Computer Graphics (Fall 2003)

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Computer Graphics (Fall 2003)

• COMS 4160, Lecture 17 Ray Tracing
  Ravi Ramamoorthi

http//www.cs.columbia.edu/cs4160
The Internet Ray Tracing Competition
http//www.irtc.org
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Image courtesy Paul Heckbert 1983
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Effects needed for Realism

• Shadows
• Reflections (Mirrors)
• Transparency
• Interreflections
• Detail (Textures etc.)
• Complex Illumination
• Realistic Materials
• And many more

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Turner Whitted 1980
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Ray Tracing History

• Appel 68
• Whitted 80 recursive ray tracing (picture)
• Landmark in computer graphics
• Lots of work on various geometric primitives
• Lots of work on accelerations
• Current Research
• Real-Time raytracing (historically, slow
  technique)
• Ray tracing architecture

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The Pinhole Camera
Image plane
Pinhole
Illustration courtesy Greg Humphries
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Ray Casting
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Ray Tracing

• Shoot rays through pixels into the world
• For each pixel,
• Find closest intersection in scene
• Evaluate illumination model to color pixel

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Comparison to Scan-Line

• Per-pixel evaluation, per-pixel rays (not
  scan-convert each object). On face of it, costly
• More complex shading, lighting effects possible

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Ray paths

• LRE
• Arbitrary paths realism
• Trace from light or eye?
• Most light rays dont hit eye
• Importance sampling
• Eye Ray tracing
• Primary Rays
• Shadow Rays
• Reflected/Transmitted Rays

Appel 68
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Recursive Ray Tracing

• For each pixel
• Trace Primary Ray, find intersection
• Trace Shadow Ray(s) to light(s)
• Color Visible ? Illumination Model 0
• Trace Reflected Ray
• Color reflectivity Color of reflected ray

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Shadow Rays

• How much light is reaching point P?
• Fire a shadow ray towards each light in the scene
• Numerical problems?

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Problems with Recursion

• Reflection rays may be traced forever
• Generally, set maximum recursion depth
• Same for transmitted rays (take refraction into
  account)

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Ray/Object Intersections

• Heart of Ray Tracer
• One of the main initial research areas
• Optimized routines for wide variety of primitives
• Various types of info
• Shadow rays Intersection/No Intersection
• Primary rays Point of intersection, material,
  normals
• Texture coordinates
• Work out examples
• Triangle, sphere, general implicit surface

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More on Intersections

• Basic Algorithm
• Test each object for intersection
• Sort objects to find closest one
• Trace shadow ray. If unblocked, compute
  illumination
• Issues
• Precision self shadowing
• Aliasing, Supersampling
• Stochastic, Jittered sampling

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Precision

• Floating point calculations are imprecise!
• Often, a rays origin is supposed to be on a
  surface, but this might happen
• Typical hack is to only allow t values above some
  small threshold, like .0000001

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Comparisons

• Scan Conversion vs. Ray tracing
• Ray tracing is (has been) much much slower
• Is this still true if number of objects large?
  Fractals?
• Acceleration structures (next), but still very
  slow usually
• Realism in imagery
• Reflections, Refractions, soft shadows, complex
  lighting, shading trivial in ray tracing. In
  scan conversion?
• Future?
• Currently OpenGL uses scan conversion
• Real-Time raytracing? (already possible)
• Ray Tracing architecture (research at Stanford)

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Acceleration

• Testing each object for each ray is slow
• Fewer Rays
• Adaptive sampling HW , depth control
• Generalized Rays
• Beam tracing, cone tracing, pencil tracing etc.
• Faster Intersections
• Optimized Ray-Object Intersections
• Fewer Intersections

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Acceleration Structures

• Reducing number of intersections
• Bounding Volume hierarchy
• If no intersection with bounding box, neednt
  check objects
• Grids
• Uniform, Hierarchical
• Spatial Hierarchies
• Oct-trees, kd trees, BSP trees

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Acceleration Structures