What would be the equation of the following surface?

Prashant Kumar answered . 2024-11-28 01:56:36

You can probably try this quadratic function , where is a constant, and , .

Update 1: Another candidate function for the surface is hyperbolic function, .

Update 2: If you insist on using the periodic trigonometric function on a non-oscillatory surface, then modify the fitting model to become so that it fits the local data.

[X, Y] = meshgrid(-1:0.05:1);
%% Polynomial function
c      = 1;
b      = 1/2;
a      = b;
Z      = c - b*Y.^2 - a*X.^2;   % can try higher-order polynomial functions
surf(X, Y, Z), grid on
title('Quadratic function'), xlabel x, ylabel y, zlabel f(x,y)

%% Hyperbolic function
c      = 1/(1 - sech(1));
b      = [1, (c*sech(1))/2];
a      = b;
Z      = c - b(2)*cosh(b(1)*Y) - a(2)*cosh(a(1)*X);
surf(X, Y, Z), grid on
title('Hyperbolic function'), xlabel x, ylabel y, zlabel f(x,y)

%% Trigonometric function (local)
c      = 0;
b      = [pi/2, 1/2];
a      = b;
Z      = c + b(2)*cos(b(1)*Y).^2 + a(2)*cos(a(1)*X).^2;
surf(X, Y, Z), grid on
title('Trigonometric function'), xlabel x, ylabel y, zlabel f(x,y)

%% Gaussian function (local)
c      = 1/(1 - exp(1));
b      = exp(1)/(2*(exp(1) - 1));
a      = b;
Z      = c + b*exp(-Y.^2) + a*exp(-X.^2);   % can sech(x) if you like single-hump functions
surf(X, Y, Z), grid on
title('Gaussian function'), xlabel x, ylabel y, zlabel f(x,y)

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