2D transformations Homogeneous coordinates

10/5/99


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Table of Contents

2D transformations Homogeneous coordinates

Uses of Transformations

Transformations

Transformations

Transformations

Transformations and matrices

Transformations and matrices

Problem

Homogeneous coordinates

Homogeneous coordinates

Homogeneous Transformations

Homogeneous Transformations

Matrices of basic transformations

Homogeneous line equation

Homogeneous line equation

Intersection of two lines

How to intersect two lines

Line through two points

Intersection of two lines

Mapping quads to quads

Transform from 3 points

Mapping quads to quads

Intersections of sides and diagonals

Mapping rectangles to quads

Points at infinity

Mapping rectangles to quads

Texture Mapping

Texture Mapping

Putting it all together

Implementation

Inverse matrix

Author: Denis Zorin

Email: dzorin@mrl.nyu.edu