plot (X^2/cosh^​2(v))+(y^2​/sinh^2(v)​)=1

Hi,

How I can plot this function as v= constant such as for

v=0,pi/2,and pi

(X^2/cosh^2(v))+(y^2/sinh^2(v))=1

Thanks

Answer 1

[Star Strider]

One option (if I understood your Question correctly):

v = pi/2;
f = @(X,Y) (X.^2./cosh(v).^2)+(Y.^2./sinh(v).^2)-1;
x = linspace(-5, 5, 50);
[X,Y] = meshgrid(x);

figure(1)
surf(X, Y, f(X,Y))
grid on
xlabel('X')
ylabel('Y')
title('v = ^{\pi}/_2')

[Ali Kareem]

Hi,

Thank you for your reply. I mean if I take v as constant. how I can plot it. it shout be like ellipse. when v is constant and when I change v I will get another ellipse

Regards

[Walter Roberson]

Then you repeat the process with a different v.

[Ali Kareem]

Hi,

Then how I can combine all plots in one? for different Vs

Regards

[Star Strider]

My pleasure.

Use the subplot function. That will plot them in different axes in the same figure. I would not combine all plots in the same axes with surface plots. Try something like this:

f = @(X,Y,v) (X.^2./cosh(v).^2)+(Y.^2./sinh(v).^2)-1;
x = linspace(-5, 5, 50);
[X,Y] = meshgrid(x);

figure(1)
subplot(3,1,1)
surf(X, Y, f(X,Y,0))
xlabel('X')
ylabel('Y')
title('v = 0')
grid on
subplot(3,1,2)
surf(X, Y, f(X,Y,pi/2))
xlabel('X')
ylabel('Y')
title('v = ^{\pi}/_2')
grid on
subplot(3,1,3)
surf(X, Y, f(X,Y,pi))
xlabel('X')
ylabel('Y')
title('v = pi')
grid on

That should work.

Answer 2

[Walter Roberson]

v = [0, pi/2, pi];

for K = 1 : length(v)
  f = @(X,y) (X.^2/cosh(v(K))^2) + (y.^2/sinh(v(K))^2) - 1;
  figure
  ezplot(f, [-15 15])
  title(sprintf('v = %g', v(K)));
end

You might note that the v = 0 case comes out blank. That is because sinh(0) is 0 so you have a division by 0, which is going to be infinity (except at y=0 where you have 0/0 which is undefined)

[Ali Kareem]

Thank you for your reply. I tried this code but it is not combine all plot in one diagram.

Regars

[Walter Roberson]

v = [0, pi/2, pi];

linecolortab = hsv(length(v));  %choose different colors

for K = 1 : length(v)
  f = @(X,y) (X.^2/cosh(v(K))^2) + (y.^2/sinh(v(K))^2) - 1;
  h(K) = ezplot(f, [-15 15]);
  hold on
  L{K} = sprintf('v = %.3f', v(K));
  try
    set(h(K), 'LineColor', linecolortab(K,:));
  catch ME
  end
end
legend(h, L)
hold off

You will notice that there is a legend entry for v = 0 but there is no corresponding line. This is due to sinh(0) introducing a division by 0 so there is no plot for v = 0.

The colors used for the lines will automatically change if you add or remove values for v.

Technical note:

In R2014a (and probably several releases before that, but might have changed in R2014b), the output of ezplot is a hggroup that includes a LineColor property that can be set. However, there is a listener on the handle that triggers an "Index exceeds matrix dimensions" within scribe.legend/methods>layout_legend_items when the property is set, but does so after setting the property. If the command is repeated, the error does not trigger. The set() will therefore generate an error but will have the desired effect. That is why I put the set() within a try/catch block, so that the stray error message is ignored.