File:Catenary properties.svg
Summary
| Description |
English: Diagram of a catenary showing some properties |
| Date | |
| Source | Own work |
| Author | Vernanimalcula |
| SVG development | Category:Valid SVG created with Python:Icons#Catenary%20properties.svg  Category:Translation possible - SVGThis icon uses embedded text that can be easily translated using a text editor. |
Licensing
Vernanimalcula, the copyright holder of this work, hereby publishes it under the following licenses:
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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. |
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Source code
The image is the output of this Python program:
from math import cosh, sinh
# Catenary
w = 400.0
a = 100.0
b = a*cosh((w/2)/a)
l = a*sinh((w/2)/a)
h = b-a
W, H = w+120, h+120 # total size of SVG image
ox, oy = 40.0, 40.0 # offset of diagram in SVG image (in SVG coords)
def x2svg( x ):
""" Converts mathematial x to SVG coordinate """
return ox + w/2 + x
def y2svg( y ):
""" Converts mathematial y to SVG coordinate """
return oy - y
def tosvg( t ):
""" Converts t=(x,y,x,y,...) (mathematical) to SVG coordinates """
coords = ()
for i in range(0,len(t),2):
coords = coords + (x2svg(t[i]),y2svg(t[i+1]))
return coords
def print_polyline( t ):
""" SVG polyline given by mathematical coordinates """
ilist = ' '.join( ['%i'] * len(t) )
s = '<polyline points="%s" style="stroke:#00A;stroke-width:3;fill:none;"/>' % ilist
print s % tosvg(t)
fontsize=36
def print_text( x, y, txt, color='#00A' ):
""" Print text centered at mathematical coordinates """
svgx = x2svg(x) - 0.25*len(txt)*fontsize
svgy = y2svg(y) + 0.25*fontsize
print '<text x="%i" y="%i" style="font-family:sans-serif;font-size:%i;font-style:italic;color:%s">%s</text>' % (svgx,svgy,fontsize,color,txt)
def print_arrow( x0, y0, x1, y1, x2, y2, x3, y3 ):
""" Print arrow with lines given by mathematical coordinates """
print_polyline((x0,y0,x1,y1))
print_polyline((x2,y2,x0,y0,x3,y3))
def print_xarrow( x0, y0, l, d ):
""" Print horicontal arrow; l = long line; d = short line """
print_arrow( x0, y0, x0+l, y0, x0+d, y0+d, x0+d, y0-d )
def print_yarrow( x0, y0, l, d ):
""" Print vertical arrow; l = long line; d = short line """
print_arrow( x0, y0, x0, y0+l, x0+d, y0+d, x0-d, y0+d )
########################################################################
print """<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns="http://www.w3.org/2000/svg"
width="%i"
height="%i"
viewBox="%i %i %i %i">""" % (W,H,0,0,W,H)
# Background
print '<rect id="background" x="0" y="0" width="%i" height="%i" style="fill:#FFF"/>' % (W,H)
print '<rect id="curve" x="%i" y="%i" width="%i" height="%i" style="fill:#DDF"/>' % (ox,oy,w,h)
# Circle of radius a
print '<circle cx="%i" cy="%i" r="%i" style="stroke:#00A;stroke-width:3;fill:none;"/>' % (x2svg(0),y2svg(a-h),a)
print_polyline(( 0, a-h, a, a-h))
print_text( 0.5*a, 1.14*a-h, 'a' )
# Catenary
n = 100
xvals = [ w*(float(i)/n) for i in range(-n/2,n/2+1) ]
p = ' '.join([ '%i %i' % tosvg((x,a*cosh(x/a)-b)) for x in xvals ])
s = 'stroke:#000; stroke-width:5; fill:none'
print '<polyline points="%s" style="%s"/>' % (p,s)
print_text( -0.4*w, -0.1*h, 'l', color='#000' )
# Arrows
y0, l, d = 20, 0.44*w, 0.025*w
print_text( 0, y0, 'w' )
print_xarrow( -w/2, y0, l, d )
print_xarrow( w/2, y0, -l, -d )
x0, l = -0.55*w, 0.42*h
print_text( x0, -h/2, 'h' )
print_yarrow( x0, 0, -l, -d )
print_yarrow( x0, -h, l, d )
# Labels
print_text( 0, -1.25*h, 'b=h+a' )
fontsize=18
y = -1.1*h
print_text( -w/2, y, 'x=-w/2' )
print_text( 0, y, 'x=0' )
print_text( w/2, y, 'x=w/2' )
x = 0.6 * w
print_text( x, 0, 'y=0' )
print_text( x, -h, 'y=-h' )
print "</svg>"