Question

I need to find an algorithm which determines a relationship between a square and rectangle. It must be able to determine if:

• The square is completely inside the rectangle
• The square is partially inside (overlaps) the rectangle
• Square’s corner only touches a rectangle’s corner
• Square’s edge is on the rectangle’s edge

And here are the inputs (given values) that will help us to extract a mathematical formula for each case:

• x coordinate of the center of the square = squareX
• y coordinate of the center of the square = squareY
• width of the square = squareW
• x coordinate of the center of the rectangle = recX
• y coordinate of the center of the rectangle = recY
• width of the rectangle = recW
• length of the rectangle = recL

P.S: Rectangle’s sizes are always bigger than the square’s width.

I will write the code in Java once we can extract an algorithm using mathematical operations.

Edit:

For the case of corners in touch, here is the code I wrote, and it works (Math.abs means the absolute value):

((Math.abs(Math.abs(recX-squareX)-(recW+squareW)/2))<=0.001) && ((Math.abs(Math.abs(recY-squareY)-(recL+squareW)/2))<=0.001)

Answer 1

updated for doubles

double dx = Math.abs(rectX - squareX);
double dy = Math.abs(rectY - squarey);
double dw2 = (rectW + squareW) / 2;
double dh2 = (rectL + squareW) / 2;

if (Double.compare(dx, dw2) == 0 && Double.compare(dy, dh2) == 0)
    return CORNER_TOUCH;
else if (Double.compare(dx, dw2) > 0 || Double.compare(dy, dh2) > 0)
    return OUTSIDE;
else if (Double.compare(dx, dw2) == 0 || Double.compare(dy, dh2) == 0)
    return EDGE_TOUCH;
else if (Double.compare(dx, rectW - dw2) <= 0 &&
        Double.compare(dy, rectL - dh2) <= 0)
    return INSIDE;
else 
    return OVERLAPS;