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GNU GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
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Apollon
#######
About
=====
These are some python classes and functions for calculating Apollonian
Gaskets and saving them as svg. For an overview about this
mathematical object, see wikipedia_.
The code is split into the following files:
- `apollon.py`:code: contains all the pure math stuff
- `coloring.py`:code: contains helpers for color mapping
- `ag.py`:code: is a command-line tool for generating Apollonian Gaskets
- `index.cgi`:code: is an interactive online cgi version
- `colorbrewer.json`:code: contains the color schemes, copied from
https://gist.github.com/jsundram/6004447#file-colorbrewer-json
Usage
=====
CLI
---
Run `./ag.py c1 c2 c3`:code: where c1, c2, c3 are the (positive) curvatures
of the starting circles. Please also see the `--help`:code: option.
Note: The method used to calculate the circles is recursive. For depth
d, 2*3^{d+1} circles are created. It is usually safe to do this up to
d=10, but with higher values you can reach the limit of your
RAM. Because of this, and to prevent typos potentially crashing your
machine, the recursion depth is capped at d=10. If you know what you
are doing, you can use the `--force`:code: option for higher values.
CGI
---
Online interactive version. You can try it at
http://lsandig.org/cgi-bin/apollon/index.cgi
Recursion depth is limited to 5 to reduce server load and RAM
usage. This implementation might not be very fast, it is just intended
as a showcase of what you can expect from the CLI-version.
Needs python3 and the other three files to work.
Documentation
=============
For the cli-program see `ag.py --help`:code:.
For a somewhat complete documentation of the source files run
`epydoc --html apollon.py ag.py coloring.py`:code:
For a writeup on how the math behind this program works see my
blogpost here: http://lsandig.org/blog/2014/08/apollon-python/en/
TODO
====
- More logical structure of the source files
- Better documentation
- A time- and RAM-saving algorithm that excludes Circles from
recursion which are too small to be seen.
- fastcgi version of index.cgi?
Credits
=======
Colors from www.ColorBrewer.org by Cynthia A. Brewer, Geography,
Pennsylvania State University.
Thanks to Dorothee Henke for helping me figuring out the math.
Author & License
================
| Author: Ludger Sandig
| Contact: contact@lsandig.org
| Homepage: http://lsandig.org/
This software can be found on github:
https://github.com/lsandig/apollon
This software is published under the GPL, see LICENSE
.. Links
.. _wikipedia: https://en.wikipedia.org/wiki/Apollonian_gasket

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generators/apollon/ag.py Executable file
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#! /usr/bin/python3
# Command line program to create svg apollonian circles
# Copyright (c) 2014 Ludger Sandig
# This file is part of apollon.
# Apollon 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.
# Apollon 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 Apollon. If not, see <http://www.gnu.org/licenses/>.
import argparse
import sys
import math
from apollon import ApollonianGasket
from coloring import ColorMap, ColorScheme
def parseArguments(argv, colors):
description = "Generate Apollonian Gaskets and save as svg"
name = argv[0]
colors.append('none')
colors.sort()
parser = argparse.ArgumentParser(description=description, prog=name)
parser.add_argument("-d", "--depth", metavar="D", type=int, default=3, help="Recursion depth, generates 2*3^{D+1} circles. Usually safe for D<=10. For higher D use --force if you know what you are doing.")
parser.add_argument("-o", "--output", metavar="", type=str, default="", help="Output file name. If left blank, default is created from circle curvatures.")
parser.add_argument("-r", "--radii", action="store_true", default=False, help="Interpret c1, c2, c3 as radii and not as curvatures")
parser.add_argument("--color", choices=colors, metavar='SCHEME', default='none', help="Color Scheme. Choose from "+", ".join(colors))
parser.add_argument("--treshold", metavar='T', default=0.005, type=float, help="Don't save circles that are too small. Useful for higher depths to reduce filesize.")
parser.add_argument("--force", action="store_true", default=False, help="Use if you want a higher recursion depth than 10.")
parser.add_argument("c1", type=float, help="Curvature of first circle")
parser.add_argument("c2", type=float, help="Curvature of second circle")
parser.add_argument("c3", type=float, help="Curvature of third circle")
return parser.parse_args()
def colorMsg(color):
print("Available color schemes (name: resmin -- resmax)")
for i in color.info():
print("%s: %d -- %d" % (i["name"], i["low"], i["high"]))
def ag_to_svg(circles, colors, tresh=0.005):
"""
Convert a list of circles to svg, optionally color them.
