Re: cocoa-dev digest, Vol 1 #651 - 14 msgs
Re: cocoa-dev digest, Vol 1 #651 - 14 msgs
- Subject: Re: cocoa-dev digest, Vol 1 #651 - 14 msgs
- From: Simon Stapleton <email@hidden>
- Date: Mon, 01 Oct 2001 10:02:41 +0100 (BST)
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Subject: Re: Does cocoa just leak?
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Cc: email@hidden
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To: j o a r <email@hidden>
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On Sunday, September 30, 2001, at 10:07 PM, j o a r wrote:
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> On Sunday, September 30, 2001, at 08:34 , John Hvrnkvist wrote:
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>> It's quite possible that NSBezierPath calls
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>> "bezierPathByFlatteningPath" in that code and solves each
generated
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>> line segment for the point. Flattening will eat lots of memory
for
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>> complex paths.
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> This is what ObjectAlloc tells me about one of the allocations. It
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does
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> seem like it uses "bezierPathByFlatteningPath" - it seemed to me
like
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a
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> class method to return a new path - that 's why I said it copied
the
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> path. Perhaps it isn't so?
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It flattens the path, and that means replacing any curve segment by
a
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lot of short lines.
That sounds like a rather suboptimal way of carrying on, although
testing if a point is on a line segment is rather easier than
detecting if one's on a bezier. I would have thought the extra
allocs and deallocs involved would remove the benefit, myself, but if
anyone on the apple team responsible cares to tell me otherwise...
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> You are absolutely right about it requiring a lot of resources
though
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> John - is there an alternative way to obtain the x position on a
path
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> given a known y-position? It takes way to long time as it is now.
I
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was
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> never very good at math in school, mind you... ;)
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Here is the fundamental formula:
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<
http://www.bergen.org/AAST/Projects/3DSMaxTutorial/bezier_formula.gif
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and this picture illustrates the meaning:
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http://www.bergen.org/AAST/Projects/3DSMaxTutorial/bezier_diagram1.gi
f>
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You can iterate over the function until you find a point that
matches
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yours, or you can try to solve the equation for each line segment.
You
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should be able to make Newton-Raphson solve it, or you could solve
the
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cubic equation. Solving cubics is a bit messy; pick up a good math
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reference book. (I like "Beta, Mathematics Handbook" by Lennart
Rede and
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Bertil Westergren. For those that happen to be in Sweden, it should
be
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available from your nearest university bookstore, eg Cremona at
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Chalmers.)
Or simply rip the code from the Graphics Gems repository. It's in
Graphics Gems 1 if I recall correctly, although there's lots of
bezier stuff in GG5 and some in GG2 as well. a google search
for 'graphics gems' will pull up the central repository, and it's
pretty much all straight 'C' (not necessarily comprehensible 'C', but
there you go - it's certainly readable enough that you don't need the
books unless you want to really understand 'why')
Simon
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