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April 23, 2014, 06:28
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Airfoil representation by bezier curves
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#1 |
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New Member
shikhar
Join Date: Apr 2010
Posts: 22
Rep Power: 16  |
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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April 23, 2014, 13:54
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#2 |
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Senior Member
Hamid Zoka
Join Date: Nov 2009
Posts: 282
Rep Power: 18 |
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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August 19, 2014, 07:32
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#3 |
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New Member
shikhar
Join Date: Apr 2010
Posts: 22
Rep Power: 16 |
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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August 31, 2014, 11:05
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#4 |
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New Member
Zhong, Hong Min
Join Date: Oct 2012
Location: UESTC, Chengdu in China
Posts: 8
Rep Power: 13 |
You may refer to the 29th section "Circles and quadratic Bézier curves" @ http://pomax.github.io/bezierinfo/
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April 8, 2015, 08:04
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represent airfoil by using 2 bezier curves
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#5 |
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New Member
samira
Join Date: Feb 2015
Location: Iran
Posts: 16
Rep Power: 11 |
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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April 10, 2015, 02:45
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#6 |
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New Member
shikhar
Join Date: Apr 2010
Posts: 22
Rep Power: 16 |
check this link on Bezier Curve Fitting.
http://www.dtic.mil/cgi-bi/GetTRDoc?AD=ADA350611 |
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April 11, 2015, 04:06
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#7 |
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Member
shahrooz
Join Date: Aug 2011
Posts: 41
Rep Power: 14 |
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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