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Summary
DescriptionDomain coloring x2-1 x-2-i x-2-i d x2+2+2i.xcf |
Français : Coloration de régions de la fonction complexe sur le domaine . La couleur (teinte) représente l'argument de la fonction. Les lignes noires et blanches (saturation, valeur) représentent les valeurs de la fonction à module constant. Ce fichier comporte 4 calques : les lignes blanches indiquant les lignes iso-argument tous les pi/6, la grille transformée du plan complexe, les variations d'intensité représentant le module, la couleur représentant l'argument
English: Domain coloring of the complex function on the domain . Phase is coded by the hue and module by the value. Image generated by python script conformal.py v0.4 (Michael J Gruber and JB Cuenot) with Gimp v2.8 |
Date | |
Source | Own work |
Author | Djiboun |
Other versions |
|
XCF development InfoField |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Python src code
#!/usr/bin/env python
# conformal.py
# Copyright (C) 2006-2011 Michael J. Gruber <conformal@drmicha.warpmail.net>
#
# 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, version 2 of the License.
#
# 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., 675 Mass Ave, Cambridge, MA 02139, USA.
confversion = "0.3+"
# allow access through module and without
import math, cmath
from math import *
from cmath import *
from array import array
from gimpfu import *
# try importing typical math modules
try:
from fpconst import *
import scipy.special
except ImportError:
pass
try:
import mpmath
except ImportError:
pass
def conformal_batch(width, height, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient, filename):
conformal_core(width, height, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient, filename)
def conformal(width, height, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient):
conformal_core(width, height, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient, None)
def conformal_core(width, height, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient, filename):
image = gimp.Image(width, height, RGB)
drawables = [ gimp.Layer(image, "Argument", width, height, RGBA_IMAGE, 100, NORMAL_MODE),
gimp.Layer(image, "Log. modulus", width, height, RGBA_IMAGE, 35, VALUE_MODE),
gimp.Layer(image, "Grid", width, height, RGBA_IMAGE, 10, DARKEN_ONLY_MODE)]
image.disable_undo()
l = 1
for drawable in drawables:
image.add_layer(drawable, l)
l = -1
bpp = drawables[0].bpp
gimp.tile_cache_ntiles(2 * (width + 63) / 64)
dest_rgns = [ drawable.get_pixel_rgn(0, 0, width, height, True, False) for drawable in drawables ]
progress = 0
max_progress = width * height
if filename is None:
gimp.progress_init("Conformally Mapping...")
sx = (width-1.0)/(xr-xl)
sy = (height-1.0)/(yt-yb)
w = complex(0.0)
z = complex(0.0)
cx, cy = 0, 0
mp2 = 2.0*math.pi # no need to do this 500*500 times...
ml2 = 2.0*math.log(2) # no need to do this 500*500 times...
ml = math.log(2) # no need to do this 500*500 times...
compiled=compile(code, "compiled code", "exec", 0, 1)
compiledconstraint=compile(constraint, "compiled constraint code", "exec", 0, 1)
dests = [ array("B", "\x00" * width*height*bpp) for i in range(3) ]
QUANT = 4096
args = [ i/(QUANT-1.0) for i in range(QUANT) ]
arggradsamples = list(gimp.gradient_get_custom_samples(gradient, args)) + [[0,]*bpp]
modgradsamples = list(gimp.gradient_get_custom_samples("Default", args)) + [[0,]*bpp]
sqrsamples = [ [0,]*(bpp-1) + [255,], [255,]*(bpp-1) + [255,] , [0,]*bpp ]
for col in range(QUANT+1):
arggradsamples[col] = [ ((int)(255*arggradsamples[col][i]+0.5)) for i in range(bpp)]
modgradsamples[col] = [ ((int)(255*modgradsamples[col][i]+0.5)) for i in range(bpp)]
qinf = 1.0 + 1.0/(QUANT-1) # uggely uggely
args = [0.0,] * width
mods = [0.0,] * width
sqrs = [0,] * width
for row in range(0, height):
for col in range(0, width):
z = col/sx + xl + 1j*( yt - row/sy)
p = True
