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Airfoil representation by bezier curves

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Old   April 23, 2014, 06:28
Default Airfoil representation by bezier curves
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shikhar
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Hi

I am trying to represent airfoil by using 2 bezier curves of order 12.
what i understand is i have to find control points of bezier curve by using the co-ordinates of the airfoil and doing least squares approximation.

My question is in typical least squares approx. we minimize vertical offset [i.e. we minimize {summation(y - y(t))}^2 ]. So if i do this i will find the y co-ordinates of my control points. Now, how do i find the x co-ordinates of my control points???

Can anyone please help me.
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Old   April 23, 2014, 13:54
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Hamid Zoka
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as far as I know, in case of bezier curves both X and Y are functions of t parameter. So, you should find t such that errors of X and Y goes down.
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Old   August 19, 2014, 07:32
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shikhar
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hi hamidzoka ... thnx for your reply...

Yeah in bezier curves both x & y are functions of t parameter.

As you said errors of x and y should go down, do i need to minimize both x & y together as
minimize {summation (x-x(t))^2+(y-y(t))^2 }

???
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Old   August 31, 2014, 11:05
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Zhong, Hong Min
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You may refer to the 29th section "Circles and quadratic Bézier curves" @ http://pomax.github.io/bezierinfo/
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Old   April 8, 2015, 08:04
Default represent airfoil by using 2 bezier curves
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samira
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Hello
I'm working on airfoil shape optimization for wind turbine.I am trying to represent airfoil by using 2 bezier curves.
How can I get a Bezier curve closet to the given points (given an ordered set of m airfoil data points and find a set of control points.)
can anyone please help me on this
Thank you so much
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Old   April 10, 2015, 02:45
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shikhar
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check this link on Bezier Curve Fitting.
http://www.dtic.mil/cgi-bi/GetTRDoc?AD=ADA350611
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Old   April 11, 2015, 04:06
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doing a google search for "bezier curve fitting" results in many related articles and web pages to what you want to do judging from the titles.

http://lmgtfy.com/?q=bezier+curve+fitting
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