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January 6th, 2015, 07:45 AM  #1 
Newbie Joined: Jan 2015 From: MOntreal Posts: 1 Thanks: 0  find a polynomial by interpolating 2 other polynomials
Hi, Have a look at the attached image. This is an aircraft performance chart. When we use these charts, we plot differents parameters (altitude, temperature, etc..) and, with a pencil, follow these curves and determine the value we are seeking for (fuel, time, distance, etc.) I would like to acheive the same programmatically so I determined the polymnomials from the kown curves. However, there can be an infinite number of curves and when the plot falls between 2, I must find a way to come up with a new equation based on the interpolation of 2 polynomials. The attached image shows a dotted line down to a reference line, then the user follow the closest curve (red) down to the know Y axis value, then vertically down (orange) to the value we are seeking. What would you suggest? 
January 21st, 2015, 06:03 AM  #2 
Senior Member Joined: Aug 2008 From: Blacksburg VA USA Posts: 351 Thanks: 7 Math Focus: primes of course  family of curves
I have had some success with this type of interpolation IF the family of curves have a certain characterization ("nice") ( I think my subject was stochiometric curves of temp,press and a 3rd qty) For example, say you had 5 curves as a function of some parameter k, w/ asso quadratic fits (numbers are completely fabricated) AND they follow the same form with coefficients that track well with k. Say form is Y=Ax^2+Bx+C k=1 (A,B,C)= 5.42,3.11,4.2 k=2 (A,B,C)= 4.42,3.11,4.6 k=3 (A,B,C)= 3.42,3.11,5.0 k=4 (A,B,C)= 2.42,3.11,5.3 k=5 (A,B,C)= 1.42,3.11,5.7 From the above, one can then characterize "A" as a f{k}, as well as C. [ for example A= 6.42k etc ] This allows you to direcly interpolate for 1< k<5 If you have infinite curves, I cannot help you ! 

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