fit a 3d curve

Dear all,

I am a beginner in Matlab and I need your help. Here is my problem: I have a cloud of data obtained by measurement. Thanks to those datas I have made a matrix(49x49) which allowed me to plot a paraboloid. I would like to fit this 3d curve based on data, but I don't know how to start. Could you please help me to find a way to solve this problem?

Sincerely,

Elza

[marcelo matos]

Hi, Elza. You may try this one http://www.mathworks.com/help/curvefit/surface-fitting.html

Answer 1

[Andrew Newell]

If you have the Curve Fitting Toolbox, you could try interactive surface fitting.

EDIT: If you don't have it, you could try polyfitn, which you can download from the File Exchange.

Answer 2

[Elza]

Many thanks for your answer. Actually I don't have this tool. Do you know an other way to do it?

Thanks a million.

Elza

Answer 3

[Jarrod Rivituso]

Could you cast it as a linear regression problem and then solve the equations using backslash? Some details:

Say we are trying to fit to an equation of the form

z = c1*f1(x,y) + c2*f2(x,y) + ...

where f1 and f2 are the basis functions of the linear equation, and c1,c2,etc. are the coefficients. You could write this as a matrix equation...

z = [f1(x,y) , f2(x,y) , ...] * [c1 ; c2 ; ...]

Here's an example in MATLAB with some data I made up...

%Define grid of x,y values
x = -1:0.01:1;
y = -1:0.01:1;
[X,Y] = meshgrid(x,y);

%Make up some data
data = X.^2 + 3*Y.^2 + 0.01*rand(size(X));

%Set the basis functions
f1 = ones(size(X));
f2 = Y.^2;
f3 = X.^2;

%Write as matrix equation
A = [f1(:),f2(:),f3(:)];
y = data(:);

%Solve for coefficients
coeffs = A\y

Answer 4

[Elza]

Thanks for your help Jarrod, I'll try that and let you know if it works for me.

Many thanks

[Benjamin Lewis]

did it work?

Answer 5

[Sonali]

Rt = 30.5;

area_ratio = 31.4754;

theta = 50;

theta_exit = 16.5;

theta_n = theta*pi/180;

k = 0.8;

Ln = k*(sqrt(area_ratio)-1)*Rt/tand(theta_exit);

% FIRST CURVE (FC)

% Angles for First Curve

Angle_FC = -(pi+(45*pi/180));

FC_step = (-pi/2-Angle_FC)/100;

theta_FC = (-3*pi/4):FC_step:(-pi/2);

% Coordinates for First Curve

x_FC = cos(theta_FC)*1.5*Rt;

y_FC = sin(theta_FC)*1.5*Rt+(1.5*Rt+Rt);

x_FC1 = x_FC';

y_FC1 = y_FC';

% SECOND CURVE (SC)

% Angle for Second Curve

Angle_SC = -pi/2;

SC_step = ((theta_n-pi/2)-Angle_SC)/100;

theta_SC = -pi/2:SC_step:(theta_n-pi/2);

% Coordinates for Second Curve

x_SC = cos(theta_SC)*0.382*Rt;

y_SC = sin(theta_SC)*0.382*Rt+(0.382*Rt+Rt);

x_SC1 = x_SC';

y_SC1 = y_SC';

% THIRD CURVE (TC)

% Coordinates for Third Curve

x_TC = cos(theta_n-pi/2)*0.382*Rt;

y_TC = sin(theta_n-pi/2)*0.382*Rt+(0.382*Rt+Rt);

% Exit Coordinates

y_exit = sqrt(area_ratio)*Rt;

matrix_y = [y_TC^2 y_TC 1; y_exit^2 y_exit 1; 2*y_TC 1 0];

matrix_x = [x_TC; Ln ;1/tan(theta_n)];

x_exit = matrix_y^-1*matrix_x;

a = x_exit(1,1);

b = x_exit(2,1);

c = x_exit(3,1);

y = y_TC:0.8:y_exit;

x = a*y.^2+b*y+c;

% Complete Coordinate

Rao_x = [x_FC x_SC x];

Rao_y = [y_FC y_SC y];

% Lower Geometry

Rao_y1 = -1*Rao_y;

%Coordinates

R_X = Rao_x';

R_Y = Rao_y';

Rao = [R_X R_Y];

% Figures

figure(1)

plot (Rao_x,Rao_y,'r','LineWidth',3)

hold on

plot (Rao_x,Rao_y1,'r','LineWidth',3)

hold of

I need this code To be generate in 3D model

can you please provide