@param circles: A list of L{Circle}s
@param colors: A L{ColorMap} object
@param tresh: Only circles with a radius greater than the product of tresh and maximal radius are saved
"""
svg = []
# Find the biggest circle, which hopefully is the enclosing one
# and has a negative radius because of this. Note that this does
# not have to be the case if we picked an unlucky set of radii at
# the start. If that was the case, we're screwed now.
big = min(circles, key=lambda c: c.r.real)
# Move biggest circle to front so it gets drawn first
circles.remove(big)
circles.insert(0, big)
if big.r.real < 0:
# Bounding box from biggest circle, lower left corner and two
# times the radius as width
corner = big.m - ( abs(big.r) + abs(big.r) * 1j )
vbwidth = abs(big.r)*2
width = 500 # Hardcoded!
# Line width independent of circle size
lw = (vbwidth/width)
svg.append('<svg xmlns="http://www.w3.org/2000/svg" width="%f" height="%f" viewBox="%f %f %f %f">\n' % (width, width, corner.real, corner.imag, vbwidth, vbwidth))
# Keep stroke width relative
svg.append('<g stroke-width="%f">\n' % lw)
# Iterate through circle list, circles with radius<radmin
# will not be saved because they are too small for printing.
radmin = tresh * abs(big.r)
for c in circles:
if abs(c.r) > radmin:
fill = colors.color_for(abs(c.r))
svg.append(( '<circle cx="%f" cy="%f" r="%f" fill="%s" stroke="black"/>\n' % (c.m.real, c.m.imag, abs(c.r), fill)))
svg.append('</g>\n')
svg.append('</svg>\n')
return ''.join(svg)
def ag_to_hpgl(circles, colors, tresh=0.005):
"""
Convert a list of circles to hpgl,
@param circles: A list of L{Circle}s
@param tresh: Only circles with a radius greater than the product of tresh and maximal radius are saved
"""
hpgl = []
# Find the biggest circle, which hopefully is the enclosing one
# and has a negative radius because of this. Note that this does
# not have to be the case if we picked an unlucky set of radii at
# the start. If that was the case, we're screwed now.
big = min(circles, key=lambda c: c.r.real)
# Move biggest circle to front so it gets drawn first
circles.remove(big)
circles.insert(0, big)
eps = 0.001
if big.r.real < 0:
# Bounding box from biggest circle, lower left corner and two
# times the radius as width
corner = big.m - ( abs(big.r) + abs(big.r) * 1j )
# Gerards Hack
big.r = abs(big.r) + 2*eps
vbwidth = abs(big.r)*2
width = 500 # Hardcoded!
# Line width independent of circle size
lw = (vbwidth/width)
hpgl.append('IN;SP1;')
# Iterate through circle list, circles with radius<radmin
# will not be saved because they are too small for printing.
radmin = tresh * abs(big.r)
for c in circles:
if abs(c.r)-eps > radmin:
hpgl.append('PU'+str(c.m.real)+','+str(c.m.imag)+';CI'+str(abs(c.r)-eps)+';')
return ''.join(hpgl)
def impossible_combination(c1, c2, c3):
# If any curvatures x, y, z satisfy the equation
# x = 2*sqrt(y*z) + y + z
# then no fourth enclosing circle can be genereated, because it
# would be a line.
# We need to see for c1, c2, c3 if they could be "x".
impossible = False
sets = [(c1,c2,c3), (c2,c3,c1), (c3,c1,c2)]
for (x, y, z) in sets:
if x == 2*math.sqrt(y*z) + y + z:
impossible = True
return impossible
def main():
color = ColorScheme("colorbrewer.json")
available = [d['name'] for d in color.info()]
args = parseArguments(sys.argv, available)
# Sanity checks
for c in [args.c1, args.c2, args.c3]:
if c == 0:
print("Error: curvature or radius can't be 0")
exit(1)
if impossible_combination(args.c1, args.c2, args.c3):
print("Error: no apollonian gasket possible for these curvatures")
exit(1)
# Given curvatures were in fact radii, so take the reciprocal
if args.radii:
args.c1 = 1/args.c1
args.c2 = 1/args.c2
args.c3 = 1/args.c3
ag = ApollonianGasket(args.c1, args.c2, args.c3)
# At a recursion depth > 10 things start to get serious.
if args.depth > 10:
if not args.force:
print("Note: Number of cicles increases exponentially with 2*3^{D+1} at depth D.\nIf you want to use D>10, specify the --force option.")
args.depth = 10
ag.generate(args.depth)
# Get smallest and biggest radius
smallest = abs(min(ag.genCircles, key=lambda c: abs(c.r.real)).r.real)
biggest = abs(max(ag.genCircles, key=lambda c: abs(c.r.real)).r.real)
# Construct color map
if args.color == 'none':
mp = ColorMap('none')
else:
# TODO: resolution of 8 is hardcoded, some color schemes have
# resolutions up to 11. Make this configurable.
mp = color.makeMap(smallest, biggest, args.color, 8)
svg = ag_to_svg(ag.genCircles, mp, tresh=args.treshold)
hpgl = ag_to_hpgl(ag.genCircles, mp, tresh=args.treshold)
# User supplied filename? If not, we need to construct something.
if len(args.output) == 0:
args.output = 'ag_%.4f_%.4f_%.4f.svg' % (args.c1, args.c2, args.c3)
with open(args.output, 'w') as f:
f.write(svg)
f.close()
with open(args.output+'.hpgl', 'w') as f:
f.write(hpgl)
f.close()
if( __name__ == "__main__" ):
main()

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generators/apollon/apollon.py Executable file
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#!/usr/bin/python3
# Generate Apollonian Gaskets -- the math part.
# Copyright (c) 2014 Ludger Sandig
# This file is part of apollon.
# Apollon 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.
# Apollon 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 Apollon. If not, see <http://www.gnu.org/licenses/>.
from cmath import *
import random
class Circle(object):
"""
A circle represented by center point as complex number and radius.
"""
def __init__ ( self, mx, my, r ):
"""
@param mx: x center coordinate
@type mx: int or float
@param my: y center coordinate
@type my: int or float
@param r: radius
@type r: int or float
"""
self.r = r
self.m = (mx +my*1j)
def __repr__ ( self ):
"""
Pretty printing
"""
return "Circle( self, %s, %s, %s )" % (self.m.real, self.m.imag, self.r)
def __str__ ( self ):
"""
Pretty printing
"""
return "Circle x:%.3f y:%.3f r:%.3f [cur:%.3f]" % (self.m.real, self.m.imag, self.r.real, self.curvature().real)
def curvature (self):
"""
Get circle's curvature.
@rtype: float
@return: Curvature of the circle.
"""
return 1/self.r
def outerTangentCircle( circle1, circle2, circle3 ):
"""
Takes three externally tangent circles and calculates the fourth one enclosing them.
@param circle1: first circle
@param circle2: second circle
@param circle3: third circle
@type circle1: L{Circle}
@type circle2: L{Circle}
@type circle3: L{Circle}
@return: The enclosing circle
@rtype: L{Circle}
"""
cur1 = circle1.curvature()
cur2 = circle2.curvature()
cur3 = circle3.curvature()
m1 = circle1.m
m2 = circle2.m
m3 = circle3.m
cur4 = -2 * sqrt( cur1*cur2 + cur2*cur3 + cur1 * cur3 ) + cur1 + cur2 + cur3
m4 = ( -2 * sqrt( cur1*m1*cur2*m2 + cur2*m2*cur3*m3 + cur1*m1*cur3*m3 ) + cur1*m1 + cur2*m2 + cur3*m3 ) / cur4
circle4 = Circle( m4.real, m4.imag, 1/cur4 )
return circle4
def tangentCirclesFromRadii( r2, r3, r4 ):
"""
Takes three radii and calculates the corresponding externally
tangent circles as well as a fourth one enclosing them. The enclosing
circle is the first one.
@param r2, r3, r4: Radii of the circles to calculate
@type r2: int or float
@type r3: int or float
@type r4: int or float
@return: The four circles, where the first one is the enclosing one.
@rtype: (L{Circle}, L{Circle}, L{Circle}, L{Circle})
"""
circle2 = Circle( 0, 0, r2 )
circle3 = Circle( r2 + r3, 0, r3 )
m4x = (r2*r2 + r2*r4 + r2*r3 - r3*r4) / (r2 + r3)
m4y = sqrt( (r2 + r4) * (r2 + r4) - m4x*m4x )
circle4 = Circle( m4x, m4y, r4 )
circle1 = outerTangentCircle( circle2, circle3, circle4 )
return ( circle1, circle2, circle3, circle4 )
def secondSolution( fixed, c1, c2, c3 ):
"""
If given four tangent circles, calculate the other one that is tangent
to the last three.
@param fixed: The fixed circle touches the other three, but not
the one to be calculated.
@param c1, c2, c3: Three circles to which the other tangent circle
is to be calculated.
@type fixed: L{Circle}
@type c1: L{Circle}
@type c2: L{Circle}
@type c3: L{Circle}
@return: The circle.
@rtype: L{Circle}
"""
curf = fixed.curvature()
cur1 = c1.curvature()
cur2 = c2.curvature()
cur3 = c3.curvature()
curn = 2 * (cur1 + cur2 + cur3) - curf
mn = (2 * (cur1*c1.m + cur2*c2.m + cur3*c3.m) - curf*fixed.m ) / curn
return Circle( mn.real, mn.imag, 1/curn )
class ApollonianGasket(object):
"""
Container for an Apollonian Gasket.
"""
def __init__(self, c1, c2, c3):
"""
Creates a basic apollonian Gasket with four circles.
@param c1, c2, c3: The curvatures of the three inner circles of the
starting set (i.e. depth 0 of the recursion). The fourth,
enclosing circle will be calculated from them.
@type c1: int or float
@type c2: int or float
@type c3: int or float
"""
self.start = tangentCirclesFromRadii( 1/c1, 1/c2, 1/c3 )
self.genCircles = list(self.start)
def recurse(self, circles, depth, maxDepth):
"""Recursively calculate the smaller circles of the AG up to the
given depth. Note that for depth n we get 2*3^{n+1} circles.
@param maxDepth: Maximal depth of the recursion.
@type maxDepth: int
@param circles: 4-Tuple of circles for which the second
solutions are calculated
@type circles: (L{Circle}, L{Circle}, L{Circle}, L{Circle})
@param depth: Current depth
@type depth: int
"""
if( depth == maxDepth ):
return
(c1, c2, c3, c4) = circles
if( depth == 0 ):
# First recursive step, this is the only time we need to
# calculate 4 new circles.
del self.genCircles[4:]
cspecial = secondSolution( c1, c2, c3, c4 )
self.genCircles.append( cspecial )
self.recurse( (cspecial, c2, c3, c4), 1, maxDepth )
cn2 = secondSolution( c2, c1, c3, c4 )
self.genCircles.append( cn2 )
cn3 = secondSolution( c3, c1, c2, c4 )
self.genCircles.append( cn3 )
cn4 = secondSolution( c4, c1, c2, c3 )
self.genCircles.append( cn4 )
self.recurse( (cn2, c1, c3, c4), depth+1, maxDepth )
self.recurse( (cn3, c1, c2, c4), depth+1, maxDepth )
self.recurse( (cn4, c1, c2, c3), depth+1, maxDepth )
def generate(self, depth):
"""
Wrapper for the recurse function. Generate the AG,
@param depth: Recursion depth of the Gasket
@type depth: int
"""
self.recurse(self.start, 0, depth)

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generators/apollon/colorbrewer.json Executable file
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{"YlGn": {
"3": ["#f7fcb9","#addd8e","#31a354"],
"4": ["#ffffcc","#c2e699","#78c679","#238443"],
"5": ["#ffffcc","#c2e699","#78c679","#31a354","#006837"],
"6": ["#ffffcc","#d9f0a3","#addd8e","#78c679","#31a354","#006837"],
"7": ["#ffffcc","#d9f0a3","#addd8e","#78c679","#41ab5d","#238443","#005a32"],
"8": ["#ffffe5","#f7fcb9","#d9f0a3","#addd8e","#78c679","#41ab5d","#238443","#005a32"],
"9": ["#ffffe5","#f7fcb9","#d9f0a3","#addd8e","#78c679","#41ab5d","#238443","#006837","#004529"]
},"YlGnBu": {
"3": ["#edf8b1","#7fcdbb","#2c7fb8"],
"4": ["#ffffcc","#a1dab4","#41b6c4","#225ea8"],
"5": ["#ffffcc","#a1dab4","#41b6c4","#2c7fb8","#253494"],
"6": ["#ffffcc","#c7e9b4","#7fcdbb","#41b6c4","#2c7fb8","#253494"],
"7": ["#ffffcc","#c7e9b4","#7fcdbb","#41b6c4","#1d91c0","#225ea8","#0c2c84"],
"8": ["#ffffd9","#edf8b1","#c7e9b4","#7fcdbb","#41b6c4","#1d91c0","#225ea8","#0c2c84"],
"9": ["#ffffd9","#edf8b1","#c7e9b4","#7fcdbb","#41b6c4","#1d91c0","#225ea8","#253494","#081d58"]
},"GnBu": {
"3": ["#e0f3db","#a8ddb5","#43a2ca"],
"4": ["#f0f9e8","#bae4bc","#7bccc4","#2b8cbe"],
"5": ["#f0f9e8","#bae4bc","#7bccc4","#43a2ca","#0868ac"],
"6": ["#f0f9e8","#ccebc5","#a8ddb5","#7bccc4","#43a2ca","#0868ac"],
"7": ["#f0f9e8","#ccebc5","#a8ddb5","#7bccc4","#4eb3d3","#2b8cbe","#08589e"],
"8": ["#f7fcf0","#e0f3db","#ccebc5","#a8ddb5","#7bccc4","#4eb3d3","#2b8cbe","#08589e"],
"9": ["#f7fcf0","#e0f3db","#ccebc5","#a8ddb5","#7bccc4","#4eb3d3","#2b8cbe","#0868ac","#084081"]
},"BuGn": {
"3": ["#e5f5f9","#99d8c9","#2ca25f"],
"4": ["#edf8fb","#b2e2e2","#66c2a4","#238b45"],
"5": ["#edf8fb","#b2e2e2","#66c2a4","#2ca25f","#006d2c"],
"6": ["#edf8fb","#ccece6","#99d8c9","#66c2a4","#2ca25f","#006d2c"],
"7": ["#edf8fb","#ccece6","#99d8c9","#66c2a4","#41ae76","#238b45","#005824"],
"8": ["#f7fcfd","#e5f5f9","#ccece6","#99d8c9","#66c2a4","#41ae76","#238b45","#005824"],
"9": ["#f7fcfd","#e5f5f9","#ccece6","#99d8c9","#66c2a4","#41ae76","#238b45","#006d2c","#00441b"]
},"PuBuGn": {
"3": ["#ece2f0","#a6bddb","#1c9099"],
"4": ["#f6eff7","#bdc9e1","#67a9cf","#02818a"],
"5": ["#f6eff7","#bdc9e1","#67a9cf","#1c9099","#016c59"],
"6": ["#f6eff7","#d0d1e6","#a6bddb","#67a9cf","#1c9099","#016c59"],
"7": ["#f6eff7","#d0d1e6","#a6bddb","#67a9cf","#3690c0","#02818a","#016450"],
"8": ["#fff7fb","#ece2f0","#d0d1e6","#a6bddb","#67a9cf","#3690c0","#02818a","#016450"],
"9": ["#fff7fb","#ece2f0","#d0d1e6","#a6bddb","#67a9cf","#3690c0","#02818a","#016c59","#014636"]
},"PuBu": {
"3": ["#ece7f2","#a6bddb","#2b8cbe"],
"4": ["#f1eef6","#bdc9e1","#74a9cf","#0570b0"],
"5": ["#f1eef6","#bdc9e1","#74a9cf","#2b8cbe","#045a8d"],
"6": ["#f1eef6","#d0d1e6","#a6bddb","#74a9cf","#2b8cbe","#045a8d"],
"7": ["#f1eef6","#d0d1e6","#a6bddb","#74a9cf","#3690c0","#0570b0","#034e7b"],
"8": ["#fff7fb","#ece7f2","#d0d1e6","#a6bddb","#74a9cf","#3690c0","#0570b0","#034e7b"],
"9": ["#fff7fb","#ece7f2","#d0d1e6","#a6bddb","#74a9cf","#3690c0","#0570b0","#045a8d","#023858"]
},"BuPu": {
"3": ["#e0ecf4","#9ebcda","#8856a7"],
"4": ["#edf8fb","#b3cde3","#8c96c6","#88419d"],
"5": ["#edf8fb","#b3cde3","#8c96c6","#8856a7","#810f7c"],
"6": ["#edf8fb","#bfd3e6","#9ebcda","#8c96c6","#8856a7","#810f7c"],
"7": ["#edf8fb","#bfd3e6","#9ebcda","#8c96c6","#8c6bb1","#88419d","#6e016b"],
"8": ["#f7fcfd","#e0ecf4","#bfd3e6","#9ebcda","#8c96c6","#8c6bb1","#88419d","#6e016b"],
"9": ["#f7fcfd","#e0ecf4","#bfd3e6","#9ebcda","#8c96c6","#8c6bb1","#88419d","#810f7c","#4d004b"]
},"RdPu": {
"3": ["#fde0dd","#fa9fb5","#c51b8a"],
"4": ["#feebe2","#fbb4b9","#f768a1","#ae017e"],
"5": ["#feebe2","#fbb4b9","#f768a1","#c51b8a","#7a0177"],
"6": ["#feebe2","#fcc5c0","#fa9fb5","#f768a1","#c51b8a","#7a0177"],
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"3": ["#fbb4ae","#b3cde3","#ccebc5"],
