from pysketcher import *

Nt = 5

#u = SketchyFunc1()
#t_mesh = linspace(0, 8, Nt+1)

u = SketchyFunc3()
t_mesh = linspace(0, 6, Nt+1)
t_mesh_staggered = linspace(0.5*(t_mesh[0]+t_mesh[1]),
                            0.5*(t_mesh[-2] + t_mesh[-1]), Nt)

# Add 20% space to the left and 30% to the right of the coordinate system
t_axis_extent = t_mesh[-1] - t_mesh[0]
t_min = t_mesh[0] - 0.2*t_axis_extent
t_max = t_mesh[-1] + 0.3*t_axis_extent
u_max = 1.3*max([u(t) for t in t_mesh])
u_min = -0.2*u_max

drawing_tool.set_coordinate_system(t_min, t_max, u_min, u_max, axis=False)
drawing_tool.set_linecolor('black')

r = 0.005*(t_max-t_min)     # radius of circles placed at mesh points
u_discrete = Composition({i: Composition(dict(
    circle=Circle(point(t, u(t)), r).set_filled_curves('black'),
    u_point=Text('$u_%d$' % i,
                 point(t, u(t)) + (point(0,5*r)
                                   if i > 0 else point(-5*r,0))),
    )) for i, t in enumerate(t_mesh)})

# u' = v
#v = u.smooth.derivative(n=1)
v = SketchyFunc4()

v_discrete = Composition({i: Composition(dict(
    circle=Circle(point(t, v(t)), r).set_filled_curves('red'),
    v_point=Text(r'$v_{%d/2}$' % (2*i+1),
                 point(t, v(t)) + (point(0,5*r))),
    )) for i, t in enumerate(t_mesh_staggered)})

axes = Composition(dict(
    x=Axis(point(0,0), t_mesh[-1] + 0.2*t_axis_extent, '$t$',
           label_spacing=(1/45.,-1/30.)),
    y=Axis(point(0,0), 0.8*u_max, '$u,v$',
           rotation_angle=90)))

h = 0.03*u_max  # tickmarks height
u_nodes = Composition({i: Composition(dict(
    node=Line(point(t,h), point(t,-h)),
    name=Text('$t_%d$' % i, point(t,-3.5*h))))
                     for i, t in enumerate(t_mesh)})
v_nodes = Composition({i: Composition(dict(
    node=Line(point(t,h/1.5), point(t,-h/1.5)).set_linecolor('red'),
    name=Text(r'$t_{%d/2}$' % (2*i+1), point(t,-3.5*h))))
                     for i, t in enumerate(t_mesh_staggered)})
illustration = Composition(dict(u=u_discrete,
                                v=v_discrete,
                                u_mesh=u_nodes,
                                v_mesh=v_nodes,
                                axes=axes)).set_name('fdm_uv')
drawing_tool.erase()
# Staggered t mesh and u and v points
illustration.draw()
drawing_tool.display()
drawing_tool.savefig(illustration.get_name())

# Exact u line (u is a Spline Shape that applies 500 intervals by default
# for drawing the curve)
u_exact = u.set_linestyle('dashed').set_linewidth(1)
u_exact.draw()
#v = Curve(u.xcoor, v(u.xcoor))
t_mesh_staggered_fine = linspace(t_mesh_staggered[0],
                                 t_mesh_staggered[-1],
                                 501)
v_exact = Curve(t_mesh_staggered_fine, v(t_mesh_staggered_fine)).\
          set_linestyle('dashed').set_linewidth(1)
v_exact.draw()
drawing_tool.display()
drawing_tool.savefig('%s_uve' % illustration.get_name())

input()