# Generate an equation from a 3d surface

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Hi there,

I am wondering if it is possible to generate an equation from a 3d surface? I have a surface that is composed of three different equations at certain ranges of 'y'. Once graphed, I want to be able to create one equation which can reproduce the same shape. Is this possible? Here's a sample of the curve I have that I would like to convert to equation:

x = [0:10];

y = {0:3; 3:5; 5:10};

Eq1 = @(x,y)(x.*y);

Eq2 = @(x,y)(2.*x.*y);

Eq3 = @(x,y)(3.*x.*y);

[X1,Y1] = meshgrid(x,y{1});

[X2,Y2] = meshgrid(x,y{2});

[X3,Y3] = meshgrid(x,y{3});

Z1 = Eq1(X1,Y1);

Z2 = Eq2(X2,Y2);

Z3 = Eq3(X3,Y3);

figure(1)

s1 = surf(X1,Y1,Z1);

hold on

s2 = surf(X2,Y2,Z2);

s3 = surf(X3,Y3,Z3);

hold off

### Answers (3)

Shoaibur Rahman
on 3 Jan 2015

Edited: Shoaibur Rahman
on 3 Jan 2015

In Matlab, you can compact the three equations into one as written below. It is not a theoretical modeling anyway, but simply a easier way to implement multiple equations under certain constraints.

Eq = @(x,y) x.*y.*(y>=0 & y<3) + 2*x.*y.*(y>=3 & y<5) + 3*x.*y.*(y>=5 & y<=10);

x = 0:10; y = 0:10;

[X,Y] = meshgrid(x,y);

Z = Eq(X,Y);

surf(X,Y,Z)

Image Analyst
on 3 Jan 2015

##### 2 Comments

Image Analyst
on 3 Jan 2015

Shoaibur Rahman
on 4 Jan 2015

You can play a trick here. Use your code first:

Eq = @(x,y) x.*y.*(y>=0 & y<3) + 2*x.*y.*(y>=3 & y<5) + 3*x.*y.*(y>=5 & y<=10);

x = 0:10; y = 0:10;

[X,Y] = meshgrid(x,y);

Z = Eq(X,Y);

Get polynomial model of Z in terms of X and Y. I used curved fitting tool, and observed that you can model your data with a second degree polynomial. The polynomial is: f(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2. You will also find the coefficients while using the tool:

p00 = 4.021;

p10 = -2.545;

p01 = -2.681;

p20 = -8.291e-16;

p11 = 3.273;

p02 = 0.2681;

Now, evaluate the model function:

f = @(x,y) p00 + p10*x + p01*y + p20*x.^2 + p11*x.*y + p02*y.^2;

Z2 = f(X,Y);

And plot both original (Z) and modeled (Z2) data on same figure to see how they are similar to each other.

h(1) = surf(X,Y,Z); hold on

h(2) = surf(X,Y,Z2);

You may also set the two different colormaps for two surfaces to differentiate them clearly.

set(h(1),'CData',zeros(size(X))); % colormap 1

set(h(2),'CData',0.5*ones(size(X))); % colormap 2

legend('Original','Fitted')

##### 10 Comments

Image Analyst
on 4 Jan 2015

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