#! /usr/bin/python3
# Last edited on 2024-06-06 17:39:20 by stolfi

from math import sin, cos, pi
import sys
 
prec = 4          # Decimal digits    
eps = 0.1**prec   # Coordinate quantum.

Ne = int(sys.argv[1])  # Total number of edges. 
assert (Ne % 3) == 0, "{Ne} ust be a multiple of 3"

N = Ne//3 - 1  # Number points on circular arc.

def reven(C):
  # Rounds {C} to even multiple of {eps}.
  return eps*2*int(C/eps/2)

sys.stderr.write("N = %d\n" % N)

R = 10000     # Radius of circular arc.
h = R/20      # Prism thickness.
ang_min = pi/6            # Min arg of circular arc (radians).
ang_max = pi/2 - ang_min  # Max arg of circular arc (radians).
L = R*(sin(ang_max) - sin(ang_min))       # Height of circular arc.
Yc = 2*eps + R*cos(ang_min)      # Y of arc center.
Zc = 2*eps + L + R*sin(ang_max)  # Z of arc center.

elen = reven(R*(ang_max - ang_min)/N)  # Approx edge length.
assert elen > 5*eps

sys.stderr.write("elen = %.*f\n" % (prec, elen))

# The {(Y,Z)} coordinates of the vertices:
# Vertices 1 to {N+1} are one base, {N+2} to {2*N+2} are the other base. 
v = [ None ]

for f in range(2):
  X = reven(2*eps if f == 0 else h - 2*eps)
  v.append((X, 2*eps, 2*eps))
  for k in range(N):
    ang = ang_min + (ang_max - ang_min)*k/(N-1)
    c = cos(ang); s = sin(ang)
    Y = reven(Yc - R*c)
    Z = reven(Zc - R*s)
    v.append((X, Y, Z))
    
Nv = len(v) - 1
assert Nv == 2*(N+1), "bug len(v), Nv"

def P(st): 
  sys.stdout.write(st)

# Write the vertex coordinates:
for f in range(2):
  for k in range(N+1):
    vkf = v[1 + k + f*(N+1)]
    P("v")
    for j in range(3):
      P(" %.*f" % (prec, vkf[j]))
    P("\n")
  P("\n")
P("\n")

# Write the base faces in CCW order from outside.
# Note that OBJ indices start at 1:

P("f ")
P(" %d" % 1)
for k in range(N): P(" %d" % (N+1-k))
P("\n")
P("\n")

P("f ")
P(" %d" % (N+2))
for k in range(N): P(" %d" % (N+3+k))
P("\n")
P("\n")
  
# Write the square faces on the wall, in CCW order from outside:
for k00 in range(N+1):
  k01 = ((k00 + 1) % (N+1))
  k10 = k00 + N+1
  k11 = k01 + N+1
  P("f %d %d %d %d\n" % (k00+1, k01+1, k11+1, k10+1)) # Nesta ordem!