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Hit Detection

It’s often necessary to be able to detect if a point lies on an arbitrary path. At first glance, the -[NSBezierPath containsPoint:] selector might appear to be just the ticket. Unfortunately, it only tells you if your point is contained within the path, not on the path. What seems to be needed is an -[NSBezierPath intersectsPoint] method.

So here’s one. Make a category on NSBezierPath containing the following, and Bob’s your auntie. The more observant may notice that this is only implemented for straight segments - I’ll post the curve section later.

/” Returns true if and only if this path intersects with the point passed in. Intersection is defined by the distance from the point to the and drawn segment on the path being less than the current line width. Thus if the point lies on a ‘moveToPoint’ or ‘closePath’ segement of the path, this will not return true unless it also lies on or close enough to some drawn segment. “/

// Iterate through the elements for this path, and see if // the point intersects for (count = 0; (count < [self elementCount]) && !intersectionFound; count++) { NSPoint elementPoints[3]; NSBezierPathElement element;

 element = [self elementAtIndex:count associatedPoints:elementPoints];

 // We don't like a switch statement, but NSBezierPathElement isn't a 
 // class, so we have to use one.  Pah!
 switch (element)
   case NSMoveToBezierPathElement:    
     currentPoint = elementPoints[0];
   case NSLineToBezierPathElement: 
     intersectionFound = [self lineFrom:currentPoint
     currentPoint = elementPoints[0];
   case NSCurveToBezierPathElement:
     intersectionFound = [self curveFrom:currentPoint
     currentPoint = elementPoints[0];
   case NSClosePathBezierPathElement:
   }    }  return intersectionFound; }

/” Does a line between ‘from’ and ‘to’ intersect ‘point’ given the current line width? “/

// (Cx-Ax)(Bx-Ax) + (Cy-Ay)(By-Ay) // r = ——————————- // L^2

ratio = (((point.x-from.x)(dx) +(point.y-from.y)(dy)) / ((dx)(dx)+(dy)(dy)));

if (ratio < 0) intersection = from; else if (ratio > 1) intersection = to; else { intersection = NSMakePoint(from.x + ratio * (dx), from.y + ratio * (dy)); }

distancesqr = pow(point.x - intersection.x, 2) + pow(point.y - intersection.y, 2); maxdistancesqr = pow([self lineWidth], 2);

return (distancesqr <= maxdistancesqr) ? YES : NO; }

/” Does a curve between ‘from’ and ‘to’ with control points ‘control1’ and ‘control2’ intersect ‘point’ given the current line width? “/

Enjoy. tufty

I added the necessary code to the curveFrom:to:control:control:intersectsPoint: method above. It uses the NearestPoint.c code, which in turn requires the GraphicsGems.h and GGVecLib.c code. All those files are available from the following place:

It requires some minor changes (mainly #ifndef-ing out some duplicate #defines), but works fine. If anyone would like the modified files, please contact me (

I also have a question on the code as a whole…Why is the critical distance from the line [self lineWidth]? Should it not be half of that? Only half of the line lies on either side of the middle of the line, if you understand what I mean…

– DavidRemahl

I just made some efficiency changes (removing the costly sqrt() calls and using some temp variables). Oh, and if you want performance, do remove the pow() calls in favour of making temp variables and multiplying manually. pow is about twice as costly.

– DavidRemahl

I just tried this out and when doing hit detection on a sharp bezier curve, it is significantly out - the curve it seems to check is flatter than what the NSBezierPath draws. I would have thought that the curve geometry would be standard.

– Gideon King

since 10.4 there is a function in quartz 2d for better/easy hit detection: CGContextPathContainsPoint. there is also an example on adc which tells you how to convert NSBezierPath to CGPathRef and how to use the function:

you can also use CGPathContainsPoint.

– li