Ray Tracing

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Instructor: Christopher Rasmussen (cer@cis.udel.edu)

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Course web page:

http://goo.gl/tJ4Kn4

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April 27, 2017 ❖ Lecture 20

Outline

• Distributed ray tracing
• Soft shadows
• Glossy reflections
• Bounding volumes
• Hierarchies
• Uniform spatial subdivision
• Light paths & caustics

Basic Ray Tracing: Notes

• Global illumination effects simulated by basic algorithm are shadows, purely specular reflection/transmission
• Some outstanding issues
• Aliasing, aka jaggies
• Shadows have sharp edges, which is unrealistic
• No diffuse reflection from other objects
• Intersection calculations are expensive, and even more so for more complex objects
• Not currently suitable for real-time (i.e., games)

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Ambient Occlusion

• Extension of shadow ray idea—not every point should get full ambient illumination
• Idea: Cast multiple random rays (a “distribution of rays”) from each rendered surface point to estimate percent of sky hemisphere that is visible
• Limit length of rays so distant objects have no effect
• Cosine weighting/distribution for foreshortening
• Developers of this idea won a technical Oscar in 2010

Ambient Occlusion: Example

http://www.gavinharrison.co.uk/renderman04.php

DRT Application #2: Soft Shadows

• For point light sources, sending a single shadow ray toward each is reasonable
• But this gives hard-edged shadows
• Simulating soft shadows
• Model each light source as sphere
• Send multiple jittered shadow rays toward a light sphere; use fraction that reach it to attenuate color
• Similar to ambient occlusion, but using list of light sources instead of single hemisphere

Soft Shadows: Example

1 shadow ray

10 shadow rays

50 shadow rays

Note discrete "shadow points" -- need post-processing to smooth into contiguous region

DRT Application #3: Glossy Reflections

• Analog of hard shadows are “sharp reflections”—every reflective surface acts like a perfect mirror
• To get glossy or blurry reflections, send out multiple jittered reflection rays and average their colors

Why is the reflection sharper at the top?

DRT for Glossy Reflections

from Hill

Other DRT Effects

• Depth of field

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• Motion blur

Other DRT Effects

• Depth of field

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• Motion blur

Bounding Volumes for Efficiency

• Idea: enclose complex objects (i.e., .obj models) in simpler ones (e.g., spheres, boxes) and test simple intersection before complex intersection
• Want bounds as tight as possible

Bounding Boxes as Volumes: Multiple Objects

• With multiple objects in the scene, how to arrange bounding boxes?

A box around each object, or a single box surrounding all objects, are not optimally efficient schemes

Bounding Boxes as Volumes: Multiple Objects

• With multiple objects in the scene, how to arrange bounding boxes?

Nested boxes impose a hierarchy...

...that allow a more efficient recursive tree search

Uniform Spatial Subdivision

• Another approach is to divide space equally, such as into boxes
• Each object "belongs" to every box it intersects
• Trace ray through boxes sequentially, check every object belonging to current box

Uniform Spatial Subdivision

• Tracing ray here is a little like rasterizing a line -- must keep track of intersections with current box sides to know which box will be entered next
• Must make sure that only hits inside current box are reported
• In figure, cell (i, j) is being checked
• Object b "belongs" to (i, j) and intersects ray, but hit point is outside (i, j)

Can Ray Tracing Do This?

courtesy of H. Wann Jensen

Light Paths

• Consider the path that a light ray might take through a scene between the light source L and the eye E
• It may interact with multiple diffuse (D) and specular (S) objects along the way
• Includes reflections, refractions
• We can describe this series of interactions with the regular expression L (D | S)* E
• (If a surface is a mix of D and S, the combination is additive so it is still OK to treat in this manner)

from Sillion & Puech

Light Paths: Examples

• Direct visualization of the light: LE
• Local illumination: LDE, LSE
• Ray tracing: LS*E, LDS*E

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from Hill

Ray tracing light paths

General light paths

from Sillion & Puech

Caustics

• Definition: (Concentrated) specular reflection/refraction onto a diffuse surface
• In simplest form, follow an LSDE path
• Standard ray tracing cannot handle caustics—only paths described by LDS*E

courtesy of H. Wann Jensen

from Sillion & Puech

Caustics: Examples

More about caustics

• What is the problem with LS⁺DE paths for ray tracing?
• Review: Radiance for a viewing direction given all incoming light:

Review: BRDFs

• Bidirectional Reflectance Distribution Function (BRDF): Ratio of outgoing radiance in one direction to incident irradiance from another
• Can view BRDF as probability that incoming photon will leave in a particular direction (given its incoming direction)

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from Sillion & Puech

The Problem with Diffuse Surfaces

• For specular surfaces, we “know” where the photon will go (= “came from”, if going backwards), whereas for diffuse surfaces there’s much more uncertainty
• If we’re tracing a ray from the eye and we hit a diffuse surface, this uncertainty means that the source of the photon could be anywhere in the hemisphere
• Conventional ray tracing just looks for lights at this point, but for LS⁺DE paths we need to look for other specular surfaces
• How to find them?

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from P. Heckbert

from Sillion & Puech

Bidirectional Ray Tracing (P. Heckbert, 1990)

• Idea: Trace forward light rays into scene as well as backward eye rays
• At diffuse surfaces, light rays additively “deposit” photons in radiosity textures, or “rexes”, where they are accessed by eye rays
• Summation approximates integral term in radiance computation
• Light rays carry information on specular surface locations—they have no uncertainty

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from P. Heckbert

Bidirectional Ray Tracing: Notes

• This kind of bidirectional ray tracing simulates LS*DS*E paths
• Photons deposited in rexes are sparse, so they must be interpolated
• Use density estimation
• Still have noise issues
• Storage of illumination only on surfaces means that we ignore fog and other volume-based scattering/absorption (aka “participating media”)

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from P. Heckbert

Bidirectional Ray Tracing: Results

from P. Heckbert

Lens, mirrored sphere, and diffuse surface with caustic

of focused light

“Backwards” Ray Tracing (1986)

courtesy of J. Arvo

A technique similar to Heckbert’s was used to form this image

What’s Still Missing?

What’s Still Missing?

from http://gurneyjourney.blogspot.com

(This is a photo)

What’s Still Missing?

An LD*E

scene

courtesy of Cornell

Color Bleeding

• Transfer of color between diffuse surfaces via reflection

courtesy of K. Fatahalian & J. Hui

White light only, so red and blue on white wall are from bleeding