Understanding a transformation matrix
A transformation matrix is a powerful mathematical tool. It can perform various geometric transformations, such as rotation, scaling, and shearing, on objects or points in space. By multiplying a vector or set of coordinates by a transformation matrix, you can achieve complex transformations with ease and precision. This simplifies tasks such as rendering 3D graphics, image processing, and robotics.
Figure 4.3 shows four common 2D transformation matrices:
Figure 4.3 – Transformation matrices
When multiplying by a matrix, these transformation matrices will “distort” or “transform” that matrix. Let’s first learn about their mathematical properties, and then I will explain why we want to do that. If the transformation matrix is [w 0 0 h], it will scale the original matrix up or down by w and h. Let’s review each in detail:
- The first one is “...
