Calculate Bounding box coordinates from a rotated rectangle

actionscript-3bounding-boxgeometrymathrotation

I have the coordinates of the top left point of a rectangle as well as its width, height and rotation from 0 to 180 and -0 to -180.

I am trying to get the bounding coordinates of the actual box around the rectangle.

What is a simple way of calculating the coordinates of the bounding box

Min y, max y, min x, max x?

The A point is not always on the min y bound, it can be anywhere.

I can use matrix the transform toolkit in as3 if needed.

Best Answer

Transform the coordinates of all four corners
Find the smallest of all four x's as min_x
Find the largest of all four x's and call it max_x
Ditto with the y's
Your bounding box is (min_x,min_y), (min_x,max_y), (max_x,max_y), (max_x,min_y)

AFAIK, there isn't any royal road that will get you there much faster.

If you are wondering how to transform the coordinates, try:

x2 = x0+(x-x0)*cos(theta)+(y-y0)*sin(theta)
y2 = y0-(x-x0)*sin(theta)+(y-y0)*cos(theta)

where (x0,y0) is the center around which you are rotating. You may need to tinker with this depending on your trig functions (do they expect degrees or radians) the sense / sign of your coordinate system vs. how you are specifying angles, etc.

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Calculate the distance between two coordinates by latitude and longitude, including a Javascript implementation.

West and South locations are negative. Remember minutes and seconds are out of 60 so S31 30' is -31.50 degrees.

Don't forget to convert degrees to radians. Many languages have this function. Or its a simple calculation: radians = degrees * PI / 180.

function degreesToRadians(degrees) {
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}

function distanceInKmBetweenEarthCoordinates(lat1, lon1, lat2, lon2) {
  var earthRadiusKm = 6371;

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  lat2 = degreesToRadians(lat2);

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Here are some examples of usage:

distanceInKmBetweenEarthCoordinates(0,0,0,0)  // Distance between same 
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0

distanceInKmBetweenEarthCoordinates(51.5, 0, 38.8, -77.1) // From London
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5918.185064088764

R – How to find a tight-fitting, axis-aligned, bounding box of a rotated ellipse in AS3

I assumed atan(x) and cot(x) were interchangeable - turns out they're not. Who would've thought ;)

My working AS3 code ended up looking like this:

var r_max:uint = 45;
var r_min:uint = 20;
var rot:Number = ellipse.rotation * (Math.PI / 180);
var t_nil:Number = Math.atan( -r_min * Math.tan(rot) / r_max);
var t_inf:Number = Math.atan(r_min * (Math.cos(rot) / Math.sin(rot)) / r_max);
var rect_width:Number = 2 * (r_max * Math.cos(t_nil) * Math.cos(rot) - r_min * Math.sin(t_nil) * Math.sin(rot));
var rect_height:Number = 2* (r_min * Math.sin(t_inf) * Math.cos(rot) + r_max * Math.cos(t_inf) * Math.sin(rot));

Best Answer

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