Computer Graphics Lecture Notes

Computer Graphics Lecture Notes - Computer Graphics Lecture...

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Unformatted text preview: Computer Graphics Lecture Notes CSC418 / CSCD18 / CSC2504 Computer Science Department University of Toronto Version: November 24, 2006 Copyright c circlecopyrt 2005 David Fleet and Aaron Hertzmann CSC418 / CSCD18 / CSC2504 CONTENTS Contents Conventions and Notation v 1 Introduction to Graphics 1 1.1 Raster Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Basic Line Drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Curves 4 2.1 Parametric Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Tangents and Normals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Rendering Curves in OpenGL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Transformations 10 3.1 2D Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Affine Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.3 Homogeneous Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Uses and Abuses of Homogeneous Coordinates . . . . . . . . . . . . . . . . . . . 14 3.5 Hierarchical Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.6 Transformations in OpenGL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4 Coordinate Free Geometry 18 5 3D Objects 21 5.1 Surface Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.2 Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.3 Surface Tangents and Normals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.3.1 Curves on Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.3.2 Parametric Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.3.3 Implicit Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.4 Parametric Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.4.1 Bilinear Patch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.4.2 Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.4.3 Surface of Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.4.4 Quadric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.4.5 Polygonal Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.5 3D Affine Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.6 Spherical Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.6.1 Rotation of a Point About a Line . . . . . . . . . . . . . . . . . . . . . . . 29 5.7 Nonlinear Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Nonlinear Transformations ....
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This note was uploaded on 09/01/2010 for the course IT itp taught by Professor Nitin during the Spring '10 term at Vlerick Leuven Gent Management School.

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Computer Graphics Lecture Notes - Computer Graphics Lecture...

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