def main():
code = ps.Axis(ps.Point(1, 1), 3, "x")
code2 = ps.Axis(ps.Point(1, 1), 3, "y")
model = ps.Composition(dict(x=code, y=code2))
fig = ps.Figure(0, 5, 0, 5, backend=MatplotlibBackend)
fig.add(model)
fig.show()
def main() -> None:
d = make_dashpot(0)
s = make_spring(0)
M = ps.Rectangle(ps.Point(0, H), 4 * H, 4 * H).set_line_width(4)
left_wall = ps.Rectangle(ps.Point(-L, 0), H / 10, L).set_fill_pattern(
ps.Style.FillPattern.UP_LEFT_TO_RIGHT)
ground = ps.Wall([ps.Point(-L / 2, 0), ps.Point(L, 0)], thickness=-H / 10)
wheel1 = ps.Circle(ps.Point(H, H / 2), H / 2)
wheel2 = wheel1.translate(ps.Point(2 * H, 0))
fontsize = 24
text_m = ps.Text("$m$", ps.Point(2 * H, H + 2 * H))
text_m.style.font_size = fontsize
text_ku = ps.Text("$ku$", ps.Point(-L / 2, H + 4 * H))
text_ku.style.font_size = fontsize
text_bv = ps.Text("$bu'$", ps.Point(-L / 2, H))
text_bv.style.font_size = fontsize
x_axis = ps.Axis(ps.Point(2 * H, L), H, "$u(t)$")
x_axis_start = ps.Line(ps.Point(2 * H, L - H / 4),
ps.Point(2 * H, L + H / 4)).set_line_width(4)
model = ps.Composition({
"spring": s,
"mass": M,
"left wall": left_wall,
"ground": ground,
"wheel1": wheel1,
"wheel2": wheel2,
"text_m": text_m,
"text_ku": text_ku,
"x_axis": x_axis,
"x_axis_start": x_axis_start,
})
fig = ps.Figure(-L, x_max, -1, L + H, backend=MatplotlibBackend)
fig.add(model)
damping = ps.Composition({"dashpot": d, "text_bv": text_bv})
# or fig = Composition(dict(fig=fig, dashpot=d, text_bv=text_bv))
fig.add(damping)
fig.show()
u_points[i] = ps.Composition({"circle": circle, "u_point": text})
u_discrete = ps.Composition(u_points)
i_lines = {}
for i in range(1, len(t_mesh)):
i_lines[i] = ps.Line(ps.Point(t_mesh[i - 1], u_values[i - 1]),
ps.Point(t_mesh[i], u_values[i])).set_line_width(1)
interpolant = ps.Composition(i_lines)
x_axis_extent: float = t_mesh[-1] + 0.2 * t_axis_extent
logging.info(x_axis_extent)
axes = ps.Composition({
"x":
ps.Axis(
ps.Point(0.0, 0.0),
x_axis_extent,
"$t$",
label_spacing=(1 / 45.0, -1 / 30.0),
),
"y":
ps.Axis(ps.Point(0.0, 0.0), 0.8 * u_max, "$u$", rotation_angle=np.pi / 2),
})
h = 0.03 * u_max # tickmarks height
i_nodes = {}
for i, t in enumerate(t_mesh):
i_nodes[i] = ps.Composition({
"node":
ps.Line(ps.Point(t, h), ps.Point(t, -h)),
"name":
ps.Text("$t_%d$" % i, ps.Point(t, -3.5 * h)),
})
def main() -> None:
u = ps.SketchyFunc3()
Nt = 5
t_mesh = np.linspace(0, 6, Nt + 1)
# Add 20% space to the left and 30% to the right of the coordinate system
t_axis_extent = t_mesh[-1] - t_mesh[0]
logging.info(t_axis_extent)
t_min = t_mesh[0] - 0.2 * t_axis_extent
logging.info(t_min)
t_max = t_mesh[-1] + 0.3 * t_axis_extent
logging.info(t_max)
u_max = 1.3 * max([u(t) for t in t_mesh])
logging.info(u_max)
u_min = -0.2 * u_max
logging.info(u_max)
r = 0.005 * (t_max - t_min) # radius of circles placed at mesh points
# import random; random.seed(12)
perturbations = [0, 0.1, 0.1, 0.2, -0.4, -0.1]
u_points = {}
u_values = []