"4": ["#fbb4ae","#b3cde3","#ccebc5","#decbe4"],
"5": ["#fbb4ae","#b3cde3","#ccebc5","#decbe4","#fed9a6"],
"6": ["#fbb4ae","#b3cde3","#ccebc5","#decbe4","#fed9a6","#ffffcc"],
"7": ["#fbb4ae","#b3cde3","#ccebc5","#decbe4","#fed9a6","#ffffcc","#e5d8bd"],
"8": ["#fbb4ae","#b3cde3","#ccebc5","#decbe4","#fed9a6","#ffffcc","#e5d8bd","#fddaec"],
"9": ["#fbb4ae","#b3cde3","#ccebc5","#decbe4","#fed9a6","#ffffcc","#e5d8bd","#fddaec","#f2f2f2"]
},"Pastel2": {
"3": ["#b3e2cd","#fdcdac","#cbd5e8"],
"4": ["#b3e2cd","#fdcdac","#cbd5e8","#f4cae4"],
"5": ["#b3e2cd","#fdcdac","#cbd5e8","#f4cae4","#e6f5c9"],
"6": ["#b3e2cd","#fdcdac","#cbd5e8","#f4cae4","#e6f5c9","#fff2ae"],
"7": ["#b3e2cd","#fdcdac","#cbd5e8","#f4cae4","#e6f5c9","#fff2ae","#f1e2cc"],
"8": ["#b3e2cd","#fdcdac","#cbd5e8","#f4cae4","#e6f5c9","#fff2ae","#f1e2cc","#cccccc"]
},"Set1": {
"3": ["#e41a1c","#377eb8","#4daf4a"],
"4": ["#e41a1c","#377eb8","#4daf4a","#984ea3"],
"5": ["#e41a1c","#377eb8","#4daf4a","#984ea3","#ff7f00"],
"6": ["#e41a1c","#377eb8","#4daf4a","#984ea3","#ff7f00","#ffff33"],
"7": ["#e41a1c","#377eb8","#4daf4a","#984ea3","#ff7f00","#ffff33","#a65628"],
"8": ["#e41a1c","#377eb8","#4daf4a","#984ea3","#ff7f00","#ffff33","#a65628","#f781bf"],
"9": ["#e41a1c","#377eb8","#4daf4a","#984ea3","#ff7f00","#ffff33","#a65628","#f781bf","#999999"]
},"Set2": {
"3": ["#66c2a5","#fc8d62","#8da0cb"],
"4": ["#66c2a5","#fc8d62","#8da0cb","#e78ac3"],
"5": ["#66c2a5","#fc8d62","#8da0cb","#e78ac3","#a6d854"],
"6": ["#66c2a5","#fc8d62","#8da0cb","#e78ac3","#a6d854","#ffd92f"],
"7": ["#66c2a5","#fc8d62","#8da0cb","#e78ac3","#a6d854","#ffd92f","#e5c494"],
"8": ["#66c2a5","#fc8d62","#8da0cb","#e78ac3","#a6d854","#ffd92f","#e5c494","#b3b3b3"]
},"Set3": {
"3": ["#8dd3c7","#ffffb3","#bebada"],
"4": ["#8dd3c7","#ffffb3","#bebada","#fb8072"],
"5": ["#8dd3c7","#ffffb3","#bebada","#fb8072","#80b1d3"],
"6": ["#8dd3c7","#ffffb3","#bebada","#fb8072","#80b1d3","#fdb462"],
"7": ["#8dd3c7","#ffffb3","#bebada","#fb8072","#80b1d3","#fdb462","#b3de69"],
"8": ["#8dd3c7","#ffffb3","#bebada","#fb8072","#80b1d3","#fdb462","#b3de69","#fccde5"],
"9": ["#8dd3c7","#ffffb3","#bebada","#fb8072","#80b1d3","#fdb462","#b3de69","#fccde5","#d9d9d9"],
"10": ["#8dd3c7","#ffffb3","#bebada","#fb8072","#80b1d3","#fdb462","#b3de69","#fccde5","#d9d9d9","#bc80bd"],
"11": ["#8dd3c7","#ffffb3","#bebada","#fb8072","#80b1d3","#fdb462","#b3de69","#fccde5","#d9d9d9","#bc80bd","#ccebc5"],
"12": ["#8dd3c7","#ffffb3","#bebada","#fb8072","#80b1d3","#fdb462","#b3de69","#fccde5","#d9d9d9","#bc80bd","#ccebc5","#ffed6f"]
}}

86
generators/apollon/coloring.py Executable file
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# Select a color from colorbrewer schemes
# Copyright (c) 2014 Ludger Sandig
# This file is part of apollon.
# Apollon 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.
# Apollon 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 Apollon. If not, see <http://www.gnu.org/licenses/>.
import json
class ColorMap(object):
"""
Map numbers to colors.
