#
# Copyright 2000, University of Washington
# 
# Permission to use, copy, modify, and distribute this software and its
# documentation for any purpose and without fee is hereby granted,
# provided that the above copyright notice appear in all copies and that
# both the copyright notice and this permission notice and warranty
# disclaimer appear in supporting documentation, and that the names of
# the authors or their employers not be used in advertising or publicity
# pertaining to distribution of the software without specific, written
# prior permission.
# 
# The authors and their employers disclaim all warranties with regard to
# this software, including all implied warranties of merchantability and
# fitness.  In no event shall the authors or their employers be liable
# for any special, indirect or consequential damages or any damages
# whatsoever resulting from loss of use, data or profits, whether in an
# action of contract, negligence or other tortious action, arising out of
# or in connection with the use or performance of this software.
# 

#
# params.py
#
# This script encodes tiling vertex parameterizations for the 93
# isohedral tiling types.  It can be run from the command line and
# produces a polygon as output, one point per line.  Example:
#
#    % python params.py IH1 0.9 0.3 0.4 0.5
#    -0.4 0.5
#    0 0
#    0.9 0.3
#    1.3 0.8
#    0.9 1.3
#    0 1
#
# Written by Craig S. Kaplan (csk@cs.washington.edu), April 2000.
# See the paper "Escherization", by Craig S. Kaplan and David H. Salesin
# in the SIGGRAPH 2000 Conference Proceedings. 
#
# 24 October 2003 -- removed extraneous junk from l488_params.
# Thanks to Chris Horn for finding this.
#

import math
import sys

from geo import *

def polyArea( pts ):
	area = 0.0

	for i in range( len( pts ) ):
		ip1 = (i+1)%len(pts)
		area = area + pts[i].x*pts[ip1].y - pts[i].y*pts[ip1].x

	return abs( area * 0.5 )

def polyCenter( pts ):
	mid = Point(0.0,0.0)

	for i in range( len( pts ) ):
		mid = mid + pts[i]

	pf = 1.0 / float(len(pts))
	return mid.scale( pf, pf )

# 
# This routine is used to scale and translate the polygon (in a fairly
# mindless way) so that it lies close to the origin and so that all
# tiling polygons have roughly the same size.  But rescaling obfuscates
# the connection between the parameters you put in and the point positions
# you get out, so I'm commenting it out for now.
#
def rescale( pts, morescale = 1.0 ):
	pass

	# a = polyArea( pts )
	# m = polyCenter( pts )

	# sc = 1.0 / math.sqrt( a ) * 1.25 * morescale

	# for i in range( len( pts ) ):
	# 	np = convexSum( m, pts[ i ], sc )
	# 	pts[ i ].x = np.x - m.x
	# 	pts[ i ].y = np.y - m.y

	# na = polyArea( pts )


#
# 3.3.3.3.3.3
#
		
def parhex_params( v0, v1, v2, v3 ):
	hex = ( 
		Point( -v2, 1-v3 ), 
		Point( 0, 0 ),
		Point( v0, v1 ),
		Point( v0+v2, v1+v3 ),
		Point( v0, 1+v1 ),
		Point( 0, 1 ) )
	rescale( hex )

	return hex

def ih02_params( v0, v1, v2, v3 ):
	hex = ( 
		Point( 0, 1 ),
		Point( -v2, 0.5 ), 
		Point( 0, 0 ),
		Point( v0, v1 ),
		Point( v0+v3, v1+0.5 ),
		Point( v0, 1+v1 ) )
	rescale( hex )

	return hex

def ih03_params( v0, v1, v2, v3 ):
	hex = ( 
		Point( -v2, v3 ), 
		Point( 0, 0 ),
		Point( v0, v1 ),
		Point( v0+v2, v1+v3 ),
		Point( v0, 1+v1 ),
		Point( 0, 1 ) )
	rescale( hex )

	return hex

def ih04_params( v0, v1, v2, v3, v4, v5 ):
	hex = ( 
		Point( -v2, v3 ), 
		Point( 0, 0 ),
		Point( v0, v1 ),
		Point( v0+v4, v1+v5 ),
		Point( v0, 1+v1 ),
		Point( 0, 1 ) )
	rescale( hex )