for i, t in enumerate(t_mesh):
u_value = u(t) + perturbations[i]
u_values.append(u_value)
circle = ps.Circle(ps.Point(t, u_value),
r).set_fill_color(ps.Style.Color.BLACK)
text = ps.Text(
"$u^%d$" % i,
ps.Point(t, u_value) +
(ps.Point(0.0, 3 * r) if i > 0 else ps.Point(-3 * r, 0.0)),
)
u_points[i] = ps.Composition({"circle": circle, "u_point": text})
u_discrete = ps.Composition(u_points)
i_lines = {}
for i in range(1, len(t_mesh)):
i_lines[i] = ps.Line(ps.Point(t_mesh[i - 1], u_values[i - 1]),
ps.Point(t_mesh[i],
u_values[i])).set_line_width(1)
interpolant = ps.Composition(i_lines)
x_axis_extent: float = t_mesh[-1] + 0.2 * t_axis_extent
logging.info(x_axis_extent)
axes = ps.Composition({
"x":
ps.Axis(
ps.Point(0.0, 0.0),
x_axis_extent,
"$t$",
),
"y":
ps.Axis(ps.Point(0.0, 0.0),
0.8 * u_max,
"$u$",
rotation_angle=np.pi / 2),
})
h = 0.03 * u_max # tickmarks height
i_nodes = {}
for i, t in enumerate(t_mesh):
i_nodes[i] = ps.Composition({
"node":
ps.Line(ps.Point(t, h), ps.Point(t, -h)),
"name":
ps.Text("$t_%d$" % i, ps.Point(t, -3.5 * h)),
})
nodes = ps.Composition(i_nodes)
fig = ps.Figure(t_min, t_max, u_min, u_max, backend=MatplotlibBackend)
# Draw t_mesh with discrete u points
illustration = ps.Composition(dict(
u=u_discrete,
mesh=nodes,
axes=axes,
))
fig.erase()
fig.add(illustration)
fig.show()
# Add exact u line (u is a Spline Shape that applies 500 intervals by default
# for drawing the curve)
exact = u.set_line_style(ps.Style.LineStyle.DASHED).set_line_width(1)
fig.add(exact)
fig.show()
# Add linear interpolant
fig.add(interpolant)
fig.show()
# Linear interpolant without exact, smooth line
fig.erase()
fig.add(illustration)
fig.add(interpolant)
fig.show()
import logging import pysketcher as ps from pysketcher.backend.matplotlib import MatplotlibBackend logging.basicConfig(level=logging.INFO) code = ps.Axis(ps.Point(1, 1), 3, "x") code2 = ps.Axis(ps.Point(1, 1), 3, "y") model = ps.Composition(dict(x=code, y=code2)) fig = ps.Figure(0, 5, 0, 5, backend=MatplotlibBackend) fig.add(model) fig.show()
def main():
u = ps.SketchyFunc3()
t_mesh = np.linspace(0, 6, Nt + 1)
t_mesh_staggered = np.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
r = 0.005 * (t_max - t_min) # radius of circles placed at mesh Points
u_discrete = ps.Composition({
i: ps.Composition(
dict(
circle=ps.Circle(ps.Point(t, u(t)),
r).set_fill_color(ps.Style.Color.BLACK),
u_Point=ps.Text(
"$u_%d$" % i,
ps.Point(t, u(t)) +
(ps.Point(0, 5 * r) if i > 0 else ps.Point(-5 * r, 0)),
),
))
for i, t in enumerate(t_mesh)
})
# u' = v
# v = u.smooth.derivative(n=1)
v = ps.SketchyFunc4()
v_discrete = ps.Composition({
i: ps.Composition(
dict(
circle=ps.Circle(ps.Point(t, v(t)),
r).set_fill_color(ps.Style.Color.RED),
v_Point=ps.Text(
r"$v_{%d/2}$" % (2 * i + 1),
ps.Point(t, v(t)) + (ps.Point(0, 5 * r)),
),
))
for i, t in enumerate(t_mesh_staggered)
})
axes = ps.Composition(
dict(
x=ps.Axis(ps.Point(0, 0), t_mesh[-1] + 0.2 * t_axis_extent, "$t$"),
