CODEWITHSUNDEEP
matrixrotationgeometry2d
Skullbox
Skullbox

Reputation: 441

Rotating a matrix in a non standard 2d plane

I have some problems figuring out how to rotate a matrix in a 2d plane since my coordinate system is not a standard mathematical one, my plane has an inverted y-axis, meaning higher y value is lower on the screen. I also want to rotate the matrix clockwise instead of the standard anticlockwise.

So if I try to illustrate how I want it to work:

O = origin X = points to rotate

Then 0 degrees looks like this:

XXX
 O

I want 90 degrees to look like this:

  X
 OX
  X

180 degrees should look like this:

 O
XXX

270 degrees should look like this:

X
XO
X

Any ideas on how to calculate the new x and y for a point after rotating in this plane?

Upvotes: 2

Views: 877

Answers (1)

Keith
Keith

Reputation: 6834

The clockwise rather than anti-clockwise just means flipping the sign on the angle.

To get the full result, we just transform into 'standard coords', do the rotation, and transform back:

The coordinate transform and its inverse is:

(x') = ( 1  0 ) (x)
(y')   ( 0 -1 ) (y)

A rotation anti-clockwise is:

(x') = (  cos(angle) -sin(angle) ) (x)
(y')   (  sin(angle)  cos(angle) ) (y)

So a rotation clockwise is:

(x') = (  cos(angle)  sin(angle) ) (x)
(y')   ( -sin(angle)  cos(angle) ) (y)

Altogether this gives:

(x') = ( 1  0 )(  cos(angle)  sin(angle) ) ( 1  0 )(x)
(y')   ( 0 -1 )( -sin(angle)  cos(angle) ) ( 0 -1 )(y)

Multiply the matrices to get:

(x') = (  cos(angle)  sin(angle) ) (x)
(y')   ( -sin(angle)  cos(angle) ) (y)

Now, as you may by now have realized, this is actually the same matrix as rotating 'standard coords' in the anti-clockwise direction.

Or in code:

// Angle in radians
double x2 =  cos(angle) * x1 - sin(angle) * y1;
double y2 =  sin(angle) * x1 + cos(angle) * y1;

For example, if angle is 180 degrees, cos(angle) is -1, and sin is 0, giving:

double x2 =  -x1;
double y2 =  -y1;

Upvotes: 2

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