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mpl_embedded_in_tk_pendulum.py
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mpl_embedded_in_tk_pendulum.py
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import sys
from collections import deque
import time
import tkinter as tk
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import patches as mpl_patches
from matplotlib import lines as mpl_lines
from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg
from scipy.integrate import ode
TWOPI = 2*np.pi
PI = np.pi
# matplotlib canvas sizes
FIG_SIZE_PENDULUM = (5, 5)
X_MIN, X_MAX = -10, 10
Y_MIN, Y_MAX = -10, 10
TICK_INTERVAL = 1.5
FIG_SIZE_MONITOR = (5, 1)
update_label_interval_ms = 150
fps = 24
seconds_per_frame = 1 / fps
time_window_monitor_s = 40
update_monitor_interval_s = 0.150
class MplMap():
''' set up map consisting of two figures: fig_pendulum and fig_graphs
fig_pendulum: has one ax showing the pendulum movements
fig_graphs: has two ax showing plots of theta1 and theta2
'''
@classmethod
def settings(cls, root, fig_size_pendulum, fig_size_monitor):
# set the plot outline, including axes going through the origin
cls.root = root
cls.fig_pendulum, cls.ax_pendulum = plt.subplots(figsize=fig_size_pendulum)
cls.ax_pendulum.set_xlim(X_MIN, X_MAX)
cls.ax_pendulum.set_ylim(Y_MIN, Y_MAX)
cls.ax_pendulum.set_aspect(1)
tick_range = np.arange(
round(X_MIN + (10*abs(X_MIN) % TICK_INTERVAL*10)/10, 1),
X_MAX + 0.1, step=TICK_INTERVAL)
cls.ax_pendulum.set_xticks(tick_range)
cls.ax_pendulum.set_yticks([])
cls.ax_pendulum.tick_params(axis='x', which='major', labelsize=6)
cls.ax_pendulum.spines['left'].set_color('none')
cls.ax_pendulum.spines['right'].set_color('none')
cls.ax_pendulum.spines['bottom'].set_position('zero')
cls.ax_pendulum.spines['top'].set_color('none')
cls.fig_pendulum.tight_layout()
cls.fig_monitor, (cls.ax_monitor_1, cls.ax_monitor_2) = plt.subplots(
1, 2, figsize=fig_size_monitor)
cls.ax_monitor_1.set_ylim(-180, 180)
cls.ax_monitor_1.set_yticks([-180, -90, 0, 90, 180])
cls.ax_monitor_1.tick_params(axis='y', which='major', labelsize=6)
cls.ax_monitor_1.tick_params(axis='x', which='major', labelsize=6)
cls.ax_monitor_1.grid(True)
cls.ax_monitor_2.set_ylim(-190, 190)
cls.ax_monitor_2.set_yticks([-180, -90, 0, 90, 180])
cls.ax_monitor_2.tick_params(axis='y', which='major', labelsize=6)
cls.ax_monitor_2.tick_params(axis='x', which='major', labelsize=6)
cls.ax_monitor_2.grid(True)
cls.fig_monitor.tight_layout()
cls.canvas_pendulum = FigureCanvasTkAgg(cls.fig_pendulum, master=cls.root)
cls.canvas_monitor = FigureCanvasTkAgg(cls.fig_monitor, master=cls.root)
@classmethod
def get_canvas_pendulum(cls):
return cls.canvas_pendulum
@classmethod
def get_canvas_monitor(cls):
return cls.canvas_monitor
class DoublePendulum(MplMap):
''' class defining methods for Pendulum for positions and motions of a double
pendulum
'''
def __init__(self, _a1, _a2):
# Physical constants and initial settings
self.g = 9.8
self.damping1 = 0.0 # damping factor bob1
self.damping2 = 0.0 # dampling factor bob2
self.length_r1 = 5.0
self.length_r2 = 2.5
self.mass_bob1 = 5.0
self.mass_bob2 = 2.5
self.color_bob1 = 'green'
self.color_bob2 = 'red'
# initial state
if _a1 and _a2:
self.theta1_initial = np.radians(_a1)
self.theta2_initial = np.radians(_a2)
else:
self.theta1_initial = + 120 / 180 * np.pi
self.theta2_initial = + 180 / 180 * np.pi
self.theta1_dot_initial = 0
self.theta2_dot_initial = 0
self.theta1 = self.theta1_initial
self.theta2 = self.theta2_initial
self._time = 0
_x1, _y1 = self.calc_xy(self.length_r1, self.theta1_initial)
self.bob1 = mpl_patches.Circle((_x1, _y1), 0.2 + self.m1 * 0.02,
fc=self.color_bob1, alpha=1, zorder=2)
