Question

Lets say I’ve got two squares and I know their positions, a red and blue square:

redTopX;
redTopY;
redBotX;
redBotY;
blueTopX;
blueTopY;
blueBotX;
blueBotY;

Now, I want to check if square blue resides (partly) within (or around) square red. This can happen in a lot of situations, as you can see in this image I created to illustrate my situation better:
alt text http://www.feedpostal.com/etc/ranges.gif

Note that there’s always only one blue and one red square, I just added multiple so I didn’t have to redraw 18 times.

My original logic was simple, I’d check all corners of square blue and see if any of them are inside square red:

if (
((redTopX >= blueTopX) && (redTopY >= blueTopY) && (redTopX <= blueBotX) && (redTopY <= blueBotY)) || //top left
((redBotX >= blueTopX) && (redTopY >= blueTopY) && (redBotX <= blueBotX) && (redTopY <= blueBotY)) || //top right
((redTopX >= blueTopX) && (redBotY >= blueTopY) && (redTopX <= blueBotX) && (redBotY <= blueBotY)) || //bottom left
((redBotX >= blueTopX) && (redBotY >= blueTopY) && (redBotX <= blueBotX) && (redBotY <= blueBotY)) //bottom right
) {
    //blue resides in red
}

Unfortunately, there are a couple of flaws in this logic. For example, what if red surrounds blue (like in situation 1)?

I thought this would be pretty easy but am having trouble coming up with a good way of covering all these situations.. can anyone help me out here?

Regards,
Tom

Answer 1

A test that checks whether red rectangle resides completely outside the blue rectangle looks as follows

bool outside = 
  redBotX > blueTopX || redTopX < blueBotX || 
  redBotY > blueTopY || redTopY < blueBotY;

Now, the negative of that will tell you whether red rectangle intersects the blue rectangle

bool intersects =
  !(redBotX > blueTopX || redTopX < blueBotX || 
    redBotY > blueTopY || redTopY < blueBotY);

If you wish, you can apply the De Morgan rule and rewrite it as

bool intersects =
  redBotX <= blueTopX && redTopX >= blueBotX && 
  redBotY <= blueTopY && redTopY >= blueBotY;

Of course, the above tests assume that the coordinates are “normalized*, i.e.

assert(redBotX <= redTopX && redBotY <= redTopY);
assert(blueBotX <= blueTopX && blueBotY <= blueTopY);

Also, the comparisons might be strict or non-strict depending on whether you consider touching rectangles as intersecting or not.

EDIT: I see that you use a different convention for rectangle coordinates: Top is the lower coordinate and Bot is the higher one, i.e.

assert(redTopX <= redBotX && redTopY <= redBotY);
assert(blueTopX <= blueBotX && blueTopY <= blueBotY);

To handle this case you just need to swap the Bot and Top coordinates in all conditions. For example, the last one will now look as follows

bool intersects =
  redTopX <= blueBotX && redBotX >= blueTopX && 
  redTopY <= blueBotY && redBotY >= blueTopY;