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Computer Graphics Lecture Notes

Computer Graphics Lecture NotesCSC418 / CSCD18 / CSC2504 Computer Science DepartmentUniversity of TorontoVersion: November 24, 2006 Copyrightc 2005 David Fleet and Aaron HertzmannCSC418 / CSCD18 / CSC2504 CONTENTSC ontentsConventions and Notationv1 Introduction to Displays .. Line Drawing .. curves .. and Normals .. curves in OpenGL .. Transformations .. Transformations .. Coordinates .. and Abuses of Homogeneous Coordinates .. Transformations .. in OpenGL .. 164 Coordinate Free Geometry1853D Representations .. Tangents and Normals .. on Surfaces .. Form .. Form .. Surfaces .. Patch .. of Revolution .. Mesh .. Affine Transformations .. Coordinates .. of a Point About a Line.

CSC418 / CSCD18 / CSC2504 Curves 2 Curves 2.1 Parametric Curves There are multiple ways to represent curves in two dimensions: •Explicit: y = f(x), given x, find y. Example: The explicit form of a line is y = mx + b. There is a problem with this representation–what about vertical lines? •Implicit: f(x,y) = 0, or in vector form, f(¯p ...

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