self.bob1.set_picker(0)
self.ax_pendulum.add_patch(self.bob1)
self.stick1 = mpl_lines.Line2D([0, _x1], [0, _y1], zorder=2)
self.ax_pendulum.add_line(self.stick1)
cv_bob1 = self.bob1.figure.canvas
cv_bob1.mpl_connect('pick_event', self.on_pick)
cv_bob1.mpl_connect('motion_notify_event', self.on_motion)
cv_bob1.mpl_connect('button_release_event', self.on_release)
_x2, _y2 = self.calc_xy(self.length_r2, self.theta2_initial)
_x2 += _x1
_y2 += _y1
self.bob2 = mpl_patches.Circle((_x2, _y2), 0.2 + self.m2 * 0.02,
fc=self.color_bob2, alpha=1, zorder=2)
self.bob2.set_picker(0)
self.ax_pendulum.add_patch(self.bob2)
self.stick2 = mpl_lines.Line2D([_x1, _x2], [_y1, _y2], zorder=2)
self.ax_pendulum.add_line(self.stick2)
cv_bob2 = self.bob2.figure.canvas
cv_bob2.mpl_connect('pick_event', self.on_pick)
cv_bob2.mpl_connect('motion_notify_event', self.on_motion)
cv_bob2.mpl_connect('button_release_event', self.on_release)
self.x_traces = []
self.y_traces = []
self.trace_line, = self.ax_pendulum.plot(
[0], [0], color='black', linewidth=0.2, zorder=1)
self.current_object = None
self.current_dragging = False
self.break_the_loop = False
self.monitor = Monitor()
self.blip()
def switch_colors_of_bob(self):
print('switch color')
self.color_bob1, self.color_bob2 = self.color_bob2, self.color_bob1
self.bob1.set_color(self.color_bob1)
self.bob2.set_color(self.color_bob2)
self.blip()
def toggle_trace_visible(self):
print(self.trace_line.get_visible())
if self.trace_line.get_visible():
self.trace_line.set_visible(False)
else:
self.trace_line.set_visible(True)
self.blip()
def clear_trace(self):
self.x_traces = []
self.y_traces = []
self.trace_line.set_data([0], [0])
self.blip()
@property
def gravity(self):
return self.g
@gravity.setter
def gravity(self, value):
self.g = value
@property
def m1(self):
return self.mass_bob1
@m1.setter
def m1(self, value):
self.mass_bob1 = value
self.bob1.set_radius(0.2 + self.mass_bob1 * 0.02)
self.blip()
@property
def m2(self):
return self.mass_bob2
@m2.setter
def m2(self, value):
self.mass_bob2 = value
self.bob2.set_radius(0.2 + self.mass_bob2 * 0.02)
self.blip()
@property
def l1(self):
return self.length_r1
@l1.setter
def l1(self, value):
self.length_r1 = value
self.calc_positions()
self.blip()
@property
def l2(self):
return self.length_r2
@l2.setter
def l2(self, value):
self.length_r2 = value
self.calc_positions()
self.blip()
@property
def k1(self):
return self.damping1
@k1.setter
def k1(self, value):
self.damping1 = value
@property
def k2(self):
return self.damping2
@k2.setter
def k2(self, value):
self.damping2 = value
@property
def angle1_initial(self):
angle = self.theta1_initial
return np.degrees(-PI + (angle - PI) % TWOPI)
@property
def angle2_initial(self):
angle = self.theta2_initial
return np.degrees(-PI + (angle - PI) % TWOPI)
@property
def angle1(self):
angle = self.theta1
return np.degrees(-PI + (angle - PI) % TWOPI)
@property
def angle2(self):
angle = self.theta2
return np.degrees(-PI + (angle - PI) % TWOPI)
@property
def time(self):
return self._time
def on_pick(self, event):
if event.artist != self.bob1 and \
event.artist != self.bob2:
return
self.current_dragging = True
self.current_object = event.artist
def on_motion(self, event):
if not self.current_dragging:
return
if self.current_object == self.bob1:
self.theta1 = self.calc_theta(event.xdata, event.ydata, self.theta1)
self.theta1_initial = self.theta1
elif self.current_object == self.bob2:
_x1, _y1 = self.bob1.center
self.theta2 = self.calc_theta(
event.xdata - _x1, event.ydata - _y1, self.theta2)
self.theta2_initial = self.theta2
else:
return
self.calc_positions()
self.blip()
def on_release(self, _):
self.current_object = None
self.current_dragging = False
