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Nima Kalantari

CSCE 441 - Computer Graphics

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Ray Tracing (Intro)

Some slides from Ren Ng, Ravi Ramamoorthi, and Scott Schaefer

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Rasterization

  • Advantage
    • Fast
  • Disadvantage
    • Hard to render realistic effects

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Effects needed for Realism

  • (Soft) Shadows
  • Reflections (Mirrors and Glossy)
  • Transparency (Water, Glass)
  • Interreflections (Color Bleeding)
  • Realistic Materials (Velvet, Paints, Glass)
  • And many more

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From Wikipedia

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Ray Tracing

  • Follows the physical image formation process
  • Pixel by pixel instead of object by object in rasterization
  • Very slow!
  • Easier to handle different effects

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Light Rays

  • Three ideas about light rays
    • Light travels in straight lines
    • Light rays do not interfere with each other
    • Light rays travel from the light sources to the eye

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Outline

  • Basic ray tracing
  • Recursive ray tracing
  • Ray object intersection

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Ray Casting

  • Appel 1968 - Ray casting
    • Generate an image by casting one ray per pixel
    • Check for shadows by sending a ray to the light

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Ray Casting - Generating Eye Rays

  • Pinhole Camera Model

eye point

image plane

light source

eye ray �(starts at eye and goes through pixel)

closest scene�intersection point

note: more intersection points

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Ray Casting - Shading Pixels (Local Only)

  • Pinhole Camera Model

eye point

image plane

light source

eye ray �(starts at eye and goes through pixel)

perform shading calculation here to compute color of pixel (e.g. Phong model)

N

P

L

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Local Shading

 

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Ray Casting - Shading Pixels (no shadows)

  • Pinhole Camera Model

eye point

image plane

light source

eye ray �(starts at eye and goes through pixel)

perform shading calculation here to compute color of pixel (e.g. Phong model)

N

P

L

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Shadows

  • Cast a virtual ray to each light source
  • If ray hits an opaque object before the light, then omit contribution of that light

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Ray Casting – Shadows

  • Pinhole Camera Model

eye point

image plane

light source

eye ray �(starts at eye and goes through pixel)

perform shading calculation here to compute color of pixel (e.g. Phong model)

N

P

L

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Illumination without shadow

 

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Illumination with shadow

 

 

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Outline

  • Basic ray tracing
  • Recursive ray tracing
  • Ray object intersection

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Recursive Ray Tracing

  • “An improved Illumination �model for shaded display” �T. Whitted, CACM 1980

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  • Time:
    • VAX 11/780 (1979) 74m
    • PC (2006) 6s
    • GPU (2012) 1/30s

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Spheres and Checkerboard, T. Whitted, 1979

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Recursive Ray Tracing - Reflection

eye point

image plane

light source

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Recursive Ray Tracing - Reflection

eye point

image plane

N

R

light source

Mirror ray�(specular reflection)

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Reflection

  • Mirror-like/Shiny objects

Surface

 

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Recursive Ray Tracing - Reflection

eye point

image plane

light source

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Recursive Ray Tracing - Reflection

eye point

image plane

light source

Shadow rays

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Refraction

  • Bending of light caused by different speeds of light in different medium
  • Each (semi-)transparent object has an index of refraction ni or velocity of light ci
  • Use Snell’s law to find

refracted vector

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Image taken from http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/refr2.html

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Snell’s Law

 

 

 

Surface

 

 

 

 

 

c=speed of light in vacuum

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Recursive Ray Tracing – Reflection & Refraction

eye point

image plane

light source

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Recursive Ray Tracing – Reflection & Refraction

eye point

image plane

light source

Truncate at finite depth!

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Recursive Ray Tracing

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Truncate at finite depth!

+

 

 

+

 

+

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Recursive Ray Tracing

For each pixel

    • Trace the ray, find intersection

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    • Trace Shadow Ray(s) to all light(s)
      • Color = ka
      • Color += if visible -> illumination model; if not visible -> 0 ;

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    • Trace Reflected Ray
      • Color += reflectivity * Color of reflected ray

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Recursive Ray Tracing – Reflection

0

1

eye point

image plane

light source

2

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Outline

  • Basic ray tracing
  • Recursive ray tracing
  • Ray object intersection

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Ray Equation

unit direction

origin

“time”

point along ray

Ray equation:

Example:

Ray is defined by its origin and a direction vector

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Ray Intersection With Sphere

Ray:

Sphere:

Solve for intersection:

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Plane Equation

Plane is defined by normal vector and a point on plane

Example:

Plane Equation:

normal vector

any point

all points on plane

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Ray Intersection With Plane

Ray equation:

Plane equation:

Solve for intersection

Check:

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Ray Intersection With Triangle

  • Triangle is in a plane
    • Ray-plane intersection
    • Test if hit point is inside triangle

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Ray Intersection With Triangle Mesh

  • Simple idea: just intersect ray with each triangle
  • Simple, but slow

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Möller Trumbore Algorithm

Why care about performance?

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Ray Tracing vs Rasterization

for each pixel

for each primitive

color the pixel

for each primitive

for each pixel

color the pixel

Offline*

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Movies, Animations

Real-Time

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Games