CS4102, Algorithms, Spring 2010
Dr. Tom Horton [email protected] Course Mechanics Homework issues to resolve Course content
Topics from earlier classes CS4102 course learning objectives
Whats the course all about? A quick tour
CS 432, Algorithms: Gen
Introduction to
Computer Graphics
CS 445 / 645
Angel: Interactive Computer
Graphics
Lecture 11
Chapter 7: Camera
Transformations
Announcements
Midterm is one week from today
Old tests will be available
Detailed list of chapter coverage made available
H
Introduction to
Computer Graphics
CS 445 / 645
Lecture 12
Chapter 12: Color
Test
Sections from Hearn and Baker
All of Ch. 2 except sections: 5, 6, and 7
All of Ch. 3 except sections: 10, 11, 12, 13, 14, 16, 17end
Ch. 4-10
All of Ch. 5
All of Ch. 6 ex
CS 445 / 645
Introduction to Computer Graphics
Lecture 13
Color
Assignment 3
Due March 23
Fourth years plan for thesis collision
Well provide lots of details to keep the assignment doable
Morphing algorithm
Last Class
We discussed vision physiology and
CS 445 / 645
Introduction to Computer Graphics
Lecture 14
Assign 3
Assignment 3 - Morphing
What is morphing?
Combination of warping and blending
warp = image distortion
Map image to a coke can
Ripple effect
blend = cross dissolve
Film cut effect
Way
CS 445 / 645
Introduction to Computer Graphics
Lecture 15
Lighting
Beier & Neely Morphing
Key point:
Cross dissolve by itself fails when features are not aligned
Intermediate blend of two faces may appear to have four
Intermediate
eyes
eyes
Warping an
CS 445 / 645
Introduction to Computer Graphics
Lecture 16
Lighting
Review
We have a model for determining the brightness
We
(radiance) of a ray rooted at a point on a surface
(radiance)
and oriented towards the cameraDirect
illumination only
illumination
CS 445 / 645
Introduction to Computer Graphics
Lecture 17
Radiosity
Assignment Four
Write a ray tracer
Youll have complete control
Input file format
User interface
Data structures
Form a two-person group
From Fall 03
Shane Liesegang
William Kammersell
CS 445 / 645
Introduction to Computer Graphics
Lecture 19
Texture Maps
Texture Mapping
Limited ability to generate complex surfaces with
Limited
geometry
geometry
Images can convey the illusion of geometry
Images painted onto
Images
polygons is called tex
CS 445 / 645
Introduction to Computer Graphics
Lecture 19
Texture Maps
Texture Mapping
Limited ability to generate complex surfaces with
Limited
geometry
geometry
Images can convey the illusion of geometry
Images painted onto
Images
polygons is called tex
CS 445 / 645
Introduction to Computer Graphics
Lecture 20
Antialiasing
Environment Mapping
Used to model a object that reflects surrounding textures
Used
to the eye
to
Polished sphere reflects walls and ceiling textures
Cyborg in Terminator 2 reflects f
CS 445 / 645
Introduction to Computer Graphics
Lecture 25
Final Exam Prep
Final Exam
Monday, May 3rd from 7 10 p.m.
Room Thornton E 304
You may use one sheet of notes (8.5 x 11)
You can write on both sides of paper
Not everything from semester will be o
Introduction to Computer Graphics
Midterm Examination
Professor Brogan
Name:_
Honor Pledge: This is a closed-book, closed-notes, independent exam. Please sign the
honor pledge: On my honor as a student, I have neither given nor
received information on thi
Introduction to Computer Graphics
Midterm Examination
Professor Brogan
Name:_
Honor Pledge: This is a closed-book, closed-notes, independent exam. Please sign the
honor pledge: On my honor as a student, I have neither given nor
received information on thi
Introduction to
Computer Graphics
CS 445 / 645
Gimbal
Lecture 10
Chapter 7: Transformations
Overview
Rotation representations
Euler
Axis-angle
Quaternion
Camera Transformations
Projections
Basic 3D Transformations
Rotate around Z axis:
x' cos sin
y
Introduction to
Computer Graphics
CS 445 / 645
Lecture 9
Chapter 4: Rasterization
L. McMillan
MIT 6.837 notes
What made line drawing faster?
