# Airfoil representation by bezier curves

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 April 23, 2014, 06:28 Airfoil representation by bezier curves #1 New Member   shikhar Join Date: Apr 2010 Posts: 22 Rep Power: 9 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.

 April 23, 2014, 13:54 #2 Senior Member   Hamid Zoka Join Date: Nov 2009 Posts: 212 Rep Power: 11 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. levivad likes this.

 August 19, 2014, 07:32 #3 New Member   shikhar Join Date: Apr 2010 Posts: 22 Rep Power: 9 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 } ???

 August 31, 2014, 11:05 #4 New Member   Zhong, Hong Min Join Date: Oct 2012 Location: UESTC, Chengdu in China Posts: 8 Rep Power: 6 You may refer to the 29th section "Circles and quadratic Bézier curves" @ http://pomax.github.io/bezierinfo/

 April 8, 2015, 08:04 represent airfoil by using 2 bezier curves #5 New Member   samira Join Date: Feb 2015 Location: Iran Posts: 16 Rep Power: 4 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

 April 10, 2015, 02:45 #6 New Member   shikhar Join Date: Apr 2010 Posts: 22 Rep Power: 9 check this link on Bezier Curve Fitting. http://www.dtic.mil/cgi-bi/GetTRDoc?AD=ADA350611

 April 11, 2015, 04:06 #7 Member   shahrooz Join Date: Aug 2011 Posts: 41 Rep Power: 8 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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