Ask you a digital image geometric transformation problem. . . .

liudexu

If any image is rotated 60 degrees counterclockwise around the point P (x, y) = (100,260), find its geometric transformation formula.

azqkmo

First shift the origin to (100, 260)
Ie A = 1 0 -100
    0 1 -260
    0 0 1
Then rotate
B = cos60 -sin60 0
  sin60 cos60 0
  0 0 1
Then pan back
C = 1 0 100
    0 1 260
    0 0 0
Converted to C * B * A
Note that the homogeneous coordinates used [x, y, 1] '

wa7911412yy

Good good

xrn1009

Calculate the rotation and translation separately, calculate the coordinates of this point before and after the rotation, and then use it as the basis for translation

vikingwo

x,y represent the original image coordinates, and X,Y represent the new image coordinates.

X = (x-100) * cos60-(y-260) * sin60 + 100; (1)
Y = (x-100) * sin60 + (y-260) * cos60 + 260; (2)

Generally, the rotated image will be larger than the original image, and its width and height can be calculated from the four vertices of the original image.
From (1) and (2), we can inversely deduce the corresponding position of each point in the rotated image in the original image.

x = (X-100) * cos60 + (Y-260) * sin60 + 100; (3)
y = (Y-260) * cos60-(X-100) * sin60 + 260; (4)

yixiang

It's not done with the matrix