Preview

Notes

Satisfactory Essays
Open Document
Open Document
29488 Words
Grammar
Grammar
Plagiarism
Plagiarism
Writing
Writing
Score
Score
Notes
Computer Graphics Lecture Notes
CSC418 / CSCD18 / CSC2504
Computer Science Department University of Toronto Version: November 24, 2006

Copyright c 2005 David Fleet and Aaron Hertzmann

CSC418 / CSCD18 / CSC2504

CONTENTS

Contents
Conventions and Notation 1 Introduction to Graphics 1.1 Raster Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Basic Line Drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Curves 2.1 Parametric Curves . . . . . . . 2.1.1 Tangents and Normals 2.2 Ellipses . . . . . . . . . . . . 2.3 Polygons . . . . . . . . . . . 2.4 Rendering Curves in OpenGL v 1 1 2 4 4 6 7 8 8 10 10 11 13 14 15 16 18 21 21 21 22 22 22 23 24 24 25 26 26 27 27 29 29 30 i

2

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

3

Transformations 3.1 2D Transformations . . . . . . . . . . . . . . . 3.2 Affine Transformations . . . . . . . . . . . . . 3.3 Homogeneous Coordinates . . . . . . . . . . . 3.4 Uses and Abuses of Homogeneous Coordinates 3.5 Hierarchical Transformations . . . . . . . . . . 3.6 Transformations in OpenGL . . . . . . . . . . Coordinate Free Geometry 3D Objects 5.1 Surface Representations . . . . . . . . . 5.2 Planes . . . . . . . . . . . . . . . . . . 5.3 Surface Tangents and Normals . . . . . 5.3.1 Curves on Surfaces . . . . . . . 5.3.2 Parametric Form . . . . . . . . 5.3.3 Implicit Form . . . . . . . . . . 5.4 Parametric Surfaces . . . . . . . . . . . 5.4.1 Bilinear Patch . . . . . . . . . . 5.4.2 Cylinder . . . . . . . . . . . . 5.4.3 Surface of Revolution . . . . . 5.4.4 Quadric . . . . . . . . . . . . . 5.4.5 Polygonal Mesh . . . . . . . . 5.5 3D Affine

You May Also Find These Documents Helpful

  • Good Essays

    Notes

    • 5379 Words
    • 22 Pages

    7) What species is represented by the following information? p+ = 17 A) Cl n° = 18 e- = 18 B) Kr C) Ar+ D) ClE) Ar…

    • 5379 Words
    • 22 Pages
    Good Essays
  • Satisfactory Essays

    Notes

    • 462 Words
    • 2 Pages

    Assignment: 1. Read How to Read Literature like a Professor (see below for link to the book)first, and complete the following: Take notes that will help you to remember what the main idea of each chapter is. Remember taking notes does not equate copying the author’s words. Your notes will be graded 2. For each chapter, other than the interludes and the conclusion, make one connection from something in the chapter to any book, movie, song, TV show, etc. For instance, for the chapter on quests, you can talk about a movie that is a symbolic quest. These connections should be around a paragraph each. 3. Read The Road by Cormac McCarthy and answer the questions provided. These responses should contain details from the novel, including a quote as support or illustration of your point. Note: Watching the movie will not help you with this assignment.…

    • 462 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    Notes

    • 1570 Words
    • 7 Pages

    Celia was the name of a young female slave, who came to work for a prominent Missouri family called the Newsoms. Robert Newsom, a plantation owner in Callaway, Missouri, purchased her at age 14. Newsom was recently widowed and it seems he purchased Celia, looking for sex. He started raping her after being brought back to the farm. From then on, Newsom "visited" Celia often in a cabin he provided for her which was very close to the main household. Over the years, Celia had two children with Newsom, which he also considered "his property". The interesting thing about Celia’s story is that it recounts a tale of social strife and clearly indicates the fact that slaves were playing with a heavily stacked deck in relation to their Caucasian opposites.…

    • 1570 Words
    • 7 Pages
    Good Essays
  • Satisfactory Essays

    Notes

    • 298 Words
    • 2 Pages

    This list is not exhaustive; any additional research gathered needs to be included to enhance your answer.…

