#!/usr/bin/env python3
# -*- coding: utf-8 -*-

# ***************************************************************************
# *   Copyright (C) 2011, Paul Lutus                                        *
# *                                                                         *
# *   This program is free software; you can redistribute it and/or modify  *
# *   it under the terms of the GNU General Public License as published by  *
# *   the Free Software Foundation; either version 2 of the License, or     *
# *   (at your option) any later version.                                   *
# *                                                                         *
# *   This program is distributed in the hope that it will be useful,       *
# *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
# *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
# *   GNU General Public License for more details.                          *
# *                                                                         *
# *   You should have received a copy of the GNU General Public License     *
# *   along with this program; if not, write to the                         *
# *   Free Software Foundation, Inc.,                                       *
# *   59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.             *
# ***************************************************************************

import sys

from math import *

# see http://arachnoid.com/TankCalc/volumes_in_depth.html

# the functions vfy() and yfv() take these arguments:

# r_a: one radius of a conical frustum
# r_b: the other radius of a conical frustum
# h: the overall height of the conical frustum
# y (vfy): the height for which a partial volume is required, 0 <= y <= h
# v (yfv): the partial volume for which a height is required

# conical frustum volume for height

def vfy(r_a,r_b,h,y):
  return 1.0/3.0*(3*h**2*r_a**2*y + (r_a**2 - 2*r_a*r_b + r_b**2)*y**3 - 3*(h*r_a**2 - h*r_a*r_b)*y**2)*pi/h**2

# conical frustum height for volume

def yfv(r_a,r_b,h,v):
  return h*r_a/(r_a - r_b) - (pi*h*r_a**3 - 3*(r_a - r_b)*v)**(1.0/3.0)*(h**2)**(1.0/3.0)/((r_a - r_b)*pi**(1.0/3.0))
  
def process(r_a,r_b,h,x,inverse):
  if(inverse):
    r = yfv(r_a,r_b,h,x)
  else:
    r = vfy(r_a,r_b,h,x)
  print('%16.4f = %16.4f' % (x,r))

if(len(sys.argv) < 5):
  sys.stderr.write('usage: [-i inverse] r_a r_b h [y or start end step]\n')
  sys.exit(0)
  
inverse = False

coms = sys.argv[1:]

if(coms[0] == '-i'):
  inverse = True
  coms.pop(0)

step = y = None

# must have four arguments as a minimum

try:
  r_a,r_b,h = [float(x) for x in coms[:3]]
  coms = coms[3:]
  try:
    ys,ye,step = [float(x) for x in coms]
  except:
    y = float(coms[0])
except:
  None

if(y != None):
  process(r_a,r_b,h,y,inverse)
elif(step > 0 and ye > ys):
  print('%16s   %16s' % ('Argument','Result'))
  print('-' * 40)
  y = ys
  while(y <= ye):
    process(r_a,r_b,h,y,inverse)
    y += step
else:
  sys.stderr.write('Entry error -- try again.\n')