Encounter an error while using fimplicit?

How to plot the following equation on matlab by using fimplicit?

(x-x0).*conj((x-x0))+(y-y0).^2=r^2

close all;

r=1./2;

x0=0;

y0=1./2;

syms x y

fimplicit((x-x0).*conj((x-x0))+(y-y0).^2-r^2)

axis equal

Matlab shows

'Undefined function or variable 'fimplicit'.'

Answer 1

[Star Strider]

The fimplicit function was introduced in R2016b.

Use the contour function instead:

r=1./2;
x0=0;
y0=1./2;
f = @(x,y) (x-x0).*conj((x-x0))+(y-y0).^2-r^2;

xv = linspace(x0-r, x0+r, 25);
yv = linspace(y0-r, y0+r, 25);
[X,Y] = ndgrid(xv,yv);

figure
contour(X,Y,f(X,Y), [0 0])
grid
axis equal

.

[Wajahat]

@ Star Strider, how can we fill the color inside the circle like this

[Star Strider]

Add a patch call:

figure
hc = contour(X,Y,f(X,Y), [0 0]);
hold on
patch(hc(1,2:end), hc(2,2:end), [0.4 0.2 0.9], 'FaceAlpha',0.3)
hold off
grid
axis equal

Experiment with different colours (the ‘[0.4 0.2 0.9]’ vector) to get the result you want.

[Wajahat]

@ Star Strider, but when we change the sign, it shows the hyperbolic plot

r=1./2;

x0=0;

y0=1./2;

f = @(x,y) -(x-x0).*conj((x-x0))+(y+y0).^2-r^2;

xv = linspace(x0-r, x0+r, 25);

yv = linspace(y0-r, y0+r, 25);

[X,Y] = ndgrid(xv,yv);

figure

hc = contour(X,Y,f(X,Y), [0 0]);

hold on

patch(hc(1,2:end), hc(2,2:end), [0.8 0.1 0.9], 'FaceAlpha',0.3)

hold off

grid off

axis equal

But I need like this

[Star Strider]

This is a different problem.

With this function:

f = @(x,y) -(x-x0).*conj((x-x0))+(y+y0).^2-r^2;

the patch call changes to:

patch([hc(1,2:end) fliplr(hc(1,2:end))], [hc(2,2:end) ones(size(hc(1,2:end)))*max(ylim)], [0.4 0.2 0.9], 'FaceAlpha',0.3)

The rest of the code is not changed.

[Wajahat]

I got this

which is not same as the previous attached hyperboic image

[Star Strider]

Adjust the limits of ‘xv’ (and perhaps also ‘yv’) to match the figure you want.

For example:

xv = linspace(-1, 1, 25);

You may need to change the parameters in the ‘f’ function to exactly reproduce the figure you posted.