Affine Transformations
Overview
An affine transformation is a function between two different coordinate systems (or affine spaces) which preserves certain properties. These properties include:
- Points (points that exists in the first coordinate system will exist in the second coordinate system)
- Straight lines (lines that are straight in the first coordinate system are straight in the second)
- Parallelism (lines that are parallel in the first coordinate system are parallel in the second)
An affine transformation can encompass the following "basic" modifications:
- Translation
- Reflection
- Scaling
- Rotation
- Shearing
The Transformation Matrix
A 2D affine transformation matrix is always in the form: