#!/usr/bin/env pyformex --gui
# $Id$
##
##  This file is part of pyFormex 0.8.5     Sun Nov  6 17:27:05 CET 2011
##  pyFormex is a tool for generating, manipulating and transforming 3D
##  geometrical models by sequences of mathematical operations.
##  Home page: http://pyformex.org
##  Project page:  https://savannah.nongnu.org/projects/pyformex/
##  Copyright (C) Benedict Verhegghe (benedict.verhegghe@ugent.be) 
##  Distributed under the GNU General Public License version 3 or later.
##
##
##  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 3 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, see http://www.gnu.org/licenses/.
##
"""Diamatic dome

level = 'beginner'
topics = ['structure','domes']
techniques = ['color']

"""

u = 3.     # modular length
n = 6      # number of modules in one sector
r = 36.    # radius of the dome

# Topology for 1 sector
T = Formex('l:164',3).replic2(n,n,1,1,0,1,0,-1)


# 4 sectors
m = 4
angle = 360./m
# circulize sector
D = T.scale(u).circulize(angle)
D = D.mapd(2,lambda d:sqrt(r**2-d**2),[0,0,0],[0,1])
dome1=D.rosette(m,angle)
clear()
draw(dome1)

# 6 sectors
m = 6
angle = 360./m
a = sqrt(3.)/2
D = T.shear(0,1,0.5).scale([1,a,1])
#D = T.replic2(n,n,1,a,0,1,0.5,-1)
D = D.scale(u).circulize(angle)
D = D.mapd(2,lambda d:sqrt(r**2-d**2),[0,0,0],[0,1])
dome2=D.rosette(m,angle)

clear()
draw(dome2)

# 8 sectors
m = 8
angle = 360./m
a = sqrt(2.)/2
T = Formex([[[0,0],[1,0]],[[1,0],[a,a]],[[a,a],[0,0]]],3)
D = T.replic2(n,n,1,a,0,1,a,-1)
# circulize sector
D = D.scale(u).circulize(angle)
D = D.mapd(2,lambda d:sqrt(r**2-d**2),[0,0,0],[0,1])
dome3=D.rosette(m,angle)

clear()
draw(dome3)

# circulize1
m = 6
angle = 360./m
T = Formex('l:127',3)
D = T.replic2(n,n,1,1,0,1,1,-1)
D = D.scale(u).circulize1()
D = D.mapd(2,lambda d:sqrt(r**2-d**2),[0,0,0],[0,1])
dome4=D.rosette(m,angle)

clear()
draw(dome4)

clear()
dome4.setProp(1)
draw(dome2+dome4)



clear()
d=1.1*r
draw(dome1+dome2.translate([d,0,0])+dome3.translate([0,d,0])+dome4.translate([d,d,0]))
