MATLAB: Fill area between two polar curves

patch between polar curves

Hello , i have these two formulas, i would like to fill the area between these two curves is there a way to do it with patch command?

Thanks

phi=0.87*sin((log(r)*pi)/(log(tau)));
phi_shifted_45=0.87*sin((log(r)*pi)/(log(tau)))+0.78;

Best Answer

The patch function will not work with polar axes. It throws this error:

Error using patch
While setting property 'Parent' of class 'Patch':
Patch cannot be a child of PolarAxes.

Oh, well...

The best I can do with this is to use pol2cart:

tau = 0.5;
r = linspace(eps, 1.5, 500);
phi = 0.87*sin((log(r)*pi)/(log(tau)));
phi_shifted_45 = 0.87*sin((log(r)*pi)/(log(tau)))+0.78;
[x1,y1] = pol2cart(phi, r);
[x2,y2] = pol2cart(phi_shifted_45, r);
figure(1)
patch([x1 fliplr(x2)], [y1 fliplr(y2)], 'g')
axis equal

Note to MathWorks: Can we have a patch for polar coordinate systems when you have time to implement it?

Related Solutions

MATLAB: How to fill the area between two curves on a polar plot

Yes!

Yours are different. Yours are also an easier problem.

I set up everything in polar coordinates in that code, then used the pol2cart function to create Cartesian representations for them, and plotted them in Cartesian space. My code drew the polar coordinates the same way. It did not use polar or polarplot, since they do not offer the necessary options.

Set your data up in polar coordinates, use pol2cart, patch, then plot.

Use the Plot Full Circumference and Plot Radials section in my code your referred to, to plot the polar coordinate grid. Use the text function for the radial and angle labels if you want them. Use the values in the grid plotting part of my earlier code to get the (x,y) values for your text calls.

This code snippet should get you started:

theta = linspace(0, 2*pi, 18);                                      % Create Data (Angles)
Data1 = rand(1, 18)*0.5 + 0.5;                                      % Create Data (First Radius)
Data2 = rand(1, 18)*0.5;                                            % Create Data (Second Radius)
[x1, y1] = pol2cart(theta, Data1);                                  % Convert To Cartesian
[x2, y2] = pol2cart(theta, Data2);
figure(1)
patch([x1 fliplr(x2)], [y1 fliplr(y2)], 'g', 'EdgeColor','g')       % Fill Area Between Radius Limits
hold on
plot(x1, y1, '-k')
plot(x2, y2, '-r')
hold off
axis equal

Experiment to get the result you want. Post back if you have problems. I’ll do my best to help.

MATLAB: Conversion into cartesian formula

It is not going to be an easy conversion. I would do a direct substitution (see the subs call for the substitutions I used), then solve it numerically. No analytic solution exists (at least that I can see).

The Code —

syms phi r tau x y
Eq = phi == 0.87*sin((log(r)*pi)/(log(tau)));
Eq = subs(Eq, {phi, r}, {atan(y/x), sqrt(x^2+y^2)})
Eq = simplify(expand(Eq), 'Steps',20)
Eq =
atan(y/x) == (87*sin((pi*log((x^2 + y^2)^(1/2)))/log(tau)))/100
Eq =
87*sin((pi*log(x^2 + y^2))/(2*log(tau))) == 100*atan(y/x)

Best Answer

Related Solutions

MATLAB: How to fill the area between two curves on a polar plot

MATLAB: Conversion into cartesian formula

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