File:Catenary animation.gif
Catenary_animation.gif (150 × 80 pixels, file size: 75 KB, MIME type: image/gif, looped, 90 frames, 5.1 s)
Captions
Summary
[edit]DescriptionCatenary animation.gif |
English: Animation of a catenary curve for different seperations of the endpoints. |
Date | |
Source |
Own work |
Author | Geek3 |
Source Code
[edit]The image is created by the following source-code. Requirements:
- unix-like command line interface
- python
- scipy
- librsvg
- imagemagick
- lxml archive copy at the Wayback Machine
- gifsicle
python source code:
#!/usr/bin/python
# -*- coding: utf8 -*-
from lxml import etree
import os
import scipy as sc
import scipy.optimize as op
import scipy.integrate as ig
from math import *
class SvgDocument:
'''
creates a svg document structure using lxml.etree
'''
def __init__ (self, name, width=800, height=600, bgcolor='#ffffff',
center=None, unit=1.0):
self.name = name
self.width = int(width)
self.height = int(height)
self.unit = float(unit)
if center == None: self.center = [width / 2., height / 2.]
else: self.center = [float(i) for i in center]
# create document structure
self.svg = etree.Element('svg',
nsmap={None:'http://www.w3.org/2000/svg',
'xlink':'http://www.w3.org/1999/xlink'})
self.svg.set('version', '1.1')
self.svg.set('baseProfile', 'full')
self.svg.set('width', str(int(width)))
self.svg.set('height', str(int(height)))
# title
self.title = etree.SubElement(self.svg, 'title')
self.title.text = self.name
# background
if bgcolor != None:
self.background = etree.SubElement(self.svg, 'rect')
self.background.set('id', 'background')
self.background.set('x', '0')
self.background.set('y', '0')
self.background.set('width', str(width))
self.background.set('height', str(height))
self.background.set('fill', bgcolor)
# image elements
self.content = etree.SubElement(self.svg, 'g')
self.content.set('id', 'image')
self.content.set('transform',
'translate({0},{1}) scale({2},-{2})'.format(
self.center[0], self.center[1], self.unit))
def draw_object(self, name, params, group=None):
'''
Draw arbitraty svg object.
Params must be a dictionary of valid svg parameters.
'''
if group == None:
obj = etree.SubElement(self.content, name)
else:
obj = etree.SubElement(group, name)
for i, j in params.iteritems():
obj.set(str(i), str(j))
return obj
def write(self, filename=None):
# write content to file
if filename == None: filename = self.name
outfile = open(filename + '.svg', 'w')
outfile.write(etree.tostring(self.svg, xml_declaration=True,
pretty_print=True, encoding='utf-8'))
outfile.close()
print 'image written to', filename + '.svg'
# physics: calculate the catenary curve
def catenary(x, r):
# catenary curve f(x) with l=2 and horizontal distance 2r
if r == 1.0:
return 0.0
# search a-value for given length and distance
def fct(a):
if a == 0.0: return r - 1.0
return sinh(r * a) / a - 1.0
x0 = 1.0
while fct(x0) > 0.0: x0 /= 2.0
while fct(2.0 * x0) < 0.0: x0 *= 2.0
a = 1.0 / op.brentq(fct, x0, 2*x0)
return a * (cosh(x / a) - cosh(r / a))
render_mult = 8 # supersampling to improve quality
folder = 'frames'
commands = ['mkdir ' + folder]
for c in commands: print c; os.system(c)
# render frames
frames = 100
names = []
for i in range(frames):
name = 'catenary_{0:0>2}'.format(i)
names.append(name)
w, h = 150, 80
r0 = 65.0
doc = SvgDocument(name, width=w, height=h, center=[w/2, 10], unit=1)
a = 0.5 + 0.5 * cos(i * 2*pi / frames)
r = a**1.5 + 12*a**2 - 21*a**2.5 + 9*a**3
for ri in [-r, r]:
doc.draw_object('circle', {'cx':str(ri*r0), 'cy':'0', 'r':'7',
'style':'fill:#888; stroke:none'})
if r != 0.0:
x = sc.linspace(-r, r, 401)
path_data = zip(r0 * x, [r0 * catenary(xx, r) for xx in x])
else:
path_data = [[0.0, 0.0], [0.0, -r0], [0.0, 0.0]]
# append extra segment to have last point displayed
v = sc.array(path_data[-1]) - sc.array(path_data[-2])
v *= 0.1 / r0 / sqrt(v[0]**2 + v[1]**2)
path_data.append(sc.array(path_data[-1]) + v)
path = 'M ' + ' L '.join([str(xy[0]) + ',' + str(xy[1]) for xy in path_data])
doc.draw_object('path', {'d':path, 'stroke-linecap':'round',
'style':'fill:none; stroke:black; stroke-width:4',
'stroke-linejoin':'round', 'stroke-dasharray':'0,5'})
doc.write(filename=folder + '/' + name)
for name in names:
commands = ['rsvg -w{0} -h{1} {3}/{2}.svg {3}/{2}.png'.format(
w * render_mult, h * render_mult, name, folder),
'rm {1}/{0}.svg'.format(name, folder),
'convert -scale {0}x{1} {3}/{2}.png {3}/{2}.gif'.format(
w, h, name, folder),
'rm {1}/{0}.png'.format(name, folder)]
for c in commands: print c; os.system(c)
commands = ['gifsicle -d5 -l0 --colors 256 '
+ folder + '/*.gif > catenary_animation.gif',
'rm -rf ' + folder]
for c in commands: print c; os.system(c)
Licensing
[edit]Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
- 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.
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 10:26, 11 August 2014 | 150 × 80 (75 KB) | Ev9n (talk | contribs) | Background converted to transparent. | |
19:27, 16 October 2010 | 150 × 80 (81 KB) | Geek3 (talk | contribs) | own work |
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Unique ID of original document | xmp.did:1426D522A0236811822A9F6CF5CCF9DF |
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Software used | Adobe Photoshop CS6 (Macintosh) |