def start_swing(self):
self.break_the_loop = False
self.theta1_initial = self.theta1
self.theta2_initial = self.theta2
self.y_traces = []
self.x_traces = []
self.plot_double_pendulum()
def stop_swing(self):
self.break_the_loop = True
def calc_positions(self):
_x1, _y1 = self.calc_xy(self.l1, self.theta1)
self.bob1.center = (_x1, _y1)
self.stick1.set_data([0, _x1], [0, _y1])
_x2, _y2 = self.calc_xy(self.l2, self.theta2)
_y2 += _y1
_x2 += _x1
self.bob2.center = (_x2, _y2)
self.stick2.set_data([_x1, _x2], [_y1, _y2])
def add_to_trace(self):
_x2, _y2 = self.bob2.center
self.x_traces.append(_x2)
self.y_traces.append(_y2)
self.trace_line.set_data(self.x_traces[:], self.y_traces[:])
@staticmethod
def calc_theta(x, y, theta):
try:
return np.arctan2(x, -y)
except TypeError:
return theta
@staticmethod
def calc_xy(length, theta):
x = length * np.sin(theta)
y = - length * np.cos(theta)
return x, y
def blip(self):
self.fig_pendulum.canvas.draw()
self.fig_pendulum.canvas.flush_events()
def get_derivatives_double_pendulum(self, t, state):
''' definition of ordinary differential equation for a
double pendulum. See for derivations at
https://ir.canterbury.ac.nz/bitstream/handle/10092/12659/chen_2008_report.pdf
'''
t1, w1, t2, w2 = state
dt = t1 - t2
_sin_dt = np.sin(dt)
_den1 = (self.m1 + self.m2 * _sin_dt * _sin_dt)
_num1 = self.m2 * self.l1 * w1 * w1 * np.sin(2*dt)
_num2 = 2 * self.m2 * self.l2 * w2 * w2 * _sin_dt
_num3 = 2 * self.g * self.m2 * np.cos(t2) * _sin_dt + \
2 * self.g * self.m1 * np.sin(t1)
_num4 = 2 * (self.k1 * w1 - self.k2 * w2 * np.cos(dt))
w1_dot = (_num1 + _num2 + _num3 + _num4)/ (-2 * self.l1 * _den1)
_num1 = self.m2 * self.l2 * w2 * w2 * np.sin(2*dt)
_num2 = 2 * (self.m1 + self.m2) * self.l1 * w1 * w1 * _sin_dt
_num3 = 2 * self.g * (self.m1 + self.m2) * np.cos(t1) * _sin_dt
_num4 = 2 * (self.k1 * w1 * np.cos(dt) - \
self.k2 * w2 * (self.m1 + self.m2)/ self.m2)
w2_dot = (_num1 + _num2 + _num3 + _num4)/ (2 * self.l2 *_den1)
state_differentiated = np.zeros(4)
state_differentiated[0] = w1
state_differentiated[1] = w1_dot
state_differentiated[2] = w2
state_differentiated[3] = w2_dot
return state_differentiated
def plot_double_pendulum(self):
''' methods to plot pendulum in matplotlib
'''
# note a frame per second (fps) > 24 the actual time
# may not be able to keep up with model time
def current_time():
return time.time()
def check_drift(_time, running_time):
# check every 5 seconds
if _time % 5 < seconds_per_frame:
print(f'time (ms): {1000*_time:,.0f}, '
f'drift: {1000*(running_time - _time):,.0f}')
self._time = 0
dp_integrator = ode(self.get_derivatives_double_pendulum).set_integrator('vode')
state = np.array([self.theta1, self.theta1_dot_initial,
self.theta2, self.theta2_dot_initial])
dp_integrator.set_initial_value(state, self._time)
self.add_to_trace()
actual_start_time = current_time()
while dp_integrator.successful() and not self.break_the_loop:
self.theta1, _, self.theta2, _ = state
self.calc_positions()
self.add_to_trace()
if self._time % update_monitor_interval_s < seconds_per_frame:
self.monitor.plot_thetas(self._time, self.theta1, self.theta2)
running_time = current_time() - actual_start_time
check_drift(self._time, running_time)
while running_time < self._time:
running_time = current_time() - actual_start_time
else:
self.blip()
state = dp_integrator.integrate(dp_integrator.t + seconds_per_frame)
self._time += seconds_per_frame
class Monitor(MplMap):
''' Class to monitor theta1 and theta2
'''
def __init__(self):
self.time_values_reversed = deque([])
self.time_reversed = []
self.angle1_values = []
self.angle2_values = []
self.theta1_monitor, = self.ax_monitor_1.plot(
[0], [0], color='black', linewidth=0.5, zorder=2)
