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length of a 2D quadratic bezier curve?


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#1 VladimirM   Members   -  Reputation: 130

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Posted 22 August 2012 - 02:05 PM

Is there a formula? Or must i approximate it by dividing the curve into line segments and summing them up?

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#2 Bacterius   Crossbones+   -  Reputation: 9263

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Posted 22 August 2012 - 02:59 PM

You could analytically divide the curve into n segments and take the limit of the sum as n goes to infinity, this should give you the formula. Or use the integral form which would give the same result (by definition). Did you try this (google cache since the site seems to be down/dead)?

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

 

- Pessimal Algorithms and Simplexity Analysis


#3 VladimirM   Members   -  Reputation: 130

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Posted 22 August 2012 - 03:53 PM

Wow, i tried it and it works, thanks, but i have a question,

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what is the D in the b = 2P1 - 2DP0? And why is there no line above P0? I need to understand this so that i could simplify this equation, because i have a very simple case of a bezier curve.

#4 VladimirM   Members   -  Reputation: 130

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Posted 22 August 2012 - 03:57 PM

i figured it out from the code.. no need to explain, thanks again.




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