Curve (Spiral) Based on Changing Radius

I see plenty of solutions for plotting spirals/curves based on an angle, but is there a way to plot a curve based on a changing radius? For example, the distance between the point that is "tracing" and the point it is tracing around starts at 20 meters, but decreases to 0 meters over 1 second then increases back to 20 meters over 1 second. The point is rotating at pi/2 rad/s, so it should complete 180-deg in the 2 seconds. I have no idea what this would look like, which is why I am trying to plot it.

Answer 1

[Star Strider]

This seems to me to work, although it’s difficult to appreciate the radius effect with only a half-turn of the helix:

t = linspace(0, 2, 500);
wt = (t/2)*pi/2;
radius = cos(2*pi*t/max(t)) * 20;
c = @(r,th) [r.*cos(th); r.*sin(th)];
curve = c(radius,wt)+1;

figure(1)
plot3(curve(1,:), curve(2,:), t)
grid on
xlabel('x')
ylabel('y')
zlabel('t')

figure(2)
plot(t, curve(1,:),  t, curve(2,:),  t,radius)
grid
title('Components Of ‘plot3’ Plot')
legend('x = cos', 'y = sin', 'radius', 'Location','N')

[Paul Huter]

Thank you, this helps a lot.

[Star Strider]

As always, my pleasure.

[Paul Huter]

Why did you use:

wt = (t/2)*pi/2;

? Why not just "t"?

[Star Strider]

My error. You want ‘wt’ to go from 0 to pi, and ‘t’ goes from 0 to 2, so it should have been:

wt = (t/2)*pi;
radius = (0.5*cos(2*pi*t/max(t)) + 0.5)  * 20;

For some reason, I was thinking pi/2.

The rest of the code works without modification.