Hi,
thanks for your suggestion. I am currently looking into the problem.
I have found some interesting docs at:
http://www.antigrain.com/research/adaptive_bezier/index.htmlhttp://www.gamedev.net/community/forums/topic.asp?topic_id=313018http://people.inf.ethz.ch/fischerk/pubs/bez.pdfhttp://www.tinaja.com/glib/midpoint.pdfhttp://www.tinaja.com/glib/nubzlen1.pdfhttp://www.cit.gu.edu.au/~anthony/info/graphics/bezier.curves
Anyway, I don't think that the Casteljau's methods lets me calculate the
half-a-distance point on the curve. Please confirm. In the meantime I am
going to verify that.
To reply to Shamyl, yes I have already used the "rough subdivision" method,
but it is not so accurate and fast. I am sure there is an analytic way to do
it.
Best Regards
--
Lorenzo
email: email@hidden
> From: Ben Supnik <email@hidden>
> Date: Thu, 17 May 2007 12:35:38 -0400
> To: Lorenzo <email@hidden>
> Subject: Re: Split Bezier curve
>
> Hi Lorenzo,
>
> I'm afraid I don't have a formula for equal-length bezier curves...I've
> looked at a bunch of bezier formulas for my app. Here are a few
> formulas I have found...if any help you build a good approximation from
> pieces, let me know, I can send you code.
>
> 1. Derivative (describes the tangent at any point, whose length will
> give you a sense of how far you'll go as you increment T).
>
> 2. Zero crossings of derivatives (via the quadratic formula) give you
> the point where the bezier changes direction.
>
> 3. Arbitrary split at a time T.
>
> 4. Combining 2 and 3, you can cut any bezier into a "monotone" segment,
> one that doesn't "change direction" in any dimension...that's handy
> because the monotone segment is fully contained within the bounding
> box/cube of the endpoints of the segment.
>
> 5. Once you have the bounding box of monotone segments, you can easily
> apply recursive binary algorithms to do things like intersections.
> (That may be getting away from your original goal. :-)
>
> As a final thought, our app renders beziers not by advancing T an
> arbitrary distance, but by a recursive subdivision, e.g. we keep adding
> points to the curve until we meet a minimum error requirement or a
> maximum point count. Theoretically this helps us put our segments to
> the most good.
>
> Sorry, none is a length curve, but if any of these help you build a
> workaround, let me know.
>
> cheers
> Ben
>
>
>
>
> Lorenzo wrote:
>> Hi,
>> in my OpenGL application I draw a 3D Bezier cubic curve in the 3D space.
>>
>> Now, I have to split the 3D Bezier curve in 8 segments having the same
>> length. I iterate the curve from t = 0.0 to t = 1.0 using a t constant
>> interval of 1/8, so t = 0.125, t = 0.250... I get 8 segments, but they have
>> different length. Closer I go to the endPoint of the curve, each segment is
>> shorter.
>> Instead I would need they had the same length. So e.g, when I pass t = 0.5
>> I need to get the xyz coordinates of the point placed at half a distance
>> from the first point. Any idea?
>>
>>
>> Best Regards
>
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