Symmetry and Differential Analyzer
Symmetry
f ( x ) = mx + b
f ( x + 1) = m( x + 1) + b = mx + m + b
= f (x ) +
Introduction to
Computer Graphics
CS 445 / 645
Lecture 8
Chapter 4: Rasterization
L. McMillan
MIT 6.837 notes
Agenda
Clipping parallel lines
Special conditions handled in hardware
Assignment 2 handout
Boost handout
Midterm in 2.5 weeks
Keep up with
CS4102, Algorithms, Spring 2010 First Principles
Properties of algorithms Counting basic operations Time and space complexity Worst-case and average-case Lower Bounds and Optimality and one slide of summations
Analyzing Algorithms and Problems
We analyz
CS 4102, Algorithms: Chapter 2
Measuring time complexity
Order classes: Big-Oh etc. Proving order-class membership Properties of order-classes
More on optimality (not in text)
Improving searching of lists Binary Search: W(n), A(n) Decision Trees for l
CS 4102, Algorithms: Recurrences, D & C First design strategy: Divide and Conquer
Examples
Recursive algorithms Counting basic operations in recursive algorithms: Solving recurrence relations
By iteration method Recursion trees (quick view) The Main an
CS 4102, Algorithms: More Divide and Conquer Read: Algorithms text, Chapter 5 Examples:
Mergesort Trominos Closest Pair of Points Strassens Matrix Multiplication Algorithm
New Problem: Sorting a Sequence
The problem:
Given a sequence a0 an reorder them
CS 4102, Algorithms: More Sorting
Lets finish some sorting problems Chapter 6 in the textbook Insertion Sort, Quicksort Lower bound for sorting using key comparisons
Reminder: Common Forms of Recurrence Equations Remember these?
Divide and conquer: Like
CS 4102, Algorithms: Heapsort
Expectations:
Section 3.5 and CS216 slides Next: Sections 4.2-4.5
Graph searching
Problems to do are coming
Review from CS216
Review these slides!
Slides from 3-26-03 on Priority Queues (Binary Min Heaps)
http:/www.cs.v
MakingMovies
MakingMovies
CS445/645
MidtermExam
MidtermExam
Average:75.72
s StandardDeviation:11.13
s Median:77
s
s
Expectgradetobecurvedup
MakingMovies
MakingMovies
s
s
s
s
s
s
s
s
Concept
Storyboarding
Sound
CharacterDevelopment
Layoutandlook
Effects
An
Introduction to
Computer Graphics
CS 445 / 645
David Brogan
[email protected]
Class Web Page
http:/www.cs.virginia.edu/~gfx/Courses
Class lectures posted
Assignments distributed
Instructor/TA Coordinates
David Brogan
Olsson 216
[email protected]
Introduction to
Computer Graphics
CS 445 / 645
Lecture 2
General Graphics Systems
Daniel Rozin, Wooden Mirror (1999)
Announcement
Announcement
Class web site is up
Overview Read Chapter 2
Display devices
Graphics hardware
Input devices
Graphics Softw
Introduction to
Computer Graphics
CS 445 / 645
Lecture 4
OpenGL Programming Guide
OpenGL
Announcement
Announcement
Visit discussion forum to keep up to date
Red Book is good source for OpenGL
Intro to OpenGL
OpenGL operates as an infinite loop
Put thin
Introduction to
Computer Graphics
CS 445 / 645
Lecture 5
Transformations
M.C. Escher Smaller and Smaller (1956)
Modeling Transformations
Specify transformations for objects
Specify
Allows definitions of objects in own coordinate systems
Allows use of ob