What is an affinine transform and an affinine transform matrix ?)

The affine transform can be understood as the scaled, rotated, and obtained value of the new coordinate after translation. The value of the original coordinate in the new coordinate field after the rotation, rotation, and translation of the coordinate axis. As shown in, the coordinate axes of the XY coordinate system rotate θ and the coordinate origin moves (x0, y0 ). X, Y in xy Coordinate System ･ Cos θ-y then ･ Sin θ + x0y = x ･ sin θ + Y then ･ Cos θ + y0 is written as a matrix

| X | | COS θ Sin θ | | X0 | | | = | X Y | * | | + | | | Y | |-Sin θ cos θ | | Y0 | In order to move the value of the origin point to the matrix, you can add a redundant equation that does not affect the solution of the original equations. So we can write x = x bytes ･ Cos θ-y then ･ Sin θ + x0y = x ･ sin θ + Y then ･ Cos θ + Y01 = x defaults 0 + Y ･ 0 + 1 is written as a matrix | x | | COS θ Sin θ 0 | | Y | = | x Y 1 | * |-sin θ cos θ 0 | | 1 | | X0 y0 1 |

This matrix is the Helmert transformation matrix. Considering that the contraction rate of the Original Coordinate System on the X and Y axes can be expressed as λ x and λ y, the Helmert transformation equations can be changed to X = (λ x) X Branch ･ Cos θ-(λ y) y Branch ･ Sin θ + x0y = (λ x) x θ sin θ + (λ y) y then ･ Cos θ + y0 are written as the third-order matrix as | x | | (λ x) COS θ ( λ x) sin θ 0 | | Y | = | x Y 1 | * | (λ y)-sin θ (λ y) COS θ 0 | | 1 | | X0 y0 1 | this matrix is the affine transformation matrix, which is an affine matrix.