject test

If hit volume then test full object

Axis alignedBounding Box

Bounding Box

Bounding Sphere

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Fast BV Tests

Box-Ray test• a box is three sets of parallel planes, each

set orthogonal to the other two– Calculate tnear for each of the three plane pairs

– find max of the 3 tnear

– Calculate tfar for each of the three plane pairs

– find min of the 3 tfar

• If max tnear is greater that min tfar, then the box is not intersected

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Fast BV Tests (EG)

tnearx

tfary

tfarx

tnearx

tneary

tfarx

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Choosing a Volume

Choice depends on the cost of the test and the fit of the shape• The “void” area can be very large

More efficient fitting shapes are possible (this is still a research area e.g. k-dops)

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Hierarchical Bounding Volumes

A

B

C

D E

F

root

A+B

A B

C D+E F

D E

r1 r2

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Choosing a HBV

Scene graph might not map to a decent space partitioning• group BVs based on proximity rather than

scene graph position

You would sort the HBV using a BSP tree anyway ...

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Regular Spatial Subdivision

Regular 3D grid of “voxels”

A

B

C

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Details on the RSS

Testing• Each voxel keeps a list of

objects that intersect this voxel

• Need for a ‘mailbox’ system where voxel also keeps track of what has already intersected it to avoid duplications.

Size of voxels• Obvious trade off on

granularity of voxels

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Adaptive Spatial Subdivision

The octree idea (illustrated with a quadtree!)

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Building the Octree

Recursively split the cells into eight, until each cell meets some criteria• e.g. previous diagram was “only one object

intersects each cell” Advantage is clear - cells are not

wasted on void areas

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Tracing an Octree

Find octree cell containing start point If no intersection, find intersection (I) of

ray with cube that surround the octree Find (I) in the octree

• it is moved a little along the ray Repeat

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kD-tree / BSP Tree

Similar to octree, but orthogonal splitting planes are chosen to provide a good search tree

Split based on balancing objectnumbers andminimising volume disparity

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Ray Coherence Methods

Light Buffer Ray Classification Scheme

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Light Buffer

Haines and Greenberg, 1986 Problem with shadow rays is that for

every intersection we trace and additional n rays for each light

r

l0

l1

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Light Buffer

Enclose light in a box. Cells of box faces store objects

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Construction - 2D Analogue

A

B

C1 - <NULL> C2 - A, B, C

C3 - A C4 - <NULL>

C1

C2

C3

C4

C

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Ray Classification

Arvo and Kirk, 1987 Group together similar rays (rather than

similar objects) Similar rays should intersect the same

groups of objects Very elegant method

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Ray Classification - Rays are Points

Every ray is represented as a point in 5D space (R5) (x,y,z,u,v) where (u,v) is the directional component, and (x,y,z) is the origin

(x,y,z)

(u,v)-Y

+X

This ray is (x,y,z) inside boxin direction (u,v)

on +X plane There are 6 planes-X,+X,-Y,+Y,-Z,+Z

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Ray Classification – 5 Tasks

E is the subset of R5 containing every possible ray in the scene

E1, E2, …, En is a partition of E• formed as a 32-tree

– The 5D hypercube can be split along each of its axis to form 32 children, and so on…

For each Ei there will be a Ci - a set of objects intersected by at least one of the ray s in Ei

For any ray find the Ei to which it belongs Then intersect it with the objects in Ci (see details in the book – the important aspect to

undrestand is the idea of ray classification – similar rays will intersect similar groups of objects!).

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Virtual Light Field Approach

Very recent development For a fixed ‘uniformly distributed’ set of rays,

find for each ray all of its intersections with objects in the environment

Each ray maintains a list of objects it intersects (and where along the ray)

Given any arbitrary ray that emerges in ray tracing, find the closest ray in the ray set, and use the rays that this intersects as a candidate set of objects.

Several complications – but the idea is clear.

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Summary

Ray intersection is computationally expensive and we need to reduce it

Methods used fall into 3 classes• Bound the objects• Partition the object space• Partition the ray space

Ray tracing can be tremendously speeded up by appropriate use of modern hardware (see papers of Ward et al, and also UCL’s Virtual Light Field project www.cs.ucl.ac.uk/vlf ).