try:
    import svgwrite as svg
except ImportError:
    print 'You need to install svgwrite: http://pypi.python.org/pypi/svgwrite/'
    # documentation at http://pythonhosted.org/svgwrite/
    exit(1)

from math import *

def to_xyz(theta, phi, r=1):
    return r * sin(theta) * cos(phi), r * sin(theta) * sin(phi), r * cos(theta)

def to_theta_phi_r(x, y, z):
    return atan2(z, sqrt(x**2 + y**2)), atan2(x, y), sqrt(x**2+y**2+z**2)
    
def rotx(x, y, z, a):
    y, z = cos(a) * y + sin(a) * z, cos(a) * z - sin(a) * y
    return x, y, z

def ellipse_path(theta, phi, tilt, flip=False):
    t, p, r2 = to_theta_phi_r(*rotx(*(to_xyz(theta, phi, 1) + (tilt,))))
    a = abs(r)
    b = abs(r * sin(t))
    return 'M %f,%f A %f,%f %f %i,%i %f,%f' % (-r*cos(p), -r*sin(p),
        a, b, p*180/pi, 0, {True:1, False:0}[flip], r*cos(p), r*sin(p))

# document
size = 600, 600
doc = svg.Drawing('poincare-sphere_arrows.svg', profile='full', size=size)
doc.set_desc('poincare-sphere_arrows.svg', '''Drawing of a poincare-sphere with polarisations H, V, D, A, R and L, a coordinate system of Stokes-Vectors P1, P2 and P3 and six little images that illustrate the polarisations
rights: GNU Free Documentation license,
        Creative Commons Attribution ShareAlike license''')

# settings
dash = '8,6'
col = 'black'
r = 240
tilt = radians(-70)
phi = radians(-25)
cp, sp = cos(phi), sin(phi)

# background
doc.add(doc.rect(id='background', profile='full', insert=(0, 0), size=size, fill='white', stroke='none'))

# arrow markers
arrow_d = 'M -4,0 L 2,-3 L 1,0 L 2,3 L -4,0 z'
arrow1 = doc.marker(id='arrow1', orient='auto', overflow='visible')
arrow1.add(doc.path(d=arrow_d, fill=col, stroke='none',
    transform='rotate(180) scale(0.7)'))
doc.defs.add(arrow1)
arrow2 = doc.marker(id='arrow2', orient='auto', overflow='visible')
arrow2.add(doc.path(d=arrow_d, fill=col, stroke='none',
    transform='scale(0.7)'))
doc.defs.add(arrow2)
arrow3 = doc.marker(id='arrow3', orient='auto', overflow='visible')
arrow3.add(doc.path(d='M 8.7185878,4.0337352 L -2.2072895,0.016013256 L 8.7185884,-4.0017078 C 6.9730900,-1.6296469 6.9831476,1.6157441 8.7185878,4.0337352 z', fill=col, stroke='none',
    transform='scale(0.8) rotate(180)'))
doc.defs.add(arrow3)

# make a group for the sphere
sphere = doc.g(transform='translate(300, 300)', fill='none', stroke=col, stroke_width='2')
sphere['font-family'] = 'DejaVu Sans'
sphere['font-size'] = '42px'
doc.add(sphere)

# back ellipses
sphere.add(doc.path(d=ellipse_path(0, 0, tilt),
    stroke_dasharray=dash, stroke=col))
sphere.add(doc.path(d=ellipse_path(pi/2, phi, tilt, True),
    stroke_dasharray=dash, stroke=col))
sphere.add(doc.path(d=ellipse_path(pi/2, phi+pi/2, tilt),
    stroke_dasharray=dash, stroke=col))

# draw coordinate axes
sphere.add(doc.circle(center=(0, 0), r=5, fill=col, stroke='none'))
for i in range(3):
    xyz = [0, 0, 0]
    xyz[i] = 0.3 * r
    x, y, z = xyz
    x, y, z = rotx(x*cp + y*sp, y*cp - x*sp, z, tilt)
    line = doc.line(start=(0, 0), end=('%f' % x, '%f' % y), stroke=col)
    line['marker-end'] = arrow3.get_funciri()
    sphere.add(line)

# the six defined points
pts = []
for x,y,z in [[0,0,-1], [0,0,1], [0,-1,0], [0,1,0], [-1,0,0], [1,0,0]]:
    x, y, z = rotx(r * (x*cp + y*sp), r * (y*cp - x*sp), r * z, tilt)
    if z >= 0:
        continue
    pts.append((x, y))
    sphere.add(doc.circle(center=('%f' % x, '%f' % y), r=6,
        fill=col, stroke='none'))