self.theta2_monitor, = self.ax_monitor_2.plot(
[0], [0], color='black', linewidth=0.5, zorder=2)
self.ax_monitor_1.set_xlim(time_window_monitor_s, 0)
self.ax_monitor_2.set_xlim(time_window_monitor_s, 0)
def plot_thetas(self, _time, theta1, theta2):
''' method to plot theta's in time_window_graphs, time is
past time, so t=0 is now and t=20 is 20 seconds ago
'''
# reset when time is zero
if _time < seconds_per_frame:
self.angle1_values = []
self.angle2_values = []
self.time_values_reversed = deque([])
self.time_reversed = []
# build the time_reversed list (in reversed order to represent
# time passed) and trim the angle_values lists so they keep the
# a finite length
self.angle1_values.append(np.degrees(-PI + (theta1 - PI) % TWOPI))
self.angle2_values.append(np.degrees(-PI + (theta2 - PI) % TWOPI))
if _time < time_window_monitor_s + update_monitor_interval_s:
self.time_values_reversed.appendleft(_time)
self.time_reversed = list(self.time_values_reversed)
else:
self.angle1_values.pop(0)
self.angle2_values.pop(0)
self.theta1_monitor.set_data(self.time_reversed, self.angle1_values)
self.theta2_monitor.set_data(self.time_reversed, self.angle2_values)
self.fig_monitor.canvas.draw()
self.fig_monitor.canvas.flush_events()
class TkHandler():
''' Methods to handle the tkinter GUI and links with matplotlib canvases and pendulum
class. Methods:
__init__:
parameters:
:doublependulum: class handling the doublependulum status and positions
create_slider_status_frame:
Creates frame of the sliders and status values of initial theta1,
initial theta2, time, theta1, theta2
The slider values are connected to the pendulum class by the _set_value
function that sets values for: gravity, mass1, mass2, length1, length2,
damping1, damping2
update_labels:
Updates the status values. Update rate is set by: update_label_interval_ms
create_button_frame:
Creates frame with control buttons and links with button functions:
_quit: quits the program
The following button functions connect to the pendulum class to change
status:
_set_colors: swaps colors of the bobs
_toggle_trace_visible: toggles trace on or off
_clear_trace: clears the trace
_start: starts the pendulum swing
_stop: stops the pendulum swing
create_grid:
Creates the GUI grid
'''
def __init__(self, root, doublependulum):
self.root = root
self.pendulum = doublependulum
self.root.wm_title("Double Pendulum")
self.create_slider_status_frame()
self.create_button_frame()
self.create_grid()
self.update_labels()
tk.mainloop()
def create_slider_status_frame(self):
self.sliders_status_frame = tk.Frame(self.root)
sliders_frame = tk.Frame(self.sliders_status_frame)
sliders = {'gravity': {'label':'Gravity ', 'settings': [0, 30, 1]}, # 'settings': [min, max, resolution] # pylint: disable=C0301
'm1': {'label':'Mass bob 1', 'settings': [1, 10, 0.1]},
'm2': {'label':'Mass bob 2', 'settings': [1, 10, 0.1]},
'l1': {'label':'Length r1 ', 'settings': [0.1, 10, 0.1]},
'l2': {'label':'Length r2 ', 'settings': [0.1, 10, 0.1]},
'k1': {'label':'Damping 1 ', 'settings': [0, 1, 0.1]},
'k2': {'label':'Damping 2 ', 'settings': [0, 1, 0.1]},
}
def create_slider(slider_key, slider_params):
_min, _max, _resolution = slider_params['settings']
slider_frame = tk.Frame(sliders_frame)
label_slider = tk.Label(slider_frame, font=("TkFixedFont"),
text=f'\n{slider_params["label"]:<11s}')
slider = tk.Scale(slider_frame, from_=_min, to=_max, resolution=_resolution,
orient=tk.HORIZONTAL,
sliderlength=15,
length=150,
command=lambda value: self._set_value(value, slider_key))
slider.set(getattr(self.pendulum, slider_key))
label_slider.pack(side=tk.LEFT)
slider.pack(side=tk.LEFT)
slider_frame.pack()
for key, slider_params in sliders.items():
