Basically, you want to check if any point falls inside a region of specified size around your path.
It is actually very simple to do. First, you need a value which will define the amount of space around path you want to test. Let's say 20 points. So what you need to do is start a FOR loop, starting from -20 to 20, and at each iteration, create a copy of your path, translate the path's x and y co-odrinates, check each of them.
All of this is more clear in this code sample.
CGPoint touchPoint = /*get the point*/;
NSInteger space = 20;
for (NSInteger i = -space; i < space; i++) {
UIBezierPath *pathX = [UIBezierPath bezierPathWithCGPath:originalPath.CGPath];
[pathX applyTransform:CGAffineTransformMakeTranslation(i, 0)];
if ([pathX containsPoint:touchPoint]) {
/*YEAH!*/
}
else {
UIBezierPath *pathY = [UIBezierPath bezierPathWithCGPath:originalPath.CGPath];
[pathY applyTransform:CGAffineTransformMakeTranslation(0, i)];
if ([pathY containsPoint:touchPoint]) {
/*YEAH!*/
}
}
}