y=ps.Axis(ps.Point(0, 0),
0.8 * u_max,
"$u,v$",
rotation_angle=np.pi / 2),
))
h = 0.03 * u_max # tickmarks height
u_nodes = ps.Composition({
i: ps.Composition(
dict(
node=ps.Line(ps.Point(t, h), ps.Point(t, -h)),
name=ps.Text("$t_%d$" % i, ps.Point(t, -3.5 * h)),
))
for i, t in enumerate(t_mesh)
})
v_nodes = ps.Composition({
i: ps.Composition(
dict(
node=ps.Line(ps.Point(t, h / 1.5), ps.Point(
t, -h / 1.5)).set_line_color(ps.Style.Color.RED),
name=ps.Text(r"$t_{%d/2}$" % (2 * i + 1),
ps.Point(t, -3.5 * h)),
))
for i, t in enumerate(t_mesh_staggered)
})
illustration = ps.Composition(
dict(u=u_discrete,
v=v_discrete,
u_mesh=u_nodes,
v_mesh=v_nodes,
axes=axes))
fig = ps.Figure(t_min, t_max, u_min, u_max, backend=MatplotlibBackend)
# Staggered t mesh and u and v Points
fig.add(illustration)
fig.show()
# Exact u line (u is a Spline Shape that applies 500 intervals by default
# for drawing the curve)
u_exact = u.set_line_style(ps.Style.LineStyle.DASHED).set_line_width(1)
fig.add(u_exact)
fig.show()
# v = Curve(u.xcoor, v(u.xcoor))
t_mesh_staggered_fine = np.linspace(t_mesh_staggered[0],
t_mesh_staggered[-1], 501)
t_mesh_staggered_points = [
ps.Point(x, v(x)) for x in t_mesh_staggered_fine
]
v_exact = (ps.Curve(t_mesh_staggered_points).set_line_style(
ps.Style.LineStyle.DASHED).set_line_width(1))
fig.add(v_exact)
fig.show()
M = ps.Rectangle(ps.Point(0, H), 4 * H, 4 * H).set_line_width(4)
left_wall = ps.Rectangle(ps.Point(-L, 0), H / 10, L).set_fill_pattern(
ps.Style.FillPattern.UP_LEFT_TO_RIGHT
)
ground = ps.Wall([ps.Point(-L / 2, 0), ps.Point(L, 0)], thickness=-H / 10)
wheel1 = ps.Circle(ps.Point(H, H / 2), H / 2)
wheel2 = wheel1.translate(ps.Point(2 * H, 0))
fontsize = 24
text_m = ps.Text("$m$", ps.Point(2 * H, H + 2 * H))
text_m.style.font_size = fontsize
text_ku = ps.Text("$ku$", ps.Point(-L / 2, H + 4 * H))
text_ku.style.font_size = fontsize
text_bv = ps.Text("$bu'$", ps.Point(-L / 2, H))
text_bv.style.font_size = fontsize
x_axis = ps.Axis(ps.Point(2 * H, L), H, "$u(t)$", label_spacing=(0.04, -0.01))
x_axis_start = ps.Line(
ps.Point(2 * H, L - H / 4), ps.Point(2 * H, L + H / 4)
).set_line_width(4)
model = ps.Composition(
{
"spring": s,
"mass": M,
"left wall": left_wall,
"ground": ground,
"wheel1": wheel1,
"wheel2": wheel2,
"text_m": text_m,
"text_ku": text_ku,
"x_axis": x_axis,
dict(
circle=ps.Circle(ps.Point(t, v(t)),
r).set_fill_color(ps.Style.Color.RED),
v_Point=ps.Text(
r"$v_{%d/2}$" % (2 * i + 1),
ps.Point(t, v(t)) + (ps.Point(0, 5 * r)),
),
))
for i, t in enumerate(t_mesh_staggered)
})
axes = ps.Composition(
dict(
x=ps.Axis(
ps.Point(0, 0),
t_mesh[-1] + 0.2 * t_axis_extent,
"$t$",
label_spacing=(1 / 45.0, -1 / 30.0),
),
y=ps.Axis(ps.Point(0, 0),
0.8 * u_max,
"$u,v$",
rotation_angle=np.pi / 2),
))
h = 0.03 * u_max # tickmarks height
u_nodes = ps.Composition({
i: ps.Composition(
dict(
node=ps.Line(ps.Point(t, h), ps.Point(t, -h)),
name=ps.Text("$t_%d$" % i, ps.Point(t, -3.5 * h)),
))