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6.837 Introduction to Computer Graphics

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Luxo Jr.• Pixar Animation Studios, 1986• Director: John Lasseter

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Plan• Introduction

• Overview of the Semester

• Administrivia

• Iterated Function Systems (Fractals)6.837 Fall 04 – Durand & Cutler 4

Team• Lecturers

– Frédo Durand– Barb Cutler

• TA– Rob Jagnow

• Course secretary– Bryt Bradley

• 6.837-staff@graphics.csail.mit.edu• 6.837-ta@graphics.csail.mit.edu

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Why Computer Graphics?• Movies• Games• Simulation• CAD-CAM• Architecture• Virtual Reality• Visualization• Medical Imaging

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Movies

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Games

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Simulation

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CAD-CAM & Design

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Architecture

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Virtual Reality

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Visualization

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Medical Imaging

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What you will learn in 6.837

• Fundamentals of computer graphics algorithms

• How to implement most of theapplications just shown

• How graphics APIs and the graphics hardware work

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What you will NOT learn in 6.837

• Software packages– CAD-CAM– Photoshop and other painting tools

• Artistic skills• Game design• Graphics API

– Although you will be exposed to OpenGL

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Questions?

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Plan• Introduction

• Overview of the Semester

• Administrivia

• Iterated Function Systems (Fractals)6.837 Fall 04 – Durand & Cutler 18

Overview of the Semester• Ray Casting / Ray Tracing• The Graphics Pipeline• Textures, Shadows• Sampling, Global Illumination• Modeling, Animation, Color• Advanced Topics

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Ray Casting• For every pixel

construct a ray from the eye – For every object in the scene

• Find intersection with the ray • Keep if closest

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Ray Tracing• Shade (interaction of light and material)• Secondary rays (shadows, reflection, refraction

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Ray Tracing• Original Ray-traced

image by Whitted

• Image computed using the Dali ray tracer by Henrik Wann Jensen

• Environment map by Paul Debevec

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The Graphics PipelineRay Casting

For each pixel

For each object

Send pixels to scene

Rendering Pipeline

For each triangle

For each projected pixel

Project scene to pixels

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The Graphics Pipeline• Transformations

• Clipping

• Rasterization

• Visibility

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Textures and Shading

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Shadows

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Sampling & Antialiasing

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Traditional Ray Tracing

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Ray Tracing + Soft Shadows

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Ray Tracing + Caustics

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Global Illumination

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Modeling• Curved surfaces• Subdivision surfaces

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Animation: Keyframing

ACM © 1987 “Principles of traditional animation applied to 3D computer

animation”

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Particle system (PDE)

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Rigid Body Dynamics• Simulate all external

forces and torques

( )tx

( )tv( )1

b tp

( )3b tp

( )2b tp

( )2 tf

( )3 tf

( )1 tf

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Color

wavelength

0.75

1.00

0.50

0.25

0.00400 500 600 700

S M L

saturationhue

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Image-Based Rendering• Use images as inputs and representation• E.g. Image-based modeling and photo editing

Oh, Chen, Dorsey and Durand 2001

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Questions?

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Plan• Introduction

• Overview of the Semester

• Administrivia

• Iterated Function Systems (Fractals)

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Administrivia: Prerequisites• Not enforced• All assignments are in C++

– Optional review/introductory sessionMonday Sept 13, 7:30-9pm, 4-231

• Linear Algebra (18.06)– vectors, matrices, basis, solving systems of equations– Optional review/introductory session

Monday Sept 20, 7:30-9pm, 2-105• Algorithms (6.046)

– Orders of growth, bounds, sorting, trees

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Administrivia: Grading Policy• Assignments: 75%

– Weekly programming assignments– Must be completed individually– No final project this year

• Quiz: 10%– Tuesday, Oct 26 (in class)

• Final Exam: 10%– TBA during finals week

• Participation: 5%

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Administrivia: Assignments• Turn in code and executable (Linux or Windows)• Coding style important

– Many assignments are cumulative

• Collaboration policy:– You can chat, but code on your own– Acknowledge your collaboration!

• Late policy:– Due Wednesday @ 11:59pm– Penalized 25% per day late– Extensions only considered if requested 1 week before due date

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"Create Your Own Assignment"• Last assignment, ~ 1 week effort• Extension of previous assignment OR

Exploration of other topic discussed in class• Suggestions throughout the semester• We'll review your proposal to make sure

the scope is appropriate

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Administrivia: Lab & Office Hours• http://graphics.csail.mit.edu/classes/6.837/F04/• Fredo

– Tuesday 6- 7pm in W20- 575• Barb

– Wednesdays 6- 8pm in W20- 575 • Rob

– Wednesday 8- 11pm in W20- 575• Send email to make an appointment

for some other time6.837 Fall 04 – Durand & Cutler 44

Questions

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Plan• Introduction

• Overview of the Semester

• Administrivia

• Iterated Function Systems (Fractals)6.837 Fall 04 – Durand & Cutler 46

Iterated Function Systems (IFS)

• Capture self-similarity• Contraction

(reduce distances)• An attractor is a

fixed point

Υ )(AfA i=

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Example: Sierpinski Triangle• Described by a set of n affine transformations • In this case, n = 3

– translate & scale by 0.5

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Example: Sierpinski Trianglefor “lots” of random input points (x0, y0)

for j=0 to num_iters

randomly pick transformation i

(xk+1, yk+1) = fi (xk, yk)

display (xk, yk)

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Example: Sierpinski Trianglefor “lots” of random input points (x0, y0)

for j=0 to num_iters

randomly pick transformation i

(xk+1, yk+1) = fi (xk, yk)

display (xk, yk)

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Example: Sierpinski Trianglefor “lots” of random input points (x0, y0)

for j=0 to num_iters

randomly pick transformation i

(xk+1, yk+1) = fi (xk, yk)

display (xk, yk)

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Example: Sierpinski Trianglefor “lots” of random input points (x0, y0)

for j=0 to num_iters

randomly pick transformation i

(xk+1, yk+1) = fi (xk, yk)

display (xk, yk)

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Example: Sierpinski Trianglefor “lots” of random input points (x0, y0)

for j=0 to num_iters

randomly pick transformation i

(xk+1, yk+1) = fi (xk, yk)

display (xk, yk)

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for “lots” of random input points (x0, y0)

for j=0 to num_iters

randomly pick transformation i

(xk+1, yk+1) = fi (xk, yk)

display (xk, yk)

Example: Sierpinski Triangle

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for “lots” of random input points (x0, y0)

for j=0 to num_iters

randomly pick transformation i

(xk+1, yk+1) = fi (xk, yk)

display (xk, yk)

Example: Sierpinski Triangle

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Example: Sierpinski Trianglefor “lots” of random input points (x0, y0)

for j=0 to num_iters

randomly pick transformation i

(xk+1, yk+1) = fi (xk, yk)

display (xk, yk)

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Example: Sierpinski Trianglefor “lots” of random input points (x0, y0)

for j=0 to num_iters

randomly pick transformation i

(xk+1, yk+1) = fi (xk, yk)

display (xk, yk)

Increasing the number of iterations

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Another IFS: The Dragon

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Application: Fractal Compression• Exploit the self-similarity in an image

Compressed using Fractal Photo Lab

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Assignment 0: IFS • Get familiar with:

– C++ environment– Vector, Matrix & Image classes

• Due Wednesday Sept 15 at 11:59pm• Optional C++ review/introductory session

Monday Sept 13, 7:30-9pm, 4-231• http://graphics.lcs.mit.edu/classes/6.837/F03/

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Questions?