Affine transformations are a fundamental concept in geometry and computer graphics. They are transformations that preserve lines and parallelism, meaning that parallel lines remain parallel after the transformation. There are four primary types of affine transformations:
1. Translation
Translation is the simplest affine transformation. It involves moving every point in a space by a fixed distance and direction.
Examples:
- Moving a shape 5 units to the right.
- Shifting a point (2, 3) to (5, 7).
2. Scaling
Scaling involves changing the size of an object. It can be uniform, where all dimensions are scaled by the same factor, or non-uniform, where different dimensions are scaled by different factors.
Examples:
- Doubling the size of a square.
- Stretching a rectangle horizontally while keeping its height constant.
3. Rotation
Rotation involves turning an object around a fixed point called the center of rotation. The angle of rotation determines the amount of turning.
Examples:
- Rotating a triangle by 90 degrees counterclockwise.
- Spinning a wheel around its axle.
4. Shear
Shearing involves distorting an object in a particular direction while keeping one line fixed. It can be horizontal or vertical, depending on the direction of distortion.
Examples:
- Transforming a rectangle into a parallelogram by shearing it horizontally.
- Distorting a square into a rhombus by shearing it vertically.
These four types of affine transformations can be combined to create more complex transformations. For example, you can rotate an object, then scale it, and finally translate it to a new position.