	return hex

def ih05_params( v0, v1, v2, v3, v4 ):
	hex = ( 
		Point( -v2, v3 ), 
		Point( 0, 0 ),
		Point( v0, v1 ),
		Point( v0+v4, v1+0.5 ),
		Point( v0, 1+v1 ),
		Point( 0, 1 ) )
	rescale( hex )

	return hex

def ih06_params( v0, v1, v2, v3, v4 ):
	hex = ( 
		Point( v0 + v2, v3 - v1 ),
		Point( v0 + v4, v1 + 1 ),
		Point( v4, 1 ),
		Point( -v2, v3 ),
		Point( 0, 0 ),
		Point( v0, -v1 ) )
	rescale( hex )

	return hex

def ih07_params( v0, v1 ):
	m = 0.5 / math.sqrt(3.0)
	T1 = match( Point(v0,v1), Point(1,0) )
	T2 = match( Point(0,0), Point(v0,v1) )

	hex = ( 
		Point( 0, 0 ),
		Point( 0.5, -m ),
		Point( 1, 0 ),
		T1 * Point( 0.5, m ),
		Point( v0, v1 ),
		T2 * Point( 0.5, m ) )
	rescale( hex )

	return hex

def ih09_params( v0, v1, v2 ):
	hex = ( 
		Point( 0, 0 ),
		Point( v0, v1 ),
		Point( v0 + v2, v1 + 0.5 ),
		Point( v0, v1 + 1.0 ),
		Point( 0.0, 1.0 ),
		Point( -v2, 0.5 ) )
	rescale( hex )

	return hex

def hex_params():
	r32 = math.sqrt(3.0) * 0.5

	hex = ( 
		Point( 0, 0 ),
		Point( 1, 0 ),
		Point( 1.5, r32 ),
		Point( 1.0, 2.0*r32 ),
		Point( 0.0, 2.0*r32 ),
		Point( -0.5, r32 ) )
	rescale( hex )

	return hex

def ih12_params( v0, v1 ):
	hex = ( 
		Point( 0, 0 ),
		Point( v0, 0 ),
		Point( v0 + v1, 0.5 ),
		Point( v0, 1.0 ),
		Point( 0.0, 1.0 ),
		Point( -v1, 0.5 ) )
	rescale( hex )

	return hex

def ih13_params( v0, v1, v2 ):
	hex = ( 
		Point( 0, 0 ),
		Point( v0, 0 ),
		Point( v0 + v1, v2 ),
		Point( v0, 1.0 ),
		Point( 0.0, 1.0 ),
		Point( -v1, v2 ) )
	rescale( hex )

	return hex

def ih14_params( v0, v1 ):
	hex = ( 
		Point( v0 + v1, 0.5 ),
		Point( v0, 1.0 ),
		Point( 0.0, 1.0 ),
		Point( -v1, 0.5 ),
		Point( 0, 0 ),
		Point( v0, 0 ) )
	rescale( hex )

	return hex

def ih15_params( v0, v1, v2 ):
	hex = ( 
		Point( -v1, 0.5 ),
		Point( 0.0, 0.0 ),
		Point( v0, 0.0 ),
		Point( v0 + v2, 0.5 ),
		Point( v0, 1.0 ),
		Point( 0.0, 1.0 ) )
	rescale( hex )

	return hex

def ih16_params( v0 ):
	m = 0.5 / math.sqrt(3.0)
	T1 = match( Point(0.5,v0), Point(1,0) )
	T2 = match( Point(0,0), Point(0.5,v0) )

	hex = ( 
		Point( 0.5, -m ),
		Point( 1, 0 ),
		T1 * Point( 0.5, m ),
		Point( 0.5, v0 ),
		T2 * Point( 0.5, m ),
		Point( 0, 0 ) )
	rescale( hex )

	return hex

#
# 3^4.6
#

def ih21_params( v0, v1 ):
	T1 = match( Point(0.0,0.0), Point(v0,v1) )

	pent = (
		Point( 1.0, 0.0 ),
		Point( v0, v1 ),
		T1 * Point( 0.5, 0.5 / math.sqrt( 3.0 ) ),
		Point( 0.0, 0.0 ),
		Point( 0.5, -0.5 * math.sqrt( 3.0 ) ) )
	rescale( pent )

	return pent
	
# 
# 3^3.4^2
#

def ih22_params( v0, v1, v2 ):
	pent = ( 
		Point( v0, v1 ),
		Point( v0 + v2, v1 + 0.5 ),
		Point( v0, v1 + 1.0 ),
		Point( 0.0, 1.0 ),
		Point( 0.0, 0.0 ) )
	rescale( pent )

