Rectangle rotation around clipping rectangle center

0
votes

I have two rectangles where one is a clipping for the other one. Now I want to rotate the bigger rectangle around the center of the clipping rectangle and adjust x/y values.

enter image description here

How can I calculate the new x/y values after rotation?

I actually just want to rotate the x/y of the bigger box around the center of the smaller box. So the x/y point of the bigger box is relative to the top/left point of the smaller box. I have the width and height of the smaller box so I can calculate x/y point of the big box relative to the center of small box. The angle to rotate is in degrees. The rotation can be any degree, for example 10.

3
mathgeometry
What do you mean by " one is a clipping for the other one" ? – Yunnosch
What is the significance of the inner rectangle? Does it ever make a difference from just rotating around the point c? When? How? – Yunnosch
How far have you got yourself? Can you calculate the distance and angle of (x,y) to c? You do know the coordinates of c, don't you? – Yunnosch
What is the angle by which you want to rotate? Looks like roughly 26.31 degrees. Is the angle to rotate by in degrees or in radians? – Yunnosch
I actually just want to rotate the x/y of the bigger box around the center of the smaller box. so the x/y point of the bigger box is relative to the top/left point of the smaller box. I have the Width and height of the smaller box so i can calculate y/x big box relative to the center of small box. The angle to rotate is in degrees. The rotation can be any degree, for example 10. – Adnan Mujkanovic

3 Answers

0
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If you want to rotate a given point P around a point C, which are defined in the same coordinate system you can use a simple rotation matrix. Calculate the P coordinates with respect to C (subtraction), then apply rotation with the matrix and go back to original coordinates by adding C again.

enter image description here

1
votes

You can do as follows:

  • determine the angle by which you want to rotate, make sure it suitable for the trigonometric functions (sin(), cos(), ...), i.e. right angle is usually Pi/2
  • in case of rotating counterclockwise, it is negative
  • determine the coordinates of c, as cx,cy
  • process each of the corners of the rectanlge, one by one, for a total of four
  • for each corner P, currently at coordinates px,py and to move to px2,py2
    • determine angle between current P and C, using atan2(py-cy, px-cx)
    • to get from degrees to radians (for use with trigonometry) calculate radians=(pi*degrees)/180.0
    • add the desired rotation angle to that current angle, to get newangle
    • determine the distance of current P to C, sqrt((px-cx)(px-cx) + (py-cy)(py-cy))
    • multiply the distance (which is not changing by rotation), with the appropriate trigonometric function
    • px2 = distance * cos(newangle)
    • py2 = distance * sin(newangle)
0
votes

All that matters is the coordinates of the rotation center and the angle.

The most compact formulation is by means of complex numbers (of which I hope you have some understanding; you actually don't need a complex data type, you can expand the formulas).

Let C be the center and α the angle. Then for any point P, the image Q is given by

Q = (P - C) cis(α) + C

where cis(α) = cos(α) + i sin(α).

The inverse rotation is simply given by

P = (Q - C) cis(-α) + C.