# inset images
rect = doc.rect((-22, -22), (44, 44), fill='white', stroke=col, fill_opacity=0.88)

gV = doc.g(transform='translate(%f, %f)' % pts[1])
gV.add(rect)
gV.add(doc.line(start=(0,-11), end=(0,11), stroke_width=3,
    marker_end=arrow1.get_funciri(), marker_start=arrow2.get_funciri()))
sphere.add(gV)

gA = doc.g(transform='translate(%f, %f)' % pts[2])
gA.add(rect)
gA.add(doc.line(start=(-7,-7), end=(7,7), stroke_width=3,
    marker_end=arrow1.get_funciri(), marker_start=arrow2.get_funciri()))
sphere.add(gA)

gL = doc.g(transform='translate(%f, %f)' % pts[0])
gL.add(rect)
gL.add(doc.path(d='M -12,0 A 12,12 0 1,0 0,-12', stroke_width=3,
    marker_end=arrow1.get_funciri()))
sphere.add(gL)

# V label
sphere.add(doc.text('V', text_anchor='middle',
    transform='translate(144, -86)', stroke='none', fill=col))

# Stokes-Vector labels
sphere.add(doc.text('S₁', text_anchor='middle',
    transform='translate(-56, 33)', stroke='none', fill=col))
sphere.add(doc.text('S₂', text_anchor='middle',
    transform='translate(63, -2)', stroke='none', fill=col))
sphere.add(doc.text('S₃', text_anchor='middle',
    transform='translate(-29, -59)', stroke='none', fill=col))

# sphere surface
grad1 = doc.defs.add(doc.radialGradient(id='grad1',
    center=(0.375, 0.15), r=0.75, gradientUnits='objectBoundingBox'))
grad1.add_stop_color(offset=0, color='#ffffff', opacity=0.3)
grad1.add_stop_color(offset=1, color='#dddddd', opacity=0.3)
sphere.add(doc.circle(center=(0, 0), r=str(r),
    fill='url(#grad1)', stroke='none'))
grad2 = doc.defs.add(doc.radialGradient(id='grad2',
    center=(0.45, 0.45), r=0.575, gradientUnits='objectBoundingBox'))
grad2.add_stop_color(offset=0.6, color='#cccccc', opacity=0)
grad2.add_stop_color(offset=0.8, color='#cccccc', opacity=0.2)
grad2.add_stop_color(offset=1, color='#333333', opacity=0.2)
sphere.add(doc.circle(center=(0, 0), r=str(r),
    fill='url(#grad2)', stroke='none'))

# the six defined points
for x,y,z in [[0,0,-1], [0,0,1], [0,-1,0], [0,1,0], [-1,0,0], [1,0,0]]:
    x, y, z = rotx(r * (x*cp + y*sp), r * (y*cp - x*sp), r * z, tilt)
    if z < 0:
        continue
    pts.append((x, y))
    sphere.add(doc.circle(center=('%f' % x, '%f' % y), r=6,
        fill=col, stroke='none'))

# H, D, A, R, L labels
sphere.add(doc.text('H', text_anchor='middle',
    transform='translate(-144, 115)', stroke='none', fill=col))
sphere.add(doc.text('D', text_anchor='middle',
    transform='translate(272, 52)', stroke='none', fill=col))
sphere.add(doc.text('A', text_anchor='middle',
    transform='translate(-272, -26)', stroke='none', fill=col))
sphere.add(doc.text('R', text_anchor='middle',
    transform='translate(0, -261)', stroke='none', fill=col))
sphere.add(doc.text('L', text_anchor='middle',
    transform='translate(0, 291)', stroke='none', fill=col))

# front ellipses
sphere.add(doc.path(d=ellipse_path(0, 0, tilt, True)))
sphere.add(doc.path(d=ellipse_path(pi/2, phi, tilt)))
sphere.add(doc.path(d=ellipse_path(pi/2, phi+pi/2, tilt, True)))

# circle edge
sphere.add(doc.circle(center=(0, 0), r=str(r)))

# inset images
gH = doc.g(transform='translate(%f, %f)' % pts[4])
gH.add(rect)
gH.add(doc.line(start=(-11,0), end=(11,0), stroke_width=3,
    marker_end=arrow1.get_funciri(), marker_start=arrow2.get_funciri()))
sphere.add(gH)

gD = doc.g(transform='translate(%f, %f)' % pts[5])
gD.add(rect)
gD.add(doc.line(start=(-7,7), end=(7,-7), stroke_width=3,
    marker_end=arrow1.get_funciri(), marker_start=arrow2.get_funciri()))
sphere.add(gD)

gR = doc.g(transform='translate(%f, %f)' % pts[3])
gR.add(rect)
gR.add(doc.path(d='M 12,0 A 12,12 0 1,1 0,-12', stroke_width=3,
    marker_end=arrow1.get_funciri()))
sphere.add(gR)

doc.save()