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>"