JavaScript image processing: affine transformations

Objective

In a previous article, we explained the image pyramid, and this article is about affine transformations.

An imitation?!

Any affine transformation can be converted to, multiplied by a matrix (linear variation), plus a vector (translational change).

In fact, affine is the transformation relation of two pictures.

For example, we can use the affine transformation of the Image: Scaling, rotation, translation and so on.

A mathematical problem

Before we solve the affine problem, let's do a math problem.

As in the figure, for the point (x1, y1), rotate an angle relative to the origin a, then where is this point?

We turn the coordinate system into polar coordinate system, then the point (x1, y1) becomes (r,β), and the rotation becomes (r,α+β).

Back to the rectangular coordinate system, the rotated point becomes (cos (α + β) * r, sin (α + β) * r).