# Geometric Transformations

## Table of Contents

#### How Are Transformations Used in Computer Graphics? Problem: How to move an object Cartesian Coordinate Spaces Moving an Object in a Coordinate System Vectors & Vector Space 2D Object Definition 2D to 3D Object Definition Moving Objects with Vectors Adding Vectors Visually Scalar Multiplication Algebraic Properties of Vectors The Dot Product Rule for Dot Product Finding the Length of a Vector Finding the Angle Between Two Vectors More Uses of the Dot Product Basic Transformations of the Plane Translation Scaling Rotation Sets of Linear Equations and Matrices Types of Transformations Some Important Matrices Two Other Matrices Matrix-Vector Multiplication Finding a Matrix Combining Transformations Homogenous Coordinates What is ? Homogenous Coordinate Transformations Composition of 2D Transforms Scale, Rotate, and Translate Commutative and Non-Commutative Combinations of Transformations in 2D 3D Basic Transformations (right-handed coordinate system) Homogeneous Coordinates Finding a Matrix--Solutions Addendum--Matrix Notation But, There's a Problem... Solution to Notational Problem Homogeneous Coordinate Example Matrix Notation and Composition

Next

##### sl@cs.brown.edu

Generated with CERN WebMaker