Calabi_Yau_manifold_sv.py

"""
in n_dimension s d=2 n=2
in a_radian s d=0.4 n=2
in x_dim s d=20 n=2
in y_dim s d=20 n=2
out verts v
out edges s
out faces s
"""


import cmath
import numpy as np
from math import sin, cos, sinh, cosh, pi
from mathutils import Vector


def calcZ1(x, y, k, n):
    return cmath.exp(1j*(2*cmath.pi*k/n)) * (cmath.cos(x+y*1j)**(2/n))

def calcZ2(x, y, k, n):
    return cmath.exp(1j*(2*cmath.pi*k/n)) * (cmath.sin(x+y*1j)**(2/n))

def calcZ1Real(x, y, k, n):
    return (calcZ1(x, y, k, n)).real

def calcZ2Real(x, y, k, n):
    return (calcZ2(x, y, k, n)).real

def calcZ(x, y, k1_, k2_, n, a_):
    z1 = calcZ1(x, y, k1, n)
    z2 = calcZ2(x, y, k2, n)
    return z1.imag * cos(a_) + z2.imag*sin(a_)

x = np.linspace(0, pi/2, x_dim)
y = np.linspace(-pi/2, pi/2, y_dim)
x, y = np.meshgrid(x, y)

verts = [[]]
edges = [[]]
edge_set = []
faces = [[]]
face_set = []

n = n_dimension
for i in range(n*n):
    edge_set.append(set())
    face_set.append(set())

count = 0
for k1 in range(n):
    for k2 in range(n):
        # calc X, Y, Z values
        X = np.frompyfunc(calcZ1Real, 4, 1)(x, y, k1, n).astype('float32')
        Y = np.frompyfunc(calcZ2Real, 4, 1)(x, y, k2, n).astype('float32')
        Z = np.frompyfunc(calcZ, 6, 1)(x, y, k1, k2, n, a_radian).astype('float32')

        X_ = X.flatten()
        Y_ = Y.flatten()
        Z_ = Z.flatten()
        
        v = []
        for x1, y1, z1 in zip(X_, Y_, Z_):
            v.append((x1, y1, z1))
        verts[0].extend(v)
            
        for i in range(x_dim * y_dim):
            y_index = i / y_dim
            x_index = i % y_dim
            j = i + count * x_dim * y_dim
            if (y_index < y_dim - 1) and (x_index < x_dim - 1):
                edge_set[count].add(tuple(sorted([j, j+y_dim])))
                edge_set[count].add(tuple(sorted([j+y_dim, j+y_dim+1])))
                edge_set[count].add(tuple(sorted([j+y_dim+1, j+1])))
                edge_set[count].add(tuple(sorted([j+1, j])))
                face_set[count].add(tuple(([j, j+y_dim, j+y_dim+1, j+1])))
        
        count += 1

for i in range(n*n):
    edges[0].extend(list(edge_set[i]))
    faces[0].extend(list(face_set[i]))