	return pent

def ih23_params( v0, v1, v2, v3 ):
	pent = ( 
		Point( v0, v1 ),
		Point( v0 + v2, v1 + v3 ),
		Point( v0, v1 + 1.0 ),
		Point( 0.0, 1.0 ),
		Point( 0.0, 0.0 ) )
	rescale( pent )

	return pent

def ih26_params( v0, v1 ):
	pent = ( 
		Point( v0, 0.0 ),
		Point( v0 + v1, 0.5 ),
		Point( v0, 1.0 ),
		Point( 0.0, 1.0 ),
		Point( 0.0, 0.0 ) )
	rescale( pent )

	return pent

#
# 3^2.4.3.4
#

def ih27_params( v0, v1, v2 ):
	pent = (
		Point( v2, 1.0 ),
		Point( -v2, 1.0 + 2.0 * v1 ),
		Point( 0.0, 0.0 ),
		Point( v0, -v1 ),
		Point( v0 + v2, v1 + 1.0 ) )
	rescale( pent )

	return pent

def ih28_params( v0, v1 ):
	T1 = match( Point( v0, v1 ), Point( 0.5, 0.0 ) )
	T2 = match( Point( -0.5, 0.0 ), Point( v0, v1 ) )
	p1 = T1 * Point( 0.5, 0.5 )
	p2 = T2 * Point( 0.5, 0.5 )

	pent = (
		Point( -0.5, 0.0 ),
		Point( 0.5, 0.0 ),
		p1,
		Point( v0, v1 ),
		p2 )
	rescale( pent )

	return pent

def ih29_params( v0 ):
	T = match( Point( 0.0, v0 ), Point( 0.5, 0.0 ) )
	p = T * Point( 0.5, 0.5 )

	pent = (
		Point( -0.5, 0.0 ),
		Point( 0.5, 0.0 ),
		p,
		Point( 0.0, v0 ),
		Point( -p.x, p.y ) )
	rescale( pent )

	return pent

#
# 3.4.6.4
#

def ih30_params( v0 ):
	T = rotateAround( Point( -v0, 1.0 ), 2.0 * math.pi / 3.0 )

	q2 = T * Point( 0.0, 0.0 )
	q2a = T * Point( -v0, 0.0 )
	xint = q2.x - q2.y * ( q2a.x - q2.x ) / ( q2a.y - q2.y )

	quad = (
		Point( 0.0, 0.0 ),
		Point( xint, 0.0 ),
		q2,
		Point( -v0, 1.0 ) )
	rescale( quad, 0.8 )

	return quad

def l3464_params():
	quad = (
		Point( -math.sqrt( 3.0 ) * 0.25, 0.75 ),
		Point( 0.0, 0.0 ),
		Point( math.sqrt( 3.0 ) * 0.25, 0.75 ),
		Point( 0.0, 1.0 ) )
	rescale( quad, 0.8 )

	return quad

#
# 3.6.3.6
#

def l3636_params():
	quad = (
		Point( 0.0, 0.5 ),
		Point( -0.5 * math.sqrt( 3.0 ), 0.0 ),
		Point( 0.0, -0.5 ),
		Point( 0.5 * math.sqrt( 3.0 ), 0.0 ) )
	rescale( quad, 0.8 )

	return quad

#
# 3.12.12
#

def l31212_params():
	tri = (
		Point( -0.5, 0.0 ),
		Point( 0.5, 0.0 ),
		Point( 0.0, 0.5 / math.sqrt( 3.0 ) ) )
	rescale( tri, 0.8 )

	return tri

#
# 4.4.4.4
#

def parallelogram_params( v0, v1 ):
	quad = (
		Point( 0.0, 0.0 ),
		Point( v0, v1 ),
		Point( v0, v1 + 1 ),
		Point( 0, 1 ) )
	rescale( quad )
	
	return quad

def ih44_params( v0, v1 ):
	quad = (
		Point( v1, v0 ),
		Point( 0.0, 1.0 ),
		Point( -v1, v0 ),
		Point( 0.0, 0.0 ) )
	rescale( quad )
	
	return quad

def ih45_params( v0, v1 ):
	quad = (
		Point( 1.0, 0.0 ),
		Point( 1.0 - v1, v0 ),
		Point( v1, v0 ),
		Point( 0.0, 0.0 ) )
	rescale( quad )
	
