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GR2Advanced Computer

GraphicsAGR

GR2Advanced Computer

GraphicsAGR

Lecture 14Improving the Efficiency of

Ray TracingLight Source Effects

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Advantages and Disadvantages of Ray

Tracing

Advantages and Disadvantages of Ray

Tracing

Ray tracing is attractive because– shadows, reflections, refractions

are easily incorporated Ray tracing is expensive because

– the cost of computing ray-object intersections is very high

This part of the lecture looks at efficiency issues in ray tracing

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Ray Tracing - A ReminderRay Tracing - A Reminder

pixel positionson view plane

camera

The intensity calculationis now:I = I local + k r * I reflected

+ k t * I transmitted

I reflected and I transmitted

are calculated recursively

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Adaptive Tree Depth Control

Adaptive Tree Depth Control

Basic algorithm follows rays until they leave the scene (or hit diffuse surface) - in theory the tree depth can then be considerable

In practice, it is not usually necessary to trace rays to any great depth

As tree formed, a running product is kept of transmission and reflection coefficients– this product attenuates all intensities lower in

tree– once product less than threshold, branch is

stopped

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Bounding VolumesBounding Volumes

Enclose groups of objects in a simple bounding volume– sphere or box

Test for intersection against bounding volume– if none, then ray does not intersect

objects within– if intersection occurs, test against each

object in turn Idea can be extended to hierarchies

of bounding volumes (usually boxes)

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Spatial SubdivisionSpatial Subdivision

Idea: divide space into subregions, noting objects in each subregion– termed ‘spatial subdivision’ or ‘spatial

coherence’ Calculation changes from:

– for each object or bounding box, find ray intersection

to– as ray proceeds through space, are there any

objects in the current subregion?– if yes, calculate intersections; if not, move on– find next subregion entered by the ray

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How do we Subdivide Space

How do we Subdivide Space

One idea is octree partitioning We illustrate in 2D - known as

quadtreeFirst divide space intofour regions

Count number of objectsin each region

If a region contains an object, subdivide again

Continue to a specified levelof subdivision

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OctreeOctree

A tree structure emerges, with the nodes at the leaves ofthe tree containing (hopefully) a small number of objects,or empty.

This is quadtree - in 3Dwe subdivide cube into8 each time, getting anoctree

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Ray Tracing through Octree

Ray Tracing through Octree

We trace ray from subregion to subregion, only doingintersection tests for the small number of objects in thesubregion.

Find region correspondingto start point. Test ray forintersections with any objects.

If none, find next region - bycalculating intersection withregion boundaries. Advancea short way into next region -say to (x,y,z)

Find region which includes(x,y,z) and continue.

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Finding Region Containing (x,y,z)

Finding Region Containing (x,y,z)

We use octree itself to locate region. Starting at top, asimple test determines in which of eight (4 for quadtree) regions the point (x,y,z) lies. Proceed down tree untilleaf node reached.

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Binary Space PartitioningBinary Space Partitioning

An alternative to octrees is just to split into two at each step– separating plane typically chosen to

divide space into regions of equal complexity

Known as Binary Space Partitioning, or BSP, trees

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Octrees versus BSP treesOctrees versus BSP trees

Octrees:– good for scenes where density of objects

varies widely– possible to have small objects in large

regions– stepping from region to region slow because

trees tend to be unbalanced BSP trees:

– depth of tree smaller because tree balanced– memory costs lower– void areas smaller

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Ray Tracing SoftwareRay Tracing Software

Persistence Of Vision Ray Tracer (POV-RAY) is public domain ray tracing software

Download from:– http://www.povray.org

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More Teapots! The POVRAY version

More Teapots! The POVRAY version

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POVLAB modellerPOVLAB modeller

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Lecture 14Part 2

Light Source Effects

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Light Source Sequence of Images

Light Source Sequence of Images

The following sequence of images were created by Alan Watt of University of Sheffield

They illustrate effects of different light sources in a scene

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Ambient Light OnlyAmbient Light Only

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Camera Light SourceCamera Light Source

Light source atcamera only.

Note no shadows.

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Distant Light SourceDistant Light Source

Light rays parallelto each other

Note shadows

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Point Light SourcePoint Light Source

Point light sourceclose to object,in same directionas distant sourcein previous picture.

Note shadows aredifferent.

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SpotlightSpotlight

Spotlight in sameposition as previouspoint light.

Cone angle is 30 deg.

Note cone ofinfluence of thelight, and thehard shadow.

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Spotlight - Soft ShadowsSpotlight - Soft Shadows

Softer shadowobtained by havinga gradual drop-offof intensity at edge ofcone (here over last5 deg)

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Effect of Distance - No Attenuation

Effect of Distance - No Attenuation

Here there is noattenuation of lightover distance

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Effect of Distance - Attenuation

Effect of Distance - Attenuation

Intensity is attenuatedby 1/distance

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Effect of Distance - Attenuation

Effect of Distance - Attenuation

Here the attenuation factoris 1/(distance)2

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FogFog

Intensity of fogincreases linearlywith depth.

How is thisachieved?