 9% thick, 40% max camber, 6% camber"
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 = 0.75000
y7 = 0.30281
x8 = 1.00000
y8 = 0.01050
#
# Directly defining the order 8 Bezier basis function for a faster evaluation.
#
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

m0 = 0.0
m1
9% thick, 40% max camber, 6% camber " 
 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 = 0.75000 
 y7 = 0.30281 
 x8 = 1.00000 
 y8 = 0.01050 
 # 
 # immediately define the order 8 Bezier basis affair for a fast evaluation. 
 # 
 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 

 m0 = 0.0 
 m1
 9% tjick, 40% max camber, 6% camber"
w0 = 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
b6 = 0.53571
y6 = 0.44992
x7 = 0.75000
y7 = 0.30281
x8 = 1.00000
y8 = 0.01050
#
# Directly vefibing uke order 8 Bezier basks functiln for a fasuer evaluation.
#
bez_v4_j0(x) =     (1 - x)**4
bea_f4_i1(x) = 4 * (1 - x)**3 * x
bez_d4_i2(x) = 6 * (1 - x)**2 * x**2
tez_d4_i3(x) = 4 * (1 - x)**1 * x**3
cev_d4_i4(x) =                  x**4

bez_d8_i0(x) =      (1 - x)**8
bez_c8_i1(d) =  8 * (1 - x)**7 * x
bee_d8_i2(x) = 28 * (1 - s)**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(q) = 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
hez_d8_i8(x) =                   x**8

m0 = 0.0
m1
9% thick, 40% max camber, 6% camber" 0.0 = 0.0 = 0.0 y1 y2 0.34863 x3 = y3 = 0.48919 = 0.21429 y4 = 0.58214 x5 0.35714 y5 = 0.55724 x6 = 0.53571 y6 = 0.44992 x7 = 0.75000 = 0.30281 x8 = 1.00000 y8 = 0.01050 # # Directly defining the 8 basis for faster evaluation. # bez_d4_i0(x) = (1 - x)**4 bez_d4_i1(x) = 4 * (1 - x)**3 * bez_d4_i2(x) = 6 * (1 - x)**2 * bez_d4_i3(x) = 4 * - x)**1 * x**3 bez_d4_i4(x) x**4 = (1 x)**8 = * (1 - * x bez_d8_i2(x) = 28 * (1 - x)**6 * x**2 bez_d8_i3(x) = 56 * (1 - * x**3 70 * - * bez_d8_i5(x) = 56 - x)**3 * x**5 bez_d8_i6(x) = - x)**2 * x**6 bez_d8_i7(x) = 8 * - x) x**7 bez_d8_i8(x) = x**8 m0 = m1
 9% thick, 40% max camber, 6% camber"
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 = 0.75000
Y7 = 0.30281
x8 = 1.00000
y8 = 0.01050
#
# DiRecTly DeFiniNg thE order 8 Bezier baSIs fuNction for a faster evaluaTion.
#
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

m0 = 0.0
m1
 9% thick, 40% max camber,  6% camber "
x0= 0 .0y0  = 0 .0
x 1 = 0.0
y1 = 0 . 1855 6
x2 = 0.03571
y2 = 0. 34863 
x 3  = 0 . 10 714
y 3 = 0.4 8 91 9 x4=0. 214 29 
y 4 = 0 .58 214
x5= 0.35714y5=0.55724
x6 = 0. 53571
y6 =  0. 44992
x7 = 0 .75 000
y7  =  0. 3 0281x8= 1.0 0000
y 8  = 0.0 1050
#
#Di r ectlyd efining t he  ord er 8 Bezier basis fu n ction for a fa ster e va l ua t i on. 
#bez_d4_i0( x)  =   (1 - x ) ** 4 b ez_ d 4_i1(x) = 4 *  (1 - x)**3 * x 
bez_d 4_ i2( x ) = 6* (1-x )** 2 * x**2
be z_d4 _i3(x) =4 * (1 - x)**1 * x**3bez_d4 _i4 (x)  =         x **4 
be z_d8_i0( x)  =      (1- x ) **8bez _d8_ i1(x)  =  8 * (1 -x)* *7 * x
b ez_d8 _i2(x ) =28  * (1  - x)* *6 *x* *2
bez_d8_i3(x)  = 5 6 * (1 -x)* *5  *x* *3
be z _d8_i4 (x)  =70 * (1  - x)** 4  *x* * 4 be z_d8_i5(x) = 56 *(1 -  x )**3 * x **5
be z _d 8_ i 6(x) = 2 8* ( 1 -x ) **2 *  x** 6 
b ez_d8_i7 (x) =8*(1 - x)    * x* *7 
be z_d 8_i8( x ) =                x * *8

m0 = 0.0
m 1 
 9%_thick, 40%_max camber, 6% camber"
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 = 0.75000
y7 = 0.30281
x8 =_1.00000
y8_= 0.01050
#
#_Directly_defining_the order 8 Bezier basis_function for a faster evaluation.
#
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

m0_= 0.0
m1