	return quad

def ih46_params( v0, v1, v2, v3 ):
	quad = (
		Point( 0.0, 0.0 ),
		Point( 1.0, 0.0 ),
		Point( v0, v1 ),
		Point( v2, v3 ) )
	rescale( quad )
	
	return quad

def rect_params( v0 ):
	quad = (
		Point( 0.0, 0.0 ),
		Point( 1.0 + v0, 0.0 ),
		Point( 1.0 + v0, 1.0 ),
		Point( 0.0, 1.0 ) )
	rescale( quad )
	
	return quad

def trap_params( v0, v1, v2 ):
	quad = (
		Point( 0.0, 0.0 ),
		Point( 1.0, 0.0 ),
		Point( v2 - v1, v0 ),
		Point( -v1, v0 ) )
	rescale( quad )
	
	return quad

def ih51_params( v0, v1, v2 ):
	quad = (
		Point( 0.0, 0.0 ),
		Point( 1.0, -v0 ),
		Point( v1 + 1.0, v2 + v0 ),
		Point( v1, v2 ) )
	rescale( quad )

	return quad

def ih53_params( v0, v1, v2 ):
	quad = (
		Point( 0, 1 ),
		Point( -v2, 0.5 ),
		Point( 0, 0 ), 
		Point( v0, v1 ) )
	rescale( quad )

	return quad

def ih54_params( v0, v1 ):
	quad = (
		Point( 0.0, 1.0 ),
		Point( 0.0, 0.0 ),
		Point( v0, 0.0 ),
		Point( v0, v1 ) )
	rescale( quad )

	return quad

def square_params():
	quad = (
		Point( 0.0, 0.0 ),
		Point( 1.0, 0.0 ),
		Point( 1.0, 1.0 ),
		Point( 0.0, 1.0 ) )
	rescale( quad )
	
	return quad

def ih56_params( v0 ):
	quad = (
		Point( 1.0 + v0, 0.0 ),
		Point( 1.0, 1.0 ),
		Point( 0.0, 1.0 - v0 ),
		Point( 0.0, 0.0 ) )
	rescale( quad )
	
	return quad

def rhomb_params( v0 ):
	quad = (
		Point( 0.5, 0.0 ),
		Point( 0.0, v0 ),
		Point( -0.5, 0.0 ),
		Point( 0.0, -v0 ) )
	rescale( quad )
	
	return quad

def ih69_params( v0, v1 ):
	quad = (
		Point( 0.0, 1.0 ),
		Point( -v1, v0 ),
		Point( 0.0, 0.0 ),
		Point( v1, v0 ) )
	rescale( quad )
	
	return quad

#
# 4.6.12
#

def ih77_params():
	tri = (
		Point( 0.0, 0.0 ),
		Point( 1.0, 0.0 ),
		Point( 1.0, math.sqrt( 3.0 ) ) )
	rescale( tri )

	return tri

#
# 4.8.8
# 

def ih78_params( v0 ):
	tri = (
		Point( 0.0, 0.0 ),
		Point( 1.0, 0.0 ),
		Point( 1.0, v0 ) )
	rescale( tri )

	return tri

def l488_params():
	tri = (
		Point( 0.0, 0.0 ),
		Point( 1.0, 0.0 ),
		Point( 1.0, 1.0 ) )
	rescale( tri )

	return tri

#
# 6.6.6
# 

def isosceles_params( v0 ):
	tri = (
		Point( 1.0, 0.0 ),
		Point( 0.5, v0 ),
		Point( 0.0, 0.0 ) )
	rescale( tri )

	return tri

def equi_params():
	tri = (
		Point( 0.0, 0.0 ),
		Point( 1.0, 0.0 ),
		Point( 0.5, math.sqrt( 3.0 ) * 0.5 ) )
	rescale( tri )

	return tri

def ih91_params( v0 ):
	tri = (
		Point( 0.0, 0.0 ),
		Point( 1.0, 0.0 ),
		Point( 0.5, v0 ) )
	rescale( tri )

	return tri

def tri_params( v0, v1 ):
	tri = (
		Point( 0.0, 0.0 ),
		Point( 1.0, 0.0 ),
		Point( v0, v1 ) )
	rescale( tri )

