Surface-Fit

Polynomial surface	Specify the polynomial degree here, that is 1,2 or 3, leading to 3, 6, or 10 unknown coefficients.
An ''Ansatz'' defined by yourself	Please specify the number of terms (coefficients) here: n= Important: 1 <= n < = 10

Data should be generated artificially

Specify the ''original'' vector of coefficients: a(1),...,a(n) a= 1,2,1.2 Please specify the rectangle for the free variables x,y: xl= xr= yl= yr= Important: xl < xr , yl < yr Please specify the number of points which should be used as data. Important n <= m <= 1000 m= Please specify the level of generated errors for the function values. 1 means 100 percent: level = Important 0 <= level <= 1 !

Your own data

You want ot specify m data points in 3-space: Specify m please: m= Important: n <= m <= 1000 Please write the list of data in the following textarea. This is formatfree, that means you simply type or paste 3*m numbers here, separated by comma, blank or newline. (x,y,z)= 0.1000000E+01 0.1000000E+01 0.7496227E+01 0.1000000E+01 0.2000000E+01 0.5775908E+00 0.1000000E+01 0.3000000E+01 0.4113566E+01 0.1000000E+01 0.4000000E+01 -0.5999093E+00 0.1000000E+01 0.5000000E+01 -0.9021067E+01 0.2000000E+01 0.1000000E+01 0.2392682E+01 0.2000000E+01 0.2000000E+01 -0.4493752E+01 0.2000000E+01 0.3000000E+01 -0.1322496E+01 0.2000000E+01 0.4000000E+01 -0.6462291E+01 0.2000000E+01 0.5000000E+01 -0.1497941E+02 0.3000000E+01 0.1000000E+01 0.1644580E+01 0.3000000E+01 0.2000000E+01 -0.5606573E+01 0.3000000E+01 0.3000000E+01 0.1695359E+01 0.3000000E+01 0.4000000E+01 0.1383910E+01 0.3000000E+01 0.5000000E+01 -0.6046355E+01 0.4000000E+01 0.1000000E+01 -0.1638937E+01 0.4000000E+01 0.2000000E+01 -0.9316410E+01 0.4000000E+01 0.3000000E+01 0.2813868E+01 0.4000000E+01 0.4000000E+01 0.8146273E+01 0.4000000E+01 0.5000000E+01 0.1986436E+01 0.5000000E+01 0.1000000E+01 -0.2909889E+01 0.5000000E+01 0.2000000E+01 -0.1068333E+02 0.5000000E+01 0.3000000E+01 0.2533809E+01 0.5000000E+01 0.4000000E+01 0.9136642E+01 0.5000000E+01 0.5000000E+01 0.3262778E+01

The graphical output requires the specification of your view point, defined here by the rotation angle of the x-axis (in [0,180] , degrees) and the z-axis (in [0,360], degrees). phi=0 means x-axis is horizontally on the screen, y-axis vertical on the screen and psi=0 the z-axis orthogonal to the screen (you look vertically down (seeing little)).
phi=
psi=

If you have chosen to use an ''Ansatz'' of your own, then you must specify your "Ansatz" functions, of course n different (or more precisely: linearly independent) ones, here.
In each row you type or paste a formula depending on x, y and constants. If you have n<10, then write a zero in the remaining rows!

phi(1,x,y) =
phi(2,x,y) =
phi(3,x,y) =
phi(4,x,y)=
phi(5,x,y) =
phi(6,x,y) =
phi(7,x,y) =
phi(8,x,y) =
phi(9,x,y) =
phi(10,x,y) =

Click on "evaluate", in order to submit your input.