Determine if line intersects CGRect - graphics

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

Answer 2

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)));
}

Answer 3

Swift version:
extension CGRect {
private func lineIntersectsLine(_ line1Start: CGPoint, _ line1End: CGPoint, _ line2Start: CGPoint, _ line2End: CGPoint) -> Bool {
// Distance between the lines' starting rows times line2's horizontal length
var q = (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)
let 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 false
}
let 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);
let s = q / d
if r < 0 || r > 1 || s < 0 || s > 1 {
return false
}
return true
}
func instersectsLine(start lineStart: CGPoint, end lineEnd: CGPoint) -> Bool
{
/*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, CGPoint(x:self.origin.x, y: self.origin.y), CGPoint(x: self.origin.x + self.size.width, y: self.origin.y)) ||
lineIntersectsLine(lineStart, lineEnd, CGPoint(x: self.origin.x + self.size.width, y: self.origin.y), CGPoint(x: self.origin.x + self.size.width, y: self.origin.y + self.size.height)) ||
lineIntersectsLine(lineStart, lineEnd, CGPoint(x: self.origin.x + self.size.width, y: self.origin.y + self.size.height), CGPoint(x: self.origin.x, y: self.origin.y + self.size.height)) ||
lineIntersectsLine(lineStart, lineEnd, CGPoint(x: self.origin.x, y: self.origin.y + self.size.height), CGPoint(x: self.origin.x, y: self.origin.y)) ||
(contains(lineStart) && contains(lineEnd)))
}
}