$How do I negate the effect that the rotation of a plane has on a rectangle?$

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$How do I negate the effect that the rotation of a plane has on a rectangle?$

I have a map (the plane) which can be rotated 360 degrees. When this happens, the rectangle shape that I'm drawing on the map also gets rotated along with the plane. I would like to negate this rotation and have the rectangle drawn as if the plane wasn't rotated.

So essentially, I want the rectangle to look like this image:

Check out the gif in the attachments to see a demo of the actual behavior.

Geometry

Nkalpak

19

Matchmaticians How do I negate the effect that the rotation of a plane has on a rectangle? File #1

File #1 (gif)

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Daniel90

0

The question is vague. What do you mean by "I would like to negate this rotation and have the rectangle drawn as if the plane wasn't rotated"? Are you talking about doing it on google maps or something, or are you talking about a mathematical way of doing it?
Nkalpak

0

I've added the gif and image as a way to visualize the problem. I'm not looking for a solution related to Google Maps, I'm looking for the mathematical way of doing it, I would then translate that to my specific implementation.

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Daniel90

0

The question is vague. What do you mean by "I would like to negate this rotation and have the rectangle drawn as if the plane wasn't rotated"? Are you talking about doing it on google maps or something, or are you talking about a mathematical way of doing it?
Nkalpak

0

I've added the gif and image as a way to visualize the problem. I'm not looking for a solution related to Google Maps, I'm looking for the mathematical way of doing it, I would then translate that to my specific implementation.

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I would define the rectangle by the cooridnates of its lower left (x1, y1) and upper right corner (x2,y2). Any rectangle can be represented this way. I specity the rotation by angle $\theta$.

When a point (x,y) gets rotated by angle $\theta$, its new coordinates are:
\[x\cos(\theta) - y\sin(\theta) \text{and} y\cos(\theta) + x\sin(\theta)\]

To put the rectangle back, you need to rotate its coordinates by angle $-\theta$. Thus, to put the aforementioned rectangle back where it was before rotation the lower left corner will be at

x-coordinate: $x_1\cos(-\theta) - y_1\sin(-\theta) = x_1\cos(\theta) + y_1\sin(\theta)$
y-coordinate: $ y\cos(-\theta) + x\sin(-\theta) = y\cos(\theta) - x\sin(\theta)$

and similarly you can compute the coordinates for the upper right corner.

Shadmehr

29

$How do I negate the effect that the rotation of a plane has on a rectangle?$

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