Polar plot using polyfit

I'm trying to fit the VALUES to make a polar plot but it seems I couldn't fit one value 1400e2 which the polyfit doesn't take it? what other function should I use to make the polar plot correct so that it contains the values exactly at that degree ?

VGV = [ 2000e2 1800e2 1600e2 1400e2 ]; % [0 45 90 135 ]  

angle  = (pi/180).* [ 0 45 90 135 ];
alpha  = (0:0.1:360);
alpha1 = (pi/180).*(0:0.1:360);

for k=1:1:length(alpha)
 
 p  = polyfit(angle,VGV,2);
 
 f = polyval(p,alpha1(1:1:901));
 f1 = fliplr(f(1:1:900));
 f2 = fliplr(f1);
 f3 = fliplr(f2);
 
 Vp = [ f f1 f2 f3];
 
end

figure;polar(alpha1(1:1:3601),Vp,'o')

Answer 1

[Image Analyst]

It seems you want to fit a section between 0 and 135 degrees, then squish that to between 0 and 90, then replicate that around the circle for all 360 degrees. Seems kinds weird, but okay, whatever...

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 22;
fprintf('Beginning to run %s.m ...\n', mfilename);

% Create training data.
VGV = [ 2000e2 1800e2 1600e2 1400e2 ]; % [0 45 90 135 ]
angleDegrees  = [ 0 45 90 135 ];
angleRadians  = (pi/180).* angleDegrees;
% Plot training data
polar(angleRadians, VGV, 'bo')
% Fit a quadratic
coefficients  = polyfit(angleRadians, VGV, 1)

% Create 90 more angles to fit between our training angles.
alpha = linspace(min(angleRadians), max(angleRadians), 90);

% Get a fit over 0-135 degrees only.
vFit = polyval(coefficients, alpha);
% Plot fitted data:
hold on;
% Make other quadrants
vFit360 = [vFit, fliplr(vFit), vFit, fliplr(vFit)];
t = linspace(0, 2*pi, length(vFit360));
polar(alpha, vFit, 'r-')
polar(t, vFit360, 'b-')
% figure
% plot(t, vFit360, 'b-');
% hold on;
% plot(alpha, vFit, 'r-', 'LineWidth', 2);
fprintf('Done running %s.m ...\n', mfilename);

Answer 2

[Alan Stevens]

I'm somewhat confused by your question and don't understand the need for all the flip commands! However, does the following meet your needs at all (incidentally, angle vs VGV is a straight line, so you don't need to get polyfit to fit a quadratic):

VGV = [ 2000e2 1800e2 1600e2 1400e2 ]; % [0 45 90 135 ]  

angle  = (pi/180).* [ 0 45 90 135 ];
alpha  = (0:0.1:360);
alpha1 = (pi/180).*(0:0.1:360);

for k=1:1:length(alpha)
 
 p  = polyfit(angle,VGV,1);
 
 f = polyval(p,alpha1);
%  f1 = fliplr(f(1:1:900));
%  f2 = fliplr(f1);
%  f3 = fliplr(f2);
%  
%  Vp = [ f f1 f2 f3];
 
end

figure;
polarplot(alpha1,f,angle,VGV,'o')

This results in

[Ramesh Bala]

Thank you for your reply.I was using Flip to get the values in all quadrants.I was trying to fit these 0,45,90,135 using a fit and then to get values for other angles based on that that's what Vp was giving.

Now,based on your code how can i get for all 360 degrees?

Answer 3

[Image Analyst]

First of all, polyfit does not need to be inside a loop since angle and VGV don't change inside the loop.

Next, you can fit a line, order 1, instead of a quadratic of order 2 since your VGV is linear.

Next, you have only 2 coefficients for p instead of 900.

% Create training data.
VGV = [ 2000e2 1800e2 1600e2 1400e2 ]; % [0 45 90 135 ]
angle  = (pi/180).* [ 0 45 90 135 ];
% Create more angles to fit between our training angles.
alpha = (pi/180).*(0:0.1:360);
% Plot training data
polar(angle, VGV, 'bo')
% Fit a quadratic
coefficients  = polyfit(angle, VGV, 1);

% Get a fit
vFit = polyval(coefficients, alpha);
% Plot fitted data:
hold on;
polar(alpha(1:1:3601), vFit, '-')

[Ramesh Bala]

Thank you for the reply. How can I obtain the entire 360 values that i require with this.if I have just 0,90 I can flip it and get all values.In this case how that can be done to get such below fig

[Image Analyst]

If you want 360 interpolated angles instead of 3601 interpolated angles, you'd have to change the way you define alpha to this:

alpha = (pi/180).*(0 : 359); % Exactly 360 angles

If you really want, you can plot blue circles with 'bo' instead of red lines with 'r-'.

If you really want that weird shape you have instead of a spiral, then you'd have to do that flipping craziness, but be aware that alpha no longer means the angle when you go to plot it.

[Ramesh Bala]

ah ! so you mean even if I flip this obtained fit ,it wont be giving the proper values (like 1400e2 at 135 and it won't be same at 270 ?)