try:
exec(compiledconstraint)
except (OverflowError, ValueError):
p = False
if not p:
w = 0.0
else:
try:
exec(compiled)
except (OverflowError, ValueError):
p = False
if not p or isnan(w) or isinf(w):
w = 0.0
try:
logw = cmath.log(w)
arg = logw.imag
if isnan(arg) or isinf(arg):
arg = 0.0
p = False
elif arg < 0.0:
arg = arg + mp2
mod = ( logw.real/ml ) % 1.0
if isnan(mod) or isinf(mod):
mod = 0.0
p = False
except (OverflowError, ValueError):
arg = 0.0
mod = 0.0
p = False
arg = arg/mp2
try:
sqr = int(w.imag/grid % 2.0) + int(w.real/grid % 2.0)
if isnan(sqr) or isinf(sqr):
sqr = 0
p = False
except (OverflowError, ValueError):
sqr = 0
p = False
sqr = sqr % 2
if not p:
arg = qinf
mod = qinf
sqr = 2
args[col] = arg
mods[col] = mod
sqrs[col] = sqr
dests[0][row*width*bpp : (row+1)*width*bpp] = array("B", [ arggradsamples [int((QUANT-1)*args[col]+0.5)][i] for col in range(0, width) for i in range(bpp) ] )
dests[1][row*width*bpp : (row+1)*width*bpp] = array("B", [ modgradsamples[int((QUANT-1)*mods[col]+0.5)][i] for col in range(0, width) for i in range(bpp) ] )
dests[2][row*width*bpp : (row+1)*width*bpp]= array("B", [ sqrsamples[sqrs[col]][i] for col in range(0,width) for i in range(bpp) ] )
progress = progress + width
if filename is None:
gimp.progress_update(float(progress) / max_progress)
for i in range(3):
dest_rgns[i][0:width, 0:height] = dests[i].tostring()
for drawable in drawables:
drawable.flush()
drawable.update(0,0,width,height)
if not checkboard:
pdb.plug_in_edge(image,drawables[2], 10, 0, 0) # amount, WRAP, SOBEL
pdb.plug_in_vinvert(image,drawables[2])
if image.parasite_find("gimp-comment"):
image.parasite.detach("gimp-comment")
image.attach_new_parasite("gimp-comment", PARASITE_PERSISTENT, """# conformal %s
code = \"\"\"
%s
\"\"\"
constraint = \"\"\"
%s
\"\"\"
xl = %f
xr = %f
yt = %f
yb = %f
grid = %f
checkboard = %d
gradient = "%s"
width = %d
height = %d
""" % (confversion, code, constraint, xl, xr, yt, yb, grid, checkboard, gradient, width, height))
if filename is None:
image.enable_undo()
gimp.Display(image)
gimp.displays_flush
else:
if filename.find('.xcf') > 0:
pdb.gimp_xcf_save(1, image, drawables[0], filename, filename)
else:
flat_layer = pdb.gimp_image_flatten(image)
pdb.gimp_file_save(image, flat_layer, filename, filename)
register(
"conformal_batch",
"Colour representation of a conformal map",
"Colour representation of a conformal map",
"Michael J Gruber",
"Michael J Gruber",
"2011",
"",
"",
[
(PF_INT, "width", "width", 512),
(PF_INT, "height", "height", 512),
(PF_TEXT, "code", "code", "w=z"),
(PF_TEXT, "constraint", "constraint", "p=True"),
(PF_FLOAT, "xl", "x left", -1.0),
(PF_FLOAT, "xr", "x right", 1.0),
(PF_FLOAT, "yt", "y top", 1.0),
(PF_FLOAT, "yb", "y bottom", -1.0),
(PF_FLOAT, "grid", "grid spacing", 1.0),
(PF_BOOL, "checkboard", "checker board grid", 0),
(PF_GRADIENT, "gradient", "gradient", "Full saturation spectrum CCW"),
(PF_FILE, "file", "file", "out.xcf.bz2"),
],
[],
conformal_batch)
register(
"conformal",
"Colour representation of a conformal map",
"Colour representation of a conformal map",
"Michael J Gruber",
"Michael J Gruber",
"2012",
"<Toolbox>/File/Create/_Conformal ...",
"",
[
(PF_INT, "width", "width", 512),
(PF_INT, "height", "height", 512),
(PF_TEXT, "code", "code", "w=z"),
(PF_TEXT, "constraint", "constraint", "p=True"),
(PF_FLOAT, "xl", "x left", -1.0),
(PF_FLOAT, "xr", "x right", 1.0),
(PF_FLOAT, "yt", "y top", 1.0),
(PF_FLOAT, "yb", "y bottom", -1.0),
(PF_FLOAT, "grid", "grid spacing", 1.0),
(PF_BOOL, "checkboard", "checker board grid", 0),
(PF_GRADIENT, "gradient", "gradient", "Full saturation spectrum CCW"),
],
[],
conformal)
main()
Items portrayed in this file
depicts
16 August 2015
image/x-xcf
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:26, 16 August 2015 | 2,000 × 2,000 (15.09 MB) | Djiboun | User created page with UploadWizard |
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