Re: Remove overlap on NSBezierPath
Re: Remove overlap on NSBezierPath
- Subject: Re: Remove overlap on NSBezierPath
- From: Jens Alfke <email@hidden>
- Date: Sun, 13 Jul 2008 22:36:37 -0700
On 13 Jul '08, at 9:14 PM, Graham Cox wrote:
Since apps like Adobe Illustrator and Flash can perform these
operations on bezier paths, clearly there are methods that exist for
doing it, even though the mathematicians claim otherwise (what they
are claiming is the lack of a general all-purpose solution to the
arbitrary intersection of bezier paths, but for real-world graphics
there wouldn't be too many pathological cases to worry about).
What the mathematicians balk at isn't the pathological cases; rather,
getting exact results.
It's not possible to find the exact points of intersection of cubic
curves, because it requires factoring a sixth-order polynomial, for
which there are no known general techniques. The best you can do is to
find approximations, using algorithms like Newton's Method. You can
make the approximations as precise as you need by increasing the
number of iterations. That's what existing programs do.
—Jens
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