 Physics Help Forum Deriving the equation of points for exact fitting and shape analysis
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 General Physics General Physics Help Forum Nov 29th 2012, 04:34 AM #1 Junior Member   Join Date: Nov 2012 Posts: 1 Deriving the equation of points for exact fitting and shape analysis Hello, I would like to ask you some questions. 1) I've a closed curve (for example an ellipse, which may represent the contour of an object) represented by the set of its (known) points. I need to find the equation of that curve to pass through all and every point (exact fit). I think that to do this I need a polynomial whose grade is equal to the number of points less 1. Something like this: a0+a1 x1+a2 x1^2+ ...+ an x1^n = y1 a0+a2 x2+a2 x2^2+ ...+ an x2^n = y2 ... a0+a2 xn+a2 xn^2+ ...+ an xn^n = yn This argument is right? Do you have suggestions (or anything else relevant) for me in this regard for which is the best way to solve my problem? This equation can be made in parametric form? 2) After I got the exact equation of this curve. Suppose we have a set of curves very similar to each other (represented by their equation), I would like to find the equation that represents the shape which best approaches to all previous curves, a sort of average curve created from those previously acquired. Do you know if this thing can be done and how? What is the best way (most efficient and / or mathematically more correct) to do this? Best Regards, Giusy   Nov 29th 2012, 06:18 AM #2 Physics Team   Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,352  Tags analysis, deriving, equation, exact, fitting, points, shape Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post MMM Advanced Mechanics 28 Mar 15th 2015 07:38 AM blaZkowicZ Advanced Mechanics 1 Oct 25th 2009 09:41 PM revolution2000 Kinematics and Dynamics 2 Apr 5th 2009 09:02 AM zobe2500 Kinematics and Dynamics 2 Feb 13th 2009 06:44 AM 