#!/usr/bin/env python

from math import *
M_PI = pi
true=1
false=0

from epix import *

####################################################################
# Converted from tori.xp
####################################################################

N1=24  # latitudes
N2=48  # longitudes

LIGHT=P(1,1,0.5)  # location of light, for shading
VIEWPT=P(6, 3, 4)

r_0=0.95   # minor radius
EPS=0.0025 # shrinkage
du=2.0/N1
dv=2.0/N2

class mesh_quad:
  def __init__(self, f, u0, v0):
    self.pt1=f(u0+EPS,v0+EPS)
    self.pt2=f(u0+du-EPS,v0+EPS)
    self.pt3=f(u0+du-EPS,v0+dv-EPS)
    self.pt4=f(u0+EPS,v0+dv-EPS)
    
    center = 0.25*(self.pt1 + self.pt2 + self.pt3 + self.pt4)
    temp = camera.get_viewpt()

    self.distance = norm(center-temp)

  def how_far(self):
    return self.distance

  def draw(self):
    normal = (self.pt2 - self.pt1)*(self.pt4 - self.pt1)
    normal *= 1/norm(normal)

    dens  = 0.75*(1-pow(normal|LIGHT, 2)/(LIGHT|LIGHT))

    gray(dens) 
    quad(self.pt1, self.pt2, self.pt3, self.pt4) 

def sgn(x):
  if x < 0:
    return -1
  if x > 0:
    return 1

  return 0

def by_distance(arg1, arg2):
  return sgn(arg2.how_far() - arg1.how_far())

def f1(u, v):
  return polar(2+r_0*Cos(M_PI*u), M_PI*v) + P(0,0,r_0*Sin(M_PI*u)) # torus

def f2(u, v):
  return P(r_0*Sin(M_PI*u), 
	   2+(2+r_0*Cos(M_PI*u))*Cos(M_PI*v),
	     (2+r_0*Cos(M_PI*u))*Sin(M_PI*v))

bounding_box(P(-3,-3),P(3,3))
unitlength("1in")
picture(4,4)

begin()

viewpoint(VIEWPT)
camera.look_at(P(0,1,0))
camera.range(10)

crop()
fill()

mesh = []

for i in range(N1):
  for j in range(N2):
    mesh.append(mesh_quad(f1, -1+du*i, -1+dv*j))
    mesh.append(mesh_quad(f2, -1+du*i, -1+dv*j))

mesh.sort(by_distance)

for M in mesh:
  M.draw()

end()