# paste this code at the end of VectorFieldPlot 2.2
doc = FieldplotDocument('VFPt_sphere-magnet_potential', commons=True,
    width=600, height=600)

R = 1.0
c = np.array([0., 0.])
M = np.array([0., 1.])
field_outside = Field([ ['dipole', {'x':c[0], 'y':c[1], 'px':M[0]*4./3.*pi*R**3, 'py':M[1]*4./3.*pi*R**3}] ])
Bfield_inside = Field([ ['homogeneous', {'Fx':2./3.*M[0], 'Fy':2./3.*M[1]}] ])
Hfield_inside = Field([ ['homogeneous', {'Fx':-1/3.*M[0], 'Fy':-1/3.*M[1]}] ])

def spheremagnet_Bfield(xy):
    if vabs(xy - c) < R:
        return Bfield_inside.F(xy)
    else:
        return field_outside.F(xy)

def spheremagnet_potential(xy):
    if vabs(xy - c) < R:
        return Hfield_inside.V(xy)
    else:
        return field_outside.V(xy)

field = Field([ ['custom', {'F':spheremagnet_Bfield, 'V':spheremagnet_potential}] ])

U0 = field.V(c + R * vnorm(M))
doc.draw_scalar_field(func=field.V, cmap=doc.cmap_AqYlFs, vmin=-U0, vmax=U0)

nlines = 20
for iline in range(nlines):
    p0 = (R * (2 * (iline + 0.5) / nlines - 1), 0.)
    line = FieldLine(field, p0, directions='both', maxr=7)
    if fabs(iline - (nlines - 1) / 2.) < 1.:
        of = 0.2
    elif fabs(iline - (nlines - 1) / 2.) < 2.:
        of = 0.23
    elif fabs(iline - (nlines - 1) / 2.) < 3.:
        of = 0.3
    elif fabs(iline - (nlines - 1) / 2.) < 4.:
        of = 0.53
    elif fabs(iline - (nlines - 1) / 2.) < 5.:
        of = 0.4
    elif fabs(iline - (nlines - 1) / 2.) < 6.:
        of = 0.38
    else:
        of = 0.3
    off = {'start':0.9, 'leave_image':of, 'enter_image':of, 'end':0.9}
    doc.draw_line(line, arrows_style={'dist':2.0,
        'max_arrows':2, 'offsets':off})

# draw the spherical magnet
g = doc.draw_object('g', {'id':'sphere',
    'transform':'translate({},{})'.format(*c)})
defs = doc.draw_object('defs', {}, group=g)
grad = doc.draw_object('radialGradient', {'id':'grad', 'r':str(1.2*R),
    'cx':'0', 'cy':str(0.2*R), 'fx':'0', 'fy':str(0.6*R),
    'gradientUnits':'userSpaceOnUse'}, group=defs)
for col, of, opa in [['#ffffff', '0', '0.8'], ['#ffffff', '0.04', '0.7'],
        ['#ffffff', '0.11', '0.4'], ['#ffffff', '0.22', '0.2'],
        ['#555555', '0.7', '0.3'], ['#000000', '1', '0.6']]:
    stop = doc.draw_object('stop', {'stop-color':col, 'offset':of,
        'stop-opacity':opa}, group=grad)
clip = doc.draw_object('clipPath', {'id':'circle_clip'}, group=defs)
doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':str(R)}, group=clip)

gc = doc.draw_object('g', {'clip-path':'url(#circle_clip)'}, group=g)
doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':str(R),
    'style':'fill:#00cc00; stroke:none;'}, group=gc)
doc.draw_object('path', {'d':'M -1,0 A 1,1 0 0 0 1,0 L -1,0 Z',
    'style':'fill:#ff0000; stroke:none;'}, group=gc)
text_N = doc.draw_object('text', {'text-anchor':'middle', 'x':'0', 'y':'0',
    'transform':'translate({},{}) scale({},{})'.format(0, 0.56*R-0.2, 0.05, -0.05),
    'style':'fill:#000000; stroke:none; ' +
    'font-size:12px; font-family:Bitstream Vera Sans;'}, group=g)
text_N.text = 'N'
text_S = doc.draw_object('text', {'text-anchor':'middle', 'x':'0', 'y':'0',
    'transform':'translate({},{}) scale({},{})'.format(0, -0.56*R-0.2, 0.05, -0.05),
    'style':'fill:#000000; stroke:none; ' +
    'font-size:12px; font-family:Bitstream Vera Sans;'}, group=g)
text_S.text = 'S'
doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':str(R),
    'style':'fill:url(#grad); stroke:none;',
    'transform':'rotate(30) scale(1.4,1)'}, group=gc)
doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':str(R),
     'style':'fill:none; stroke:#000000; stroke-width:0.04;'}, group=g)

doc.write()