- 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

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