How to calculate distance between two rectangles? (Context: a game in Lua.)

Question

Given two rectangles with x, y, width, height in pixels and a rotation value in degrees -- how do I calculate the closest distance of their outlines toward each other?

Answer 1

This question depends on what kind of distance. Do you want, distance of centers, distance of edges or distance of closest corners?

I assume you mean the last one. If the X and Y values indicate the center of the rectangle then you can find each the corners by applying this trick

//Pseudo code
Vector2 BottomLeftCorner = new Vector2(width / 2, heigth / 2);
BottomLeftCorner = BottomLeftCorner * Matrix.CreateRotation(MathHelper.ToRadians(degrees));
//If LUA has no built in Vector/Matrix calculus search for "rotate Vector" on the web.
//this helps: http://www.kirupa.com/forum/archive/index.php/t-12181.html

BottomLeftCorner += new Vector2(X, Y); //add the origin so that we have to world position.

Do this for all corners of all rectangles, then just loop over all corners and calculate the distance (just abs(v1 - v2)).

I hope this helps you