Computer Graphics

Chapter 2

Transforms in 2D

2.1     Vectors and matrices

2.2     Transforms in 2D

2.3     Basic linear transformations

2.3.1     Scale transformation

2.3.2     Reflect transformation

2.3.3     Rotate transformation

2.3.4     Shear transformation

2.3.5     Composite transformations

2.4     Homogeneous coordinates

2.1   Vectors and matrices

We start with a 2-dimensional case because 1D is just too simple and 3D is much more complex. We will study some important concepts and notions in a 2-dimensional case. They are easy to explain because in 2D all can be simply drawn on a sheet of paper.

A two-dimensional coordinate space is a plane with an attached coordinate system. The system allows us to use coordinates instead of points. In this case ...