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Catenary_animation.gif (150 × 80 pixels, file size: 75 KB, MIME type: image/gif, looped, 90 frames, 5.1 s)

Summary

Description
English: Animation of a catenary curve for different seperations of the endpoints.
Date
Source

Own work

see sourcecode below
Author Geek3

Source Code

The image is created by the following source-code. Requirements:

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

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head 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.
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
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.
You may select the license of your choice.

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depicts

October 2010

image/gif

c58f33fb2dba9864f699017027d46ad4c67095b6

77,108 byte

5.099999999999992 second

80 pixel

150 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current10:26, 11 August 2014Thumbnail for version as of 10:26, 11 August 2014150 × 80 (75 KB)Ev9nBackground converted to transparent.
19:27, 16 October 2010Thumbnail for version as of 19:27, 16 October 2010150 × 80 (81 KB)Geek3own work

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