graphics - Determine if line intersects CGRect

Question

What is the most efficient way to determine if a line intersects a rectangle?

I'm looking for something similar to this:

CGPoint startLine = CGPointMake(5.0f,5.0f);
CGPoint endLine = CGPointMake(25.0f,25.0f);

CGRect intersectingRect = CGRectMake(10.0f,10.0f,50.0f,50.0f);

if (CGRectContainsLine(intersectingRect,startLine,endLine)) { //true
    //line intersects rectangle
}

Answer 1

There's nothing built in, but this ought to do it:

BOOL RectContainsLine(CGRect r, CGPoint lineStart, CGPoint lineEnd)
{
    BOOL (^LineIntersectsLine)(CGPoint, CGPoint, CGPoint, CGPoint) = ^BOOL(CGPoint line1Start, CGPoint line1End, CGPoint line2Start, CGPoint line2End)
    {
        CGFloat q =
            //Distance between the lines' starting rows times line2's horizontal length
            (line1Start.y - line2Start.y) * (line2End.x - line2Start.x)
            //Distance between the lines' starting columns times line2's vertical length
            - (line1Start.x - line2Start.x) * (line2End.y - line2Start.y);
        CGFloat d =
            //Line 1's horizontal length times line 2's vertical length
            (line1End.x - line1Start.x) * (line2End.y - line2Start.y)
            //Line 1's vertical length times line 2's horizontal length
            - (line1End.y - line1Start.y) * (line2End.x - line2Start.x);

        if( d == 0 )
            return NO;

        CGFloat r = q / d;

        q =
            //Distance between the lines' starting rows times line 1's horizontal length
            (line1Start.y - line2Start.y) * (line1End.x - line1Start.x)
            //Distance between the lines' starting columns times line 1's vertical length
            - (line1Start.x - line2Start.x) * (line1End.y - line1Start.y);

        CGFloat s = q / d;
        if( r < 0 || r > 1 || s < 0 || s > 1 )
            return NO;

        return YES;
    };

    /*Test whether the line intersects any of:
     *- the bottom edge of the rectangle
     *- the right edge of the rectangle
     *- the top edge of the rectangle
     *- the left edge of the rectangle
     *- the interior of the rectangle (both points inside)
     */

    return (LineIntersectsLine(lineStart, lineEnd, CGPointMake(r.origin.x, r.origin.y), CGPointMake(r.origin.x + r.size.width, r.origin.y)) ||
            LineIntersectsLine(lineStart, lineEnd, CGPointMake(r.origin.x + r.size.width, r.origin.y), CGPointMake(r.origin.x + r.size.width, r.origin.y + r.size.height)) ||
            LineIntersectsLine(lineStart, lineEnd, CGPointMake(r.origin.x + r.size.width, r.origin.y + r.size.height), CGPointMake(r.origin.x, r.origin.y + r.size.height)) ||
            LineIntersectsLine(lineStart, lineEnd, CGPointMake(r.origin.x, r.origin.y + r.size.height), CGPointMake(r.origin.x, r.origin.y)) ||
            (CGRectContainsPoint(r, lineStart) && CGRectContainsPoint(r, lineEnd)));
}

Trivially ported from this question: How to know if a line intersects a rectangle