norm

import numpy as np

p1 = [3, 11, 27, -114]
p2 = [36, 66, 175.5, -774]
p3 = [3, 22, 49, -213]
p4 = [3, 20, 54, -222]

p5 = [-3, 11, 27, -114]
p6 = [-36, 66, 175.5, -774]
p7 = [-3, 22, 49, -213]
p8 = [-3, 20, 54, -222]

p9 = [-3, -11, 27, -114]
p10 = [-36, -66, 175.5, -774]
p11 = [-3, -22, 49, -213]
p12 = [-3, -20, 54, -222]

p13 = [3, -11, 27, -114]
p14 = [36, -66, 175.5, -774]
p15 = [3, -22, 49, -213]
p16 = [3, -20, 54, -222]

p17 = [3, 11, -27, -114]
p18 = [36, 66, -175.5, -774]
p19 = [3, 22, -49, -213]
p20 = [3, 20, -54, -222]

p21 = [-3, 11, -27, -114]
p22 = [-36, 66, -175.5, -774]
p23 = [-3, 22, -49, -213]
p24 = [-3, 20, -54, -222]

p25 = [-3, -11, -27, -114]
p26 = [-36, -66, -175.5, -774]
p27 = [-3, -22, -49, -213]
p28 = [-3, -20, -54, -222]

p29 = [3, -11, -27, -114]
p30 = [36, -66, -175.5, -774]
p31 = [3, -22, -49, -213]
p32 = [3, -20, -54, -222]

oct1 = [p1, p2, p3, p4]
oct2 = [p5, p6, p7, p8]
oct3 = [p9, p10, p11, p12]
oct4 = [p13, p14, p15, p16]
oct5 = [p17, p18, p19, p20]
oct6 = [p21, p22, p23, p24]
oct7 = [p25, p26, p27, p28]
oct8 = [p29, p30, p31, p32]

all_v = [
    (5, 9, 0),
    (2, 0, 4),
    (0, 3, 3),
    (43 / 2, 0, 0),
    (0, 213 / 22, 0),
    (0, 0, 37 / 9),
    (-5, 9, 0),
    (-2, 0, 4),
    (-43 / 2, 0, 0),
    (5, -9, 0),
    (0, -3, 3),
    (0, -213 / 22, 0),
    (2, 0, -4),
    (0, 3, -3),
    (0, 0, -37 / 9),
    (-5, -9, 0),
    (-2, 0, -4),
    (0, -3, -3)
]


def check(r, p, v):
    r_i = []
    for p_i in p:
        r_ij = 0
        for i in range(3):
            r_ij += p_i[i] * v[i]
        r_ij += p_i[-1]
        r_i.append(r_ij)
    r.append(r_i)
    pass


oct1_result = []
for v in all_v:
    check(oct1_result, oct1, v)

print("oct1")
for i in oct1_result:
    print("\t".join(f"{x:.2f}" for x in i), sep='\t')

oct2_result = []
for v in all_v:
    check(oct2_result, oct2, v)

print("oct2")
for i in oct2_result:
    print("\t".join(f"{x:.2f}" for x in i), sep='\t')

oct3_result = []
for v in all_v:
    check(oct3_result, oct3, v)

print("oct3")
for i in oct3_result:
    print("\t".join(f"{x:.2f}" for x in i), sep='\t')

oct4_result = []
for v in all_v:
    check(oct4_result, oct4, v)

print("oct4")
for i in oct4_result:
    print("\t".join(f"{x:.2f}" for x in i), sep='\t')

oct5_result = []
for v in all_v:
    check(oct5_result, oct5, v)

print("oct5")
for i in oct5_result:
    print("\t".join(f"{x:.2f}" for x in i), sep='\t')

oct6_result = []
for v in all_v:
    check(oct6_result, oct6, v)

print("oct6")
for i in oct6_result:
    print("\t".join(f"{x:.2f}" for x in i), sep='\t')

oct7_result = []
for v in all_v:
    check(oct7_result, oct7, v)

print("oct7")
for i in oct7_result:
    print("\t".join(f"{x:.2f}" for x in i), sep='\t')

oct8_result = []
for v in all_v:
    check(oct8_result, oct8, v)

print("oct8")
for i in oct8_result:
    print("\t".join(f"{x:.2f}" for x in i), sep='\t')