"""
def __init__(self, default):
"""
@param default: Is returned when a number can't be mapped.
"""
self.pairs = []
self.default = default
def add_interval(self, left, right, color):
"""
A number in interval [left,right] gets mapped to color.
"""
self.pairs.append((left, right, color))
def color_for(self, number):
"""
Map number to color. If not found, return default value.
"""
ret = self.default
for p in self.pairs:
if (number >= p[0]) and (number <= p[1]):
ret = p[2]
break
return ret
class ColorScheme(object):
"""
Color Scheme helper class.
"""
def __init__(self, filename):
"""
Load color scheme definitions from json file.
"""
json_data = open(filename)
self.schemes=json.load(json_data)
json_data.close()
def info(self):
"""
Get information on available color schemes
"""
infos = []
for name in self.schemes:
smallest = min(self.schemes[name], key=lambda k: len(self.schemes[name][k]))
biggest = max(self.schemes[name], key=lambda k: len(self.schemes[name][k]))
infos.append({"name" : name, "low" : int(smallest), "high" : int(biggest)})
return infos
def makeMap(self, frm, to, name, res):
"""
Construct a L{ColorMap} that maps numbers between frm and to to color scheme name with resolution res.
"""
# TODO: Proper error handling when name or res are not available
delta = to-frm
step = delta/res
colors = self.schemes[name][str(res)]
mp = ColorMap("none")
# Items are (lower_bound, color)
for n in range(res):
mp.add_interval(frm + n*step, frm + (n+1)*step, colors[n])
return mp

271
generators/apollon/index.cgi Executable file
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#!/usr/bin/env python3
# Copyright (c) 2014 Ludger Sandig
# This file is part of apollon.
# Apollon 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.
# Apollon 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 Apollon. If not, see <http://www.gnu.org/licenses/>.
import cgi
import cgitb
from apollon import ApollonianGasket
from coloring import ColorScheme, ColorMap
from ag import ag_to_svg, impossible_combination
# Container for sanitized settings
class Settings(object):
def __init__(self, form):
self.color = form.getvalue("color", "Blues")
self.resolution = int(form.getvalue("res", 8))
self.c1 = float(form.getvalue("c1", 1))
self.c2 = float(form.getvalue("c2", 2))
self.c3 = float(form.getvalue("c3", 2))
self.rad_or_curv = form.getvalue("roc", "curvature")
self.depth = int(form.getvalue("depth", 3))
# Sanity check
if (self.resolution > 8) or (self.resolution < 3):
self.resolution = 8
if self.c1 <= 0: self.c1 = 1
if self.c2 <= 0: self.c2 = 1
if self.c3 <= 0: self.c3 = 1
if not (self.rad_or_curv == "curvature" or self.rad_or_curv == "radius"):
self.rad_or_curvature = "curvature"
if (self.depth < 0) or (self.depth > 5):
self.depth = 3
# For a more usable form
if self.rad_or_curv == "curvature":
self.rad_checked = ""
self.curv_checked = "checked"
else:
self.rad_checked = "checked"
self.curv_checked = ""
# Curvature or Radius?
if self.rad_or_curv == "radius":
