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- 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()
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