O/⚪ᕤᕦ⚪ИN⚪ꖴ⚪ᙏ⚪ᗩ⚪ᴥ⚪ᕤᕦ⚪Ⓞ⚪ᴥ⚪ߦ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ߦ⚪ᴥ⚪Ⓞ⚪ᕤᕦ⚪ᴥ⚪ᗩ⚪ᙏ⚪ꖴ⚪ИN⚪ᕤᕦ⚪/⚪ИN⚪Ⓞ⚪옷⚪✤⚪人⚪ߦ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ߦ⚪人⚪✤⚪옷⚪Ⓞ⚪ИN⚪/⚪ᴥ⚪ᗱᗴ⚪✤⚪人⚪ߦ⚪ᑎ⚪ᒍᒐ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᒍᒐ⚪ᑎ⚪ߦ⚪人⚪✤⚪ᗱᗴ⚪ᴥ⚪/YP..⚪ᴥ⚪ᗱᗴ⚪✤⚪Ⓞ⚪ᙁ⚪ߦ⚪◯⚪ᗱᗴ⚪ᗯ⚪ᴥ⚪ᑎ⚪ᑐᑕ⚪◯⚪ИN⚪Ⓞ⚪ꖴ⚪✤⚪ᑐᑕ⚪ᑎ⚪ꗳ⚪◯⚪ᗱᗴ⚪ᴥ⚪ᑎ⚪✤⚪ᗩ⚪ᗯ⚪ᴥ⚪ᑎ⚪ᑐᑕ⚪◯⚪ᗝ⚪ᗱᗴ⚪ꖴ⚪ꗳ⚪ꖴ⚪ᑐᑕ⚪ᗱᗴ⚪ߦ⚪ᔓᔕ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᔓᔕ⚪ߦ⚪ᗱᗴ⚪ᑐᑕ⚪ꖴ⚪ꗳ⚪ꖴ⚪ᗱᗴ⚪ᗝ⚪◯⚪ᑐᑕ⚪ᑎ⚪ᴥ⚪ᗯ⚪ᗩ⚪✤⚪ᑎ⚪ᴥ⚪ᗱᗴ⚪◯⚪ꗳ⚪ᑎ⚪ᑐᑕ⚪✤⚪ꖴ⚪Ⓞ⚪ИN⚪◯⚪ᑐᑕ⚪ᑎ⚪ᴥ⚪ᗯ⚪ᗱᗴ⚪◯⚪ߦ⚪ᙁ⚪Ⓞ⚪✤⚪ᗱᗴ⚪ᴥ⚪..PY

import numpy as np
import plotly.graph_objects as go
from math import *
import mpmath
from ipywidgets import interact, widgets, Text, Layout
from plotly.subplots import make_subplots

# Input field for formula
formula = widgets.Text(
    value='(1-cos(((4)/2)*x))/2',
    layout=widgets.Layout(width='100%'),
    description='⚪ᗩ⚪ᙁ⚪ᑎ⚪ᙏ⚪ᴥ⚪Ⓞ⚪ꗳ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ꗳ⚪Ⓞ⚪ᴥ⚪ᙏ⚪ᑎ⚪ᙁ⚪ᗩ⚪'
)

RANGE_FROM_SLIDER = widgets.FloatSlider(
    min=-4*(4*atan(1)),
    max=4*(4*atan(1)),
    value=-2*(4*atan(1)),
    step=(4*atan(1))/4,
    layout=widgets.Layout(width='100%'),
    readout_format='.256f',
    description='⚪ᙏ⚪Ⓞ⚪ᴥ⚪ꗳ⚪◯⚪ᗱᗴ⚪ᕤᕦ⚪ИN⚪ᗩ⚪ᴥ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᴥ⚪ᗩ⚪ИN⚪ᕤᕦ⚪ᗱᗴ⚪◯⚪ꗳ⚪ᴥ⚪Ⓞ⚪ᙏ⚪'
)

RANGE_TO_SLIDER = widgets.FloatSlider(
    min=-4*(4*atan(1)),
    max=4*(4*atan(1)),
    value=2*(4*atan(1)),
    step=(4*atan(1))/4,
    layout=widgets.Layout(width='100%'),
    readout_format='.256f',
    description='⚪Ⓞ⚪✤⚪◯⚪ᗱᗴ⚪ᕤᕦ⚪ИN⚪ᗩ⚪ᴥ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᴥ⚪ᗩ⚪ИN⚪ᕤᕦ⚪ᗱᗴ⚪◯⚪✤⚪Ⓞ⚪'
)

N_slider = widgets.IntSlider(
    min=1,
    max=16,
    value=8,
    layout=widgets.Layout(width='100%'),
    readout_format='.256f',
    description='⚪ᴥ⚪ᗱᗴ⚪ᗯ⚪Ⓞ⚪ߦ⚪◯⚪ᴥ⚪ᗱᗴ⚪⚭⚪ᙏ⚪ᑎ⚪ИN⚪◯⚪✤⚪ИN⚪ꖴ⚪Ⓞ⚪ᑫᑭ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᑫᑭ⚪Ⓞ⚪ꖴ⚪ИN⚪✤⚪◯⚪ИN⚪ᑎ⚪ᙏ⚪⚭⚪ᗱᗴ⚪ᴥ⚪◯⚪ߦ⚪Ⓞ⚪ᗯ⚪ᗱᗴ⚪ᴥ⚪'
)

