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Subject: Re: parabolic interpolation between 3  nearest points
Date: Sun, 26 Jun 2011 19:51:04 +0000 (UTC)
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"sk maidul  haque" <skmaidulhaque@gmail.com> wrote in message <iu6ln0\$1n6\$1@newscl01ah.mathworks.com>...
> Can somebody please explain me what does it mean by 'parabolic interpolation between 3  nearest points' . Does it mean that a parabola is to be ploted between 3 points which are nearest to the concerned point where I want to do the interpolation and then to calculate the value from the equation of parabola at concerned point.
> If it is so, then what is the form of equation of parabola to be used ?
>
> what is the related command in matlab to do parabolic interpolation between specified number of nearest neighbour points.
>
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Assuming your interpretation is the one to be used, let (x1,y1), (x2,y2), and (x3,y3) be the three "nearest" points and (x,y) be the "concerned" point.  If (x,y) is to lie on the parabola through the three points, you can express y as a quadratic function of x in the form:

y = a*(x-x2)^2 + b*(x-x2) + y2

where a and b are:

a = ((y3-y2)/(x3-x2)-(y2-y1)/(x2-x1))/(x3-x1)
b = ((y3-y2)/(x3-x2)*(x2-x1)+(y2-y1)/(x2-x1)*(x3-x2))/(x3-x1)

An alternative would be to use Lagrange's interpolation method for second degree polynomials.  See

http://en.wikipedia.org/wiki/Lagrange_polynomial

Roger Stafford
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