Linear equation of circle

Hello, consider having a general equation of circle like x^2+y^2=r^2.

A way to linear the circle is to "cut the circle into horizintal or vertical slices". Any idea how could I transfer this idea in matlab equations?

Thank you.

[Voss]

Hello, I'm not familiar with the term "to linear". Can you please explain more about what you would like to do?

[Voss]

It sounds like "to parameterize" maybe, but that's not cutting into slices.

% parameterize with parameter t:
t = 0:0.01:2*pi;
r = 1;
x = r*cos(t);
y = r*sin(t);
plot(x,y);

[ANDREAS KOUNTOURIS]

Nonlinear equations are equations that appear as curved lines when you graph them.

Linear equations are equations that appear as straight lines when you graph them.

[ANDREAS KOUNTOURIS]

I would like to avoid the ^2 and the cos(t), sin(t) from the final equation

[DGM]

How do you propose to make a circle out of a straight line? Are you asking how to create a polygon? Or to create a series of parallel lines?

[Voss]

Plotting in polar coordinates would allow you to plot a circle while avoiding non-linear terms:

t = 0:0.01:2*pi;
polarplot(t,ones(size(t)),'LineWidth',2);

Answer 1

[DGM]

You mean like this?

r = 1;
y = linspace(-r,r,50);
xr = sqrt(r^2 - y.^2);
xl = -sqrt(r^2 - y.^2);

plot([xr; xl],[y; y])

And I suppose you could rotate it if you wanted

r = 1;
t = 30;

y = linspace(-r,r,50);
xr = sqrt(r^2 - y.^2);
xl = -sqrt(r^2 - y.^2);

[th rh] = cart2pol([xr; xl],[y; y]);
[xx yy] = pol2cart(th+t*pi/180,rh);

plot(xx,yy)

[ANDREAS KOUNTOURIS]

Yes, something like this. Thank you!