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Calculate quadratic function from given points in 2 dimensions

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0

$begingroup$

The quadratic function can be defined as
$z = a+b*x+c*y+d*x^2 +e*x*y+f*y^2$

But how to find the 6 coefficients from given truples $(x_i,y_i,z_i)$?

I hope that there is a not too difficult solution. Can anybody give me a reference? In opposite to e.g. solving a cubic equation in 1D I found nothing unfortunately.

quadratics

share|cite|improve this question

edited Mar 20 at 9:15

user32038

asked Mar 19 at 16:02

user32038user32038

234

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Please use MathJax when formatting your questions.
  $endgroup$
  – John Wayland Bales
  Mar 19 at 16:12
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Each tuple gives you an equation in six variables.
  $endgroup$
  – John Wayland Bales
  Mar 19 at 16:17
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You can write the equation in determinant form directly from the tuples.
  $endgroup$
  – amd
  Mar 19 at 19:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks!! It seems solving the linear equations is not so difficult, and most of my expected problems pop up later (or earlier, e.g. on chosing the 6 points).
  $endgroup$
  – user32038
  Mar 21 at 6:40
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I solved the problem for myself now. It was easier than expected, thanks for support.
  $endgroup$
  – user32038
  Mar 29 at 12:58
  

  
  
  
  

add a comment | 

0

$begingroup$

The quadratic function can be defined as
$z = a+b*x+c*y+d*x^2 +e*x*y+f*y^2$

But how to find the 6 coefficients from given truples $(x_i,y_i,z_i)$?

I hope that there is a not too difficult solution. Can anybody give me a reference? In opposite to e.g. solving a cubic equation in 1D I found nothing unfortunately.

quadratics

share|cite|improve this question

edited Mar 20 at 9:15

user32038

asked Mar 19 at 16:02

user32038user32038

234

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Please use MathJax when formatting your questions.
  $endgroup$
  – John Wayland Bales
  Mar 19 at 16:12
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Each tuple gives you an equation in six variables.
  $endgroup$
  – John Wayland Bales
  Mar 19 at 16:17
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You can write the equation in determinant form directly from the tuples.
  $endgroup$
  – amd
  Mar 19 at 19:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks!! It seems solving the linear equations is not so difficult, and most of my expected problems pop up later (or earlier, e.g. on chosing the 6 points).
  $endgroup$
  – user32038
  Mar 21 at 6:40
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I solved the problem for myself now. It was easier than expected, thanks for support.
  $endgroup$
  – user32038
  Mar 29 at 12:58
  

  
  
  
  

add a comment | 

$begingroup$

The quadratic function can be defined as
$z = a+b*x+c*y+d*x^2 +e*x*y+f*y^2$

But how to find the 6 coefficients from given truples $(x_i,y_i,z_i)$?

I hope that there is a not too difficult solution. Can anybody give me a reference? In opposite to e.g. solving a cubic equation in 1D I found nothing unfortunately.

quadratics

share|cite|improve this question

edited Mar 20 at 9:15

user32038

asked Mar 19 at 16:02

user32038user32038

234

$endgroup$

share|cite|improve this question

edited Mar 20 at 9:15

user32038

asked Mar 19 at 16:02

user32038user32038

234

share|cite|improve this question

edited Mar 20 at 9:15

user32038

asked Mar 19 at 16:02

user32038user32038

234

asked Mar 19 at 16:02

user32038user32038

234

asked Mar 19 at 16:02

user32038user32038

234