create_slider(key, slider_params)
status_frame = tk.Frame(self.sliders_status_frame)
self.label_status1 = tk.Label(status_frame, font=("TkFixedFont"),)
self.label_status1.pack(anchor=tk.W)
self.label_status2 = tk.Label(status_frame, font=("TkFixedFont"),)
self.label_status2.pack(anchor=tk.W)
self.label_status3 = tk.Label(status_frame, font=("TkFixedFont"),)
self.label_status3.pack(anchor=tk.W)
self.label_status4 = tk.Label(status_frame, font=("TkFixedFont"),)
self.label_status4.pack(anchor=tk.W)
self.label_status5 = tk.Label(status_frame, font=("TkFixedFont"),)
self.label_status5.pack(anchor=tk.W)
sliders_frame.pack(anchor=tk.NW)
status_frame.pack(anchor=tk.W, fill=tk.X)
def update_labels(self):
self.label_status1.config(
text=f'\ntheta1 initial: {self.pendulum.angle1_initial:+3.2f}')
self.label_status2.config(
text=f'theta2 initial: {self.pendulum.angle2_initial:+3.2f}')
self.label_status3.config(
text=f'time: {self.pendulum.time:+3.1f}')
self.label_status4.config(
text=f'theta1: {self.pendulum.angle1:+3.0f}')
self.label_status5.config(
text=f'theta2: {self.pendulum.angle2:+3.0f}')
self.root.after(update_label_interval_ms, self.update_labels)
def create_button_frame(self):
self.buttons_frame = tk.Frame(self.root)
tk.Button(
self.buttons_frame, text='Quit', command=self._quit).pack(side=tk.LEFT)
tk.Button(
self.buttons_frame, text='Switch colors',
command=lambda *args: self._set_colors(*args)).pack(side=tk.LEFT)
tk.Button(
self.buttons_frame, text='Trace on/ off',
command=lambda *args: self._toggle_trace_visible(*args)).pack(side=tk.LEFT)
tk.Button(
self.buttons_frame, text='Clear trace',
command=lambda *args: self._clear_trace(*args)).pack(side=tk.LEFT)
tk.Button(
self.buttons_frame, text='Start', command=self._start).pack(side=tk.LEFT)
tk.Button(
self.buttons_frame, text='Stop', command=self._stop).pack(side=tk.LEFT)
def create_grid(self):
tk.Grid.rowconfigure(self.root, 0, weight=1)
tk.Grid.columnconfigure(self.root, 0, weight=1)
self.sliders_status_frame.grid(
row=0, column=0, sticky=tk.NW)
self.pendulum.get_canvas_pendulum().get_tk_widget().grid(
row=0, column=1, rowspan=1, columnspan=1, sticky=tk.W+tk.E+tk.N+tk.S,
padx=2, pady=0)
self.pendulum.get_canvas_monitor().get_tk_widget().grid(
row=1, column=0, rowspan=1, columnspan=2, sticky=tk.W+tk.E+tk.N+tk.S,
padx=2, pady=2)
self.buttons_frame.grid(
row=2, column=0, columnspan=2, sticky=tk.W)
def _quit(self):
self.pendulum.stop_swing()
self.root.after(100, self.root.quit)
self.root.after(100, self.root.destroy)
def _set_colors(self):
self.pendulum.switch_colors_of_bob()
def _toggle_trace_visible(self):
self.pendulum.toggle_trace_visible()
def _clear_trace(self):
self.pendulum.clear_trace()
def _set_value(self, value, name):
value = float(value)
print(name, value)
if name == 'gravity':
self.pendulum.gravity = float(value)
elif name == 'm1':
self.pendulum.m1 = float(value)
elif name == 'm2':
self.pendulum.m2 = float(value)
elif name == 'l1':
self.pendulum.l1 = float(value)
elif name == 'l2':
self.pendulum.l2 = float(value)
elif name == 'k1':
self.pendulum.k1 = float(value)
elif name == 'k2':
self.pendulum.k2 = float(value)
else:
assert False, f'wrong key value given: {name}'
def _start(self):
self.pendulum.start_swing()
def _stop(self):
self.pendulum.stop_swing()
def main(_a1, _a2):
root = tk.Tk()
MplMap.settings(root, FIG_SIZE_PENDULUM, FIG_SIZE_MONITOR)
TkHandler(root, DoublePendulum(_a1, _a2))
if __name__ == "__main__":
main_arguments = sys.argv
angle1 = None
angle2 = None
if len(main_arguments) == 3:
try:
angle1 = float(main_arguments[1])
angle2 = float(main_arguments[2])
except ValueError:
print('invalid arguments, refer to defaults ..')
main(angle1, angle2)