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 = CGPoint         


        

Answer 1

For anyone using objective-c:

- (BOOL)rectContainsLine:(CGRect)rect startPoint:(CGPoint)lineStart endPoint:(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(rect.origin.x, rect.origin.y), CGPointMake(rect.origin.x + rect.size.width, rect.origin.y)) ||
        LineIntersectsLine(lineStart, lineEnd, CGPointMake(rect.origin.x + rect.size.width, rect.origin.y), CGPointMake(rect.origin.x + rect.size.width, rect.origin.y + rect.size.height)) ||
        LineIntersectsLine(lineStart, lineEnd, CGPointMake(rect.origin.x + rect.size.width, rect.origin.y + rect.size.height), CGPointMake(rect.origin.x, rect.origin.y + rect.size.height)) ||
        LineIntersectsLine(lineStart, lineEnd, CGPointMake(rect.origin.x, rect.origin.y + rect.size.height), CGPointMake(rect.origin.x, rect.origin.y)) ||
        (CGRectContainsPoint(rect, lineStart) && CGRectContainsPoint(rect, lineEnd)));
}