"""
hyper-diamond data and simple rotation in 4D
"""
from math import pi, sin, cos, sqrt

radian = 180.0 / pi

# vertices4d 24:(w,x,y,z), belongs to tesseract number
vertices4d = [[-1.0, 0.0, 0.0, 0.0], # 1,3
              [ 1.0, 0.0, 0.0, 0.0], # 1,3
              [ 0.0,-1.0, 0.0, 0.0], # 1,3
              [ 0.0, 1.0, 0.0, 0.0], # 1,3
              [ 0.0, 0.0,-1.0, 0.0], # 1,3
              [ 0.0, 0.0, 1.0, 0.0], # 1,3
              [ 0.0, 0.0, 0.0,-1.0], # 1,3
              [ 0.0, 0.0, 0.0, 1.0], # 1,3
              
              [-0.5,-0.5,-0.5,-0.5], # 1,2
              [ 0.5, 0.5, 0.5, 0.5], # 1,2   
              [-0.5,-0.5, 0.5, 0.5], # 1,2
              [ 0.5, 0.5,-0.5,-0.5], # 1,2
              [-0.5, 0.5, 0.5,-0.5], # 1,2
              [ 0.5,-0.5,-0.5, 0.5], # 1,2
              [-0.5, 0.5,-0.5, 0.5], # 1,2
              [ 0.5,-0.5, 0.5,-0.5], # 1,2
               
              [-0.5, 0.5, 0.5, 0.5], # 2,3
              [ 0.5,-0.5,-0.5,-0.5], # 2,3
              [ 0.5,-0.5, 0.5, 0.5], # 2,3
              [-0.5, 0.5,-0.5,-0.5], # 2,3
              [ 0.5, 0.5,-0.5, 0.5], # 2,3
              [-0.5,-0.5, 0.5,-0.5], # 2,3
              [ 0.5, 0.5, 0.5,-0.5], # 2,3
              [-0.5,-0.5,-0.5, 0.5]] # 2,3

#rotate in plane axis1, axis2
def Rotate(axis1, axis2, angle):
    angle = angle / radian
    for v in vertices4d:
        c1 = v[axis1]*cos (angle) - v[axis2]*sin (angle)
        c2 = v[axis1]*sin (angle) + v[axis2]*cos (angle)
        v[axis1], v[axis2] = c1, c2

#4D axes vectors in 3D
per_axes = ((0.0, 0.0, 0.0),
            (1.0, 0.0, 0.0),
            (0.0, 1.0, 0.0),
            (0.0, 0.0, 1.0))
            
iso_x0 = sqrt(8.0 / 9.0)
iso_x12 = -sqrt(2.0 / 9.0)
iso_y1 = sqrt(2.0 / 3.0)
iso_y2 = -sqrt(2.0 / 3.0)
iso_z012 = -1.0 / 3.0

iso_axes = ((iso_x0, 0.0, iso_z012),
            (iso_x12, iso_y1, iso_z012),
            (iso_x12, iso_y2, iso_z012),
            (0.0, 0.0, 1.0))

axes_colors = ((0.8, 0.8, 0.8),
               (0.9, 0.1, 0.1),
               (0.1, 0.9, 0.1),
               (0.1, 0.1, 1.0))

axes_labels = ("w","x","y","z")