Advanced Computer Graphics (Spring 2005)

1
Advanced Computer Graphics
(Spring 2005)

• COMS 4162, Lecture 15 Ray Tracing/Global
  Illumination
• Ravi Ramamoorthi

http//www.cs.columbia.edu/cs4162
Slides adapted from unit 5 (lectures 21-22) of
COMS 4160
2
To Do

• Enjoy spring break!!
• If you want, you can work on raytracer/project
  during break, but this is not required

3
Course Outline

• 3D Graphics Pipeline

4
Course Outline

• 3D Graphics Pipeline

Rendering (Creating, shading images from
geometry, lighting, materials)
Modeling (Creating 3D Geometry)
Unit 1 Foundations of Signal and Image
Processing Understanding the way 2D images are
formed and displayed, the important concepts and
algorithms, and to build an image processing
utility like Photoshop Weeks 1 3. Assignment 1
due Feb 15
Unit 3 Ray Tracing Weeks 7 9. Ass 3 due Apr
12
Unit 2 Meshes, Modeling Weeks 4 6. Ass 2 due
Mar 10
5
This lecture

• High-level overview and summary of ray tracing /
  global illumination (from 4160)
• After spring break technical details of writing
  a ray tracer for assignment 3 and more advanced
  topics

Chapters 15.10 and 16 are useful background,
although they dont follow treatment here
6
Effects needed for Realism

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

7
Image courtesy Paul Heckbert 1983
8
Outline

• Ray Tracing
• Global Illumination and Rendering Equation

9
Ray Tracing History

• Appel 68
• Whitted 80 recursive ray tracing
• 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

10
Ray Tracing

• Different Approach to Image Synthesis as compared
  to Hardware pipeline (OpenGL)
• Pixel by Pixel instead of Object by Object
• Easy to compute shadows/transparency/etc

Demo applet http//www.cs.berkeley.edu/efros/jav
a/tracer/tracer.html
11
Ray Casting
Virtual Viewpoint
Virtual Screen
Objects
Ray misses all objects Pixel colored black
Ray intersects object shade using color, lights,
materials
Multiple intersections Use closest one (as does
OpenGL)
12
Shadows
Light Source
Virtual Viewpoint
Virtual Screen
Objects
Shadow ray to light is unblocked object visible
Shadow ray to light is blocked object in shadow
13
Shadows Numerical Issues

• Numerical inaccuracy may cause intersection to
  be
• below surface (effect exaggerated in figure)

• Causing surface to incorrectly shadow itself

• Move a little towards light before shooting
  shadow ray

14
Mirror Reflections/Refractions
Virtual Viewpoint
Virtual Screen
Objects
15
Recursive Ray Tracing

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

16
Problems with Recursion

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

17
Turner Whitted 1980
18
Effects needed for Realism

• (Soft) Shadows
• Reflections (Mirrors and Glossy)
• Transparency (Water, Glass)
• Interreflections (Color Bleeding)
• Complex Illumination (Natural, Area Light)
• Realistic Materials (Velvet, Paints, Glass)

Discussed in this lecture so far Not discussed
but possible with distribution ray tracing Hard
(but not impossible) with ray tracing radiosity
methods
19
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 in next lecture
• Triangle, sphere, polygon, general implicit
  surface

20
Ray-Tracing Transformed Objects

• We have an optimized ray-sphere test
• But we want to ray trace an ellipsoid
• Solution Ellipsoid transforms sphere
• Apply inverse transform to ray, use ray-sphere
• Allows for instancing (traffic jam of cars)
• Mathematical details worked out in class

21
Acceleration

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

22
Acceleration Structures

• Bounding boxes (possibly hierarchical)
• If no intersection bounding box, neednt check
  objects

Bounding Box
Ray
Spatial Hierarchies (Oct-trees, kd trees, BSP
trees)
23
Acceleration Structures Grids
24
Interactive Raytracing

• Ray tracing historically slow
• Now viable alternative for complex scenes
• Key is sublinear complexity with acceleration
  need not process all triangles in scene
• Allows many effects hard in hardware
• OpenRT project real-time ray tracing
  (http//www.openrt.de)

25
Raytracing on Graphics Hardware

• Modern Programmable Hardware general streaming
  architecture
• Can map various elements of ray tracing
• Kernels like eye rays, intersect etc.
• In vertex or fragment programs
• Convergence between hardware, ray tracing
• Purcell et al. 2002, 2003
• http//graphics.stanford.edu/papers/photongfx

26
(No Transcript)
27
Outline

• Ray Tracing
• Global Illumination and Rendering Equation

28
Global Illumination

• Diffuse interreflection, color bleeding Cornell
  Box

29
Global Illumination

• Caustics Focusing through specular surface
• Major research effort in 80s, 90s till today

30
Reflectance Equation (review)
Cosine of Incident angle
Reflected Light (Output Image)
Emission
BRDF
Incident Light (from light source)
31
Reflectance Equation (review)
Sum over all light sources
Cosine of Incident angle
Reflected Light (Output Image)
Emission
BRDF
Incident Light (from light source)
32
Reflectance Equation (review)
Replace sum with integral
Cosine of Incident angle
Reflected Light (Output Image)
Emission
BRDF
Incident Light (from light source)
33
Global Illumination
Surfaces (interreflection)
Cosine of Incident angle
Reflected Light (Output Image)
Emission
BRDF
Reflected Light (from surface)
34
Rendering Equation
Surfaces (interreflection)
Cosine of Incident angle
Reflected Light (Output Image)
Emission
BRDF
Reflected Light
UNKNOWN
KNOWN
KNOWN
UNKNOWN
KNOWN
35
Rendering Equation (Kajiya 86)
36
Rendering Equation as Integral Equation
Cosine of Incident angle
Reflected Light (Output Image)
Emission
BRDF
Reflected Light
UNKNOWN
KNOWN
KNOWN
UNKNOWN
KNOWN
37
Linear Operator Equation
Kernel of equation Light Transport Operator
Can be discretized to a simple matrix
equation or system of simultaneous linear
equations (L, E are vectors, K is the light
transport matrix)
38
Ray Tracing and extensions

• General class numerical Monte Carlo methods
• Approximate set of all paths of light in scene

Binomial Theorem
39
Ray Tracing
Emission directly From light sources
Direct Illumination on surfaces
Global Illumination (One bounce
indirect) Mirrors, Refraction
(Two bounce indirect) Caustics etc
40
Ray Tracing
Emission directly From light sources
Direct Illumination on surfaces
Global Illumination (One bounce
indirect) Mirrors, Refraction
OpenGL Shading
(Two bounce indirect) Caustics etc
41
Rendering Equation
Surfaces (interreflection)
Cosine of Incident angle
Reflected Light (Output Image)
Emission
BRDF
Reflected Light
UNKNOWN
KNOWN
KNOWN
UNKNOWN
KNOWN
42
Change of Variables

• Integral over angles sometimes insufficient.
  Write integral in terms of surface radiance only
  (change of variables)

43
Change of Variables

• Integral over angles sometimes insufficient.
  Write integral in terms of surface radiance only
  (change of variables)

44
Rendering Equation Standard Form

• Integral over angles sometimes insufficient.
  Write integral in terms of surface radiance only
  (change of variables)
• Domain integral awkward. Introduce binary
  visibility fn V

Same as equation 2.52 Cohen Wallace. It swaps
primed And unprimed, omits angular args of BRDF,
- sign. Same as equation above 16.3 in Shirley,
except he has no emission, slightly diff.
notation