Batman Curve

# bat functions: semicircle, ellipse, shoulders, bottom, cowl
# harmless Compat.UTF8String warnings from julia kernel on first run
σ(x) = sqrt.(1-x.^2)
e(x) = 3σ(x/7)
s(x) = 4.2 - .5x - 2.8σ(.5x-.5)
b(x) = σ(abs.(2-x)-1)-x.^2/11 + .5x - 3
c(x) = [1.7, 1.7, 2.6, .9];

# the first time in a project, it can take over a minute to precompile PyPlot
using PyPlot

# plot symmetrically across y-axis
o(x,f) = plot(-x,f(x), color="black") , plot(x,f(x), color="black")
p(x,f) = o(x,t->f.(t))             # broadcast must be explicit
p((3:.1:7),e);p(4:.1:7,t->-e(t))   # ellipse
p(1:.1:3,s);p(0:.1:4,b)            # shoulders and bottom
o([0,.5,.8,1],c);                  # cowl is piecewise linear