# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 
# set output 'airfoil.3.png'
set dummy t, y
set key fixed right top vertical Right noreverse enhanced autotitle box lt black linewidth 1.000 dashtype solid
set parametric
set style data lines
set title "Joukowski Airfoil using Complex Variables" 
set trange [ 0.00000 : 6.28319 ] noreverse
set xlabel "eps = 0.06 real" 
set xrange [ -0.600000 : 0.600000 ] noreverse
set yrange [ -0.200000 : 1.80000 ] noreverse
bez_d4_i0(x) =     (1 - x)**4
bez_d4_i1(x) = 4 * (1 - x)**3 * x
bez_d4_i2(x) = 6 * (1 - x)**2 * x**2
bez_d4_i3(x) = 4 * (1 - x)**1 * x**3
bez_d4_i4(x) =                  x**4
bez_d8_i0(x) =      (1 - x)**8
bez_d8_i1(x) =  8 * (1 - x)**7 * x
bez_d8_i2(x) = 28 * (1 - x)**6 * x**2
bez_d8_i3(x) = 56 * (1 - x)**5 * x**3
bez_d8_i4(x) = 70 * (1 - x)**4 * x**4
bez_d8_i5(x) = 56 * (1 - x)**3 * x**5
bez_d8_i6(x) = 28 * (1 - x)**2 * x**6
bez_d8_i7(x) =  8 * (1 - x)    * x**7
bez_d8_i8(x) =                   x**8
mean_y(t) = m0 * mm * bez_d4_i0(t) + 	    m1 * mm * bez_d4_i1(t) + 	    m2 * mm * bez_d4_i2(t) + 	    m3 * mm * bez_d4_i3(t) + 	    m4 * mm * bez_d4_i4(t)
mean_x(t) = p0 * bez_d4_i0(t) + 	    p1 * bez_d4_i1(t) + 	    p2 * bez_d4_i2(t) + 	    p3 * bez_d4_i3(t) + 	    p4 * bez_d4_i4(t)
z_x(x) = x0 * bez_d8_i0(x) + x1 * bez_d8_i1(x) + x2 * bez_d8_i2(x) + 	 x3 * bez_d8_i3(x) + x4 * bez_d8_i4(x) + x5 * bez_d8_i5(x) + 	 x6 * bez_d8_i6(x) + x7 * bez_d8_i7(x) + x8 * bez_d8_i8(x)
z_y(x, tk) =    y0 * tk * bez_d8_i0(x) + y1 * tk * bez_d8_i1(x) + y2 * tk * bez_d8_i2(x) +    y3 * tk * bez_d8_i3(x) + y4 * tk * bez_d8_i4(x) + y5 * tk * bez_d8_i5(x) +    y6 * tk * bez_d8_i6(x) + y7 * tk * bez_d8_i7(x) + y8 * tk * bez_d8_i8(x)
airfoil_y1(t, thick) = mean_y(z_x(t)) + z_y(t, thick)
airfoil_y2(t, thick) = mean_y(z_x(t)) - z_y(t, thick)
airfoil_y(t) = mean_y(z_x(t))
airfoil_x(t) = mean_x(z_x(t))
Zeta(t) = -eps + (a+eps)*exp(t*{0,1})
eta(t) = Zeta(t) + a*a/Zeta(t)
NO_ANIMATION = 1
mm = 0.0
thick = 0.12
pp = 0.5
x0 = 0.0
y0 = 0.0
x1 = 0.0
y1 = 0.18556
x2 = 0.03571
y2 = 0.34863
x3 = 0.10714
y3 = 0.48919
x4 = 0.21429
y4 = 0.58214
x5 = 0.35714
y5 = 0.55724
x6 = 0.53571
y6 = 0.44992
x7 = 0.75
y7 = 0.30281
x8 = 1.0
y8 = 0.0105
m0 = 0.0
m1 = 0.1
m2 = 0.1
m3 = 0.1
m4 = 0.0
p0 = 0.0
p1 = 0.2
p2 = 0.4
p3 = 0.7
p4 = 1.0
eps = 0.06
a = 0.25
plot real(eta(t)),imag(eta(t))