# Parametric plot with piecewise input

I'm trying to plot a parametric function, which is defined piecewise. For some reason, the plot just jumps to the last piece of the parametric function and plots that.

Here's what I want to plot.

```
t = var('t')
r = 2
def f(x):
if 0 <=x <=r:
return (x, -r)
elif r<x<=r + pi*r:
return (cos(x-r), -(r + sin(x-r)))
elif r + pi*r < x <= 3*r + pi*r:
return (-x + 2*r + pi*r, r)
elif 3*r + pi*r < x <= 3*r + 2*pi*r:
return (cos(x - 3*r), -(r + sin(x-r)))
else:
return (x - 4*r - 2*pi*r, -r)
parametric_plot(f(t), (t, 0, 4*r + 2*pi*r))
```

It just returns a straight line of length 4*r + 2*pi*r with y coordinate -r