Here are three functions from my open source libraries. The functions are fully tested in Java but the formulae can be easily translated to any language.

The signatures are:

public static float getAngleFromPoint(final Point centerPoint, final Point touchPoint)

public static float getTwoFingerDistance(float firstTouchX, float firstTouchY, float secondTouchX, float secondTouchY)

Point getPointFromAngle(final double angle, final double radius)

This solution assumes that the pixel density is evenly spaced.
Before rotating the object do the following:

Use getAngleFromPoint to calculate the angle from the center to the upper right corner (lets say this returns 20 degrees) meaning that the upp left corner is -20 degrees or 340 degrees.

Use the getTwoFingerDistance to return the diagonal distance between the center point and the upper right corner (this distance should obvoiusly be the same to all corners, This distance will be used in the next calculation).

Now lets say we rotate the object clockwise by 30 degrees. We now know that the upper right corner must be at 50 degrees and the upper left corner is at 10 degrees.

You should now be able to use the getPointFromAngle function on the upper left and upper right corner. using the radius returned from step 2.
The X position multiplied by 2 from the upper right corner should give you the new width and the Y position times 2 from the upper left corner should give the the new height.

These above 4 steps should be put into conditions based upon how far you have rotated your object other wise you may return the height as the width and the width as the height.

Bare in mind the angle functions are expressed in factors of 0-1 instead of 0-360 (just multiply or divide by 360 where appropriate):

//Gets an angle from two points expressed as a factor of 0 -1 (0 being 0/360, 0.25 being 90 degrees etc)

```
public float getAngleFromPoint(final Point centerPoint, final Point touchPoint) {
float returnVal = 0;
//+0 - 0.5
if(touchPoint.x > centerPoint.x) {
returnVal = (float) (Math.atan2((touchPoint.x - centerPoint.x), (centerPoint.y - touchPoint.y)) * 0.5 / Math.PI);
}
//+0.5
else if(touchPoint.x < centerPoint.x) {
returnVal = (float) (1 - (Math.atan2((centerPoint.x - touchPoint.x), (centerPoint.y - touchPoint.y)) * 0.5 / Math.PI));
}//End if(touchPoint.x > centerPoint.x)
return returnVal;
}
```

//Measures the diagonal distance between two points

```
public float getTwoFingerDistance(final float firstTouchX, final float firstTouchY, final float secondTouchX, final float secondTouchY) {
float pinchDistanceX = 0;
float pinchDistanceY = 0;
if(firstTouchX > secondTouchX) {
pinchDistanceX = Math.abs(secondTouchX - firstTouchX);
}
else if(firstTouchX < secondTouchX) {
pinchDistanceX = Math.abs(firstTouchX - secondTouchX);
}//End if(firstTouchX > secondTouchX)
if(firstTouchY > secondTouchY) {
pinchDistanceY = Math.abs(secondTouchY - firstTouchY);
}
else if(firstTouchY < secondTouchY) {
pinchDistanceY = Math.abs(firstTouchY - secondTouchY);
}//End if(firstTouchY > secondTouchY)
if(pinchDistanceX == 0 && pinchDistanceY == 0) {
return 0;
}
else {
pinchDistanceX = (pinchDistanceX * pinchDistanceX);
pinchDistanceY = (pinchDistanceY * pinchDistanceY);
return (float) Math.abs(Math.sqrt(pinchDistanceX + pinchDistanceY));
}//End if(pinchDistanceX == 0 && pinchDistanceY == 0)
}
```

//Get XY coordinates from an angle given a radius (The angle is expressed in a factor of 0-1 0 being 0/360 degrees and 0.75 being 270 etc)

```
public Point getPointFromAngle(final double angle, final double radius) {
final Point coords = new Point();
coords.x = (int) (radius * Math.sin((angle) * 2 * Math.PI));
coords.y = (int) -(radius * Math.cos((angle) * 2 * Math.PI));
return coords;
}
```

These code snippets are from my open source libraries: https://bitbucket.org/warwick/hgdialrepo and https://bitbucket.org/warwick/hacergestov2.
One is a gesture library for Android and the other is a dial control for Android. There is also an OpenGLES 2.0 implementation of the dial control at: https://bitbucket.org/warwick/hggldial