	return tri

parameterizations = {
	'IH1'	 : parhex_params,
	'IH2'    : ih02_params,
	'IH3'    : ih03_params,
	'IH4'    : ih04_params,
	'IH5'    : ih05_params,
	'IH6'    : ih06_params,
	'IH7'    : ih07_params,
	'IH8'    : parhex_params,
	'IH9'    : ih09_params,
	'IH10'   : hex_params,
	'IH11'   : hex_params,
	'IH12'   : ih12_params,
	'IH13'   : ih13_params,
	'IH14'   : ih14_params,
	'IH15'   : ih15_params,
	'IH16'   : ih16_params,
	'IH17'   : ih12_params,
	'IH18'   : hex_params,
	'IH19'   : hex_params,
	'IH20'   : hex_params,

	'IH21'	 : ih21_params,

	'IH22'	 : ih22_params,
	'IH23'	 : ih23_params,
	'IH24'	 : ih23_params,
	'IH25'	 : ih22_params,
	'IH26'	 : ih26_params,

	'IH27'	 : ih27_params,
	'IH28'	 : ih28_params,
	'IH29'	 : ih29_params,

	'IH30'	 : ih30_params,
	'IH31'	 : l3464_params,
	'IH32'	 : l3464_params,

	'IH33'	 : l3636_params,
	'IH34'	 : l3636_params,
	'IH35'	 : l3636_params,
	'IH36'	 : l3636_params,
	'IH37'	 : l3636_params,

	'IH38'	 : l31212_params,
	'IH39'	 : l31212_params,
	'IH40'	 : l31212_params,

	'IH41'   : parallelogram_params,
	'IH42'   : parallelogram_params,
	'IH43'   : parallelogram_params,
	'IH44'   : ih44_params,
	'IH45'   : ih45_params,
	'IH46'   : ih46_params,
	'IH47'   : parallelogram_params,
	'IH48'   : rect_params,
	'IH49'   : trap_params,
	'IH50'   : parallelogram_params,
	'IH51'   : ih51_params,
	'IH52'   : rect_params,
	'IH53'   : ih53_params,
	'IH54'   : ih54_params,
	'IH55' 	 : square_params,
	'IH56'   : ih56_params,
	'IH57'   : parallelogram_params,
	'IH58'   : parallelogram_params,
	'IH59'   : rhomb_params,
	'IH60'   : rect_params,
	'IH61' 	 : square_params,
	'IH62' 	 : square_params,
	'IH63' 	 : square_params,
	'IH64'   : rect_params,
	'IH65'   : rect_params,
	'IH66'   : rect_params,
	'IH67'   : trap_params,
	'IH68'   : rhomb_params,
	'IH69'	 : ih69_params,
	'IH70' 	 : square_params,
	'IH71' 	 : square_params,
	'IH72'   : rect_params,
	'IH73' 	 : square_params,
	'IH74'   : rhomb_params,
	'IH75' 	 : square_params,
	'IH76' 	 : square_params,

	'IH77'	 : ih77_params,
	'IH78'	 : ih78_params,
	'IH79'   : l488_params,
	'IH80'   : l488_params,
	'IH81'   : l488_params,
	'IH82'   : l488_params,
	'IH83'   : isosceles_params,
	'IH84'	 : tri_params,
	'IH85'	 : tri_params,
	'IH86'   : isosceles_params,
	'IH87'   : equi_params,
	'IH88'   : equi_params,
	'IH89'   : equi_params,
	'IH90'   : equi_params,
	'IH91'   : ih91_params,
	'IH92'   : equi_params,
	'IH93'   : equi_params,
}

if __name__ == '__main__':
	args = sys.argv[1:]

	if len( args ) == 0:
		print "Usage: python params.py <IH> <v_0> ... <v_n>"
		sys.exit( 0 )

	try:
		pzation = parameterizations[ args[0] ]
		vs = []

		for a in args[1:]:
			vs.append( float( a ) )

		polygon = apply( pzation, tuple( vs ) )

		for pt in polygon:
			print pt.x, pt.y
		
		sys.exit( 0 )

	except KeyError:
		print ('%s is not a valid tiling type.' % args[0])
		sys.exit( -1 )
	except TypeError:
		print 'Wrong number of parameter values.'
		sys.exit( -1 )
	except ValueError:
		print 'Invalid parameter value.'
	except:
		print 'An unknown error occured.  Please contact the author.'