self.c1 = 1/self.c1
self.c2 = 1/self.c2
self.c3 = 1/self.c3
# AG possible in the first place?
self.impossible = impossible_combination(self.c1, self.c2, self.c3)
# What to print: With form or only svg
action = form.getvalue("submit","Update")
self.onlysvg = False
if action == "Save":
self.onlysvg = True
def print_with_form(svg, settings, schemes):
# Print first chunk of html
print("Content-type: text/html")
print("""
<html>
<head>
<title>Apollonian Gasket Generator</title>
<style>
body {
font-family: sans-serif;
width: 800px;
margin: auto;
}
h1 {
padding: 10px;
border: 2px solid #ccc;
border-radius: 25px;
text-align: center;
width: 780px;
}
#gasket {
width: 500px;
float: left;
padding: 10px;
border: 2px solid #ccc;
border-radius: 25px;
}
#settings {
width: 250px;
float: right;
border: 2px solid #ccc;
border-radius: 25px;
padding: 10px;
}
#about {
width: 780px;
border: 2px solid #ccc;
border-radius: 25px;
padding: 10px;
clear: both;
}
div.wrapper {
padding-top: 2px;
clear: both;
}
input[type=number] {
width: 75px;
}
input, label, select {
display: table-cell;
}
form {
display: table;
width: inherit;
}
#settings p { display: table-row; }
</style>
</head>
<body>
<h1>Apollonian Gasket Generator</h1>
""")
print('<div id="gasket">\n%s\n</div>' % svg)
# Print form
print("""
<div id="settings">
<form method="post" action="index.cgi" id="params">
<p><label for="c1">First circle</label><input type="number" name="c1" id="c1" step="any" min="0" value="%.2f"/></p>
<p><label for="c2">Second circle</label> <input type="number" name="c2" id="c2" step="any" min="0" value="%.2f"/></p>
<p><label for="c3">Third circle</label><input type="number" name="c3" id="c3" step="any" min="0" value="%.2f"/></p>
<p><label for="curv">Curvature</label><input type="radio" name="roc" id="curv" value="curvature" %s/></p>
<p><label for="rad">Radius</label><input type="radio" name="roc" id="rad" value="radius" %s/></p>
<p><label for="depth">Recursion depth</label> <input type="number" name="depth" value="%d" min="0" max="5"/></p>
<p><label for="num">No. of colors</label><input type="number" name="res" value="%d" min="3" max="8"/> </p>
<p><label>Color scheme</label><select name="color">
""" % (settings.c1, settings.c2, settings.c3, settings.curv_checked, settings.rad_checked, settings.depth, settings.resolution))
# Sort color scheme names
info = schemes.info()
info.sort(key=lambda d: d["name"])
info.insert(0, {"name" : "none"})
for s in info:
if s["name"] == settings.color:
selected = "selected"
else:
selected = ""
print('<option value="%s" %s>%s</value>' % (s["name"], selected, s["name"]))
# Print last chunk of form and help text
print("""
</select></p>
<p><input type="submit" name="submit" value="Update"> <input type="submit" name="submit" value="Save"></p>
</form>
</div>
<div class="wrapper">
<div id="about">
<h2>About</h2>
<p> Apollonian Gaskets are groups of circles in which three are
mutally tangent to each other. You can think of it as tightly filling
a big circle with lots of smaller cicles. These sets of circles can be
computed recusively with relative ease. If you are interested in the
mathematical part, see <a
href="https://en.wikipedia.org/wiki/Apollonian_gasket">Wikipedia on
this subject</a>. </p>
<p>This site showcases a small command line program I wrote to
generate svg images of those circles. It can be found on <a
href="https://github.com/lsandig/apollon">github</a>.</p>
<p>For a more in-depth explanation of this implementation see <a
href="http://lsandig.org/blog/2014/08/apollon-python/en/">this
post</a> on my blog (English and German version)</p>
<p>Please note that the online version has a recursion limit of depth
5 to reduce the time and memory consumption on the server. With the
command line version only your RAM is the limit.</p>
<p>This is free software published under the GPLv3.</p>
</div>
</div>
</body>
</html>
""")
def print_only_image(svg):
print('Content-type: image/svg+xml\nContent-Disposition: attachment; filename="apollonian_gasket.svg"\n\n')
print(svg)
if __name__ == "__main__":
# Debugging
#cgitb.enable()
# Get settings from form
form = cgi.FieldStorage()
param = Settings(form)
# Construct color map
schemes = ColorScheme("colorbrewer.json")
if not param.impossible:
# Magic
ag = ApollonianGasket(param.c1, param.c2, param.c3)
ag.generate(param.depth)
# Get smallest and biggest radius
smallest = abs(min(ag.genCircles, key=lambda c: abs(c.r.real)).r.real)
biggest = abs(max(ag.genCircles, key=lambda c: abs(c.r.real)).r.real)
if param.color == 'none':
mp = ColorMap('none')
else:
mp = schemes.makeMap(smallest, biggest, param.color, param.resolution)
# Convert to svg
svg = ag_to_svg(ag.genCircles, mp, tresh=0.005)
# Output
if param.onlysvg:
print_only_image(svg)
else:
print_with_form(svg, param, schemes)
else:
errortext = "<h2>No Apollonian gasket possible for these curvatures :(</2>"
print_with_form(errortext, param, schemes)