    • 298 Words
    • 2 Pages
    Satisfactory Essays
  • Satisfactory Essays

    Notes

    • 910 Words
    • 4 Pages

    Sacraments call our attention to and remind us of a reality of god that is always present, but se may not always realize.…

    • 910 Words
    • 4 Pages
    Satisfactory Essays
  • Satisfactory Essays

    Notes

    • 295 Words
    • 2 Pages

    How do clinical psychologists help their patients with mental illness?: They help them solve their problems by changing harmful or ineffective behaviors.…

    • 295 Words
    • 2 Pages
    Satisfactory Essays
  • Powerful Essays

    wall board

    • 12820 Words
    • 52 Pages

    . . . . . . . . . . . . . . .…

    • 12820 Words
    • 52 Pages
    Powerful Essays
  • Satisfactory Essays

    2.2.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…

    • 7804 Words
    • 32 Pages
    Satisfactory Essays
  • Good Essays

    Notes

    • 861 Words
    • 4 Pages

    Explore how perceptions of Belonging and not belonging can be influenced by connections to places.…

    • 861 Words
    • 4 Pages
    Good Essays
  • Good Essays

    NOTES

    • 1214 Words
    • 4 Pages

    On April 16th, 1963, Martin Luther King Junior wrote one of the most memorable letters in the history of Civil Rights movement. He did so while being imprisoned in Alabama. On the fourth day of his incarceration, he produced the most beautiful prose I have ever read, in order to deliver a convincing and righteous message. Four days before the letter was written, King, and many other civil rights protestors, were arrested for failing to obtain a permit for a parade. They were arrested while participating in a peaceful demonstration referred to as the “Birmingham Campaign.” In his letter, King states that he was compelled to “bring the gospel of freedom” wherever injustice exists. The campaign was mainly designed to bring attention to the awful treatment blacks were experiencing within the city of Birmingham, Alabama. This was Martin Luther King’s thirteenth arrest and probably most “important” one, as well.…

    • 1214 Words
    • 4 Pages
    Good Essays
  • Good Essays

    Notes

    • 925 Words
    • 4 Pages

    Although Will Haygood and Zinczenko both address the topic of dieting and obesity with well thought out arguments. I find Haygood’s most persuasive because of the people he wrote about life story and what can happen if you don’t pay attention to the right foods to eat and exercise.…

    • 925 Words
    • 4 Pages
    Good Essays
  • Satisfactory Essays

    Notes

    • 270 Words
    • 2 Pages

    Question: Evaluate the relative importance of the following as factors prompting Americans to rebel in 1776: *parliamentary taxation *British military measures *restrictions of civil liberties *the legacy of colonial religious and political ideas.…

    • 270 Words
    • 2 Pages
    Satisfactory Essays
  • Satisfactory Essays

    Basic Fluid Mechanics

    • 53370 Words
    • 214 Pages

    . . . . . . . . . . . . . . . . . . . . . . . . .…

    • 53370 Words
    • 214 Pages
    Satisfactory Essays
  • Powerful Essays

    1 FX Exotic Options - an overview 1.1 Introduction . . . . . . . . . . . . . . . . 1.2 Barrier options . . . . . . . . . . . . . . 1.2.1 Barrier Options Market . . . . . 1.2.2 Pricing Barrier Options . . . . . . 1.3 Digital Options . . . . . . . . . . . . . . 1.3.1 Payoff . . . . . . . . . . . . . . . 1.3.2 Pricing . . . . . . . . . . . . . . . 1.4 One-touch digital options . . . . . . . . . 1.4.1 Payoff . . . . . . . . . . . . . . . 1.4.2 Pricing one-touch digital options 1.5 Double Barrier Options . . . . . . . . . . 1.6 Other Exotic Options . . . . . . . . . . . 7 7 8 8 9 15 15 15 16 16 17 18 19 21 21 24 27 30 31 34 36…

    • 7334 Words
    • 30 Pages
    Powerful Essays
  • Powerful Essays

    The Art of Computer Programming

    • 40124 Words
    • 161 Pages

    [Buch76] Buchberger, Bruno, Theoretical basis for the reduction of polynomials to canonical form, SIGSAM Bulletin 39 (Aug. 1976), 19–24.…

    • 40124 Words
    • 161 Pages
    Powerful Essays