O_REDILS_1_W_O_W_1_SLIDER_O = widgets.FloatSlider(
    min=-2,
    max=2,
    value=1,
    step=1/256,
    layout=widgets.Layout(width='100%'),
    readout_format='.256f',
    description='⚪·⚪◯⚪ᗱᗴ⚪ᙁ⚪⚭⚪ᗩ⚪ꖴ⚪ᴥ⚪ᗩ⚪ᗯ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᗯ⚪ᗩ⚪ᴥ⚪ꖴ⚪ᗩ⚪⚭⚪ᙁ⚪ᗱᗴ⚪◯⚪·⚪'
)

O_REDILS_2_W_O_W_2_SLIDER_O=widgets.FloatSlider(
    min=-2,
    max=2,
    value=1,
    step=1/256,
    layout=widgets.Layout(width='100%'),
    readout_format='.256f',
    description='⚪꞉⚪◯⚪ᗱᗴ⚪ᙁ⚪⚭⚪ᗩ⚪ꖴ⚪ᴥ⚪ᗩ⚪ᗯ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᗯ⚪ᗩ⚪ᴥ⚪ꖴ⚪ᗩ⚪⚭⚪ᙁ⚪ᗱᗴ⚪◯⚪꞉⚪'
)

def clamp(x):
    return max(min(1, x), -1)

def compute(formula, x, variable1, variable2):
    func_dict = {fn: eval(f'lambda *args:mpmath.{fn}(*args)') for fn in dir(mpmath)}
    return float(eval(formula, {'x': x, 'O_1_W_O_W_1_O': variable1, 'O_2_W_O_W_2_O': variable2, 'clamp': clamp, **func_dict}))

def plot(formula='1.4795/O_2_W_O_W_2_O-((x)/(4*atan(1)*O_1_W_O_W_1_O/2*O_2_W_O_W_2_O))*1.4795', RANGE_FROM=0*(4*atan(1)), RANGE_TO=4*(4*atan(1)), N=8, O_1_W_O_W_1_O=1, O_2_W_O_W_2_O=1):
    num_points = 1 + 2**N
    x_vals = np.linspace(RANGE_FROM, RANGE_TO, num_points)
    
    kappa_vals = np.array([compute(formula, x_val, O_1_W_O_W_1_O, O_2_W_O_W_2_O) for x_val in x_vals])
    theta_vals = np.cumsum(kappa_vals) * (x_vals[1] - x_vals[0]) if num_points > 1 else np.array([0])
    x_coords_ = np.cumsum(np.cos(theta_vals)) * (x_vals[1] - x_vals[0]) if num_points > 1 else np.array([0])
    y_coords_ = np.cumsum(np.sin(theta_vals)) * (x_vals[1] - x_vals[0]) if num_points > 1 else np.array([0])

    if x_coords_[0] != 0 or y_coords_[0] != 0:
        x_coords = np.insert(x_coords_, 0, 0)
        y_coords = np.insert(y_coords_, 0, 0)
    else:
        x_coords = x_coords_
        y_coords = y_coords_
    
    y_vals = [compute(formula, x_val, O_1_W_O_W_1_O, O_2_W_O_W_2_O) for x_val in x_vals]

    # Determine maximum range for consistency across all charts
    min_x_range = min(map(min, [x_coords, x_vals]))
    min_y_range = min(map(min, [y_coords, y_vals]))
    max_x_range = max(map(max, [x_coords, x_vals]))
    max_y_range = max(map(max, [y_coords, y_vals]))
    
    # Create and display the first plot
    fig1 = go.Figure()
    fig1.add_trace(go.Scatter(x=x_coords, y=y_coords, mode='lines', line=dict(color='#CECECE'), name='', hovertemplate='X:%{x:.256f}' + '<br>Y:%{y:.256f}'))
    fig1.update_layout(
    autosize=True,
    margin=dict(
        l=0, # left margin
        r=0, # right margin
        b=0, # bottom margin
        t=0, # top margin
        pad=0 # padding
    ),
        height=512,
        xaxis=dict(scaleanchor='y', scaleratio=1, gridcolor='#CECECE',zeroline=True, zerolinecolor='#CECECE', tickfont=dict(color='#9C9C9C',size=16)),
        yaxis=dict(gridcolor='#CECECE',zeroline=True, zerolinecolor='#CECECE',tickfont=dict(color='#9C9C9C',size=16)),
        hoverlabel=dict(bgcolor="#FFFFFF", font_color='#9C9C9C', bordercolor="#CECECE",font_size=16), plot_bgcolor='#FFFFFF'
    )
    fig1.update_xaxes(range=[min_x_range, max_x_range])
    fig1.update_yaxes(range=[min_y_range, max_y_range])
    fig1.show()

    # Create and display the second plot
    fig2 = go.Figure()
    fig2.add_trace(go.Scatter(x=x_vals, y=y_vals, mode='lines', line=dict(color='#CECECE'), name='', hovertemplate='X:%{x:.256f}' + '<br>Y:%{y:.256f}'))
    fig2.update_layout(
    autosize=True,
    margin=dict(
        l=0, # left margin
        r=0, # right margin
        b=0, # bottom margin
        t=0, # top margin
        pad=0 # padding
    ),
        height=512,
        xaxis=dict(scaleanchor='y', scaleratio=1, gridcolor='#CECECE',zeroline=True,zerolinecolor='#CECECE',tickfont=dict(color='#9C9C9C',size=16)),
        yaxis=dict(gridcolor='#CECECE',zeroline=True, zerolinecolor='#CECECE',tickfont=dict(color='#9C9C9C',size=16)),
        hoverlabel=dict(bgcolor="#FFFFFF", font_color='#9C9C9C', bordercolor="#CECECE",font_size=16), plot_bgcolor='#FFFFFF'
    )
    fig2.update_xaxes(range=[min_x_range, max_x_range])
    fig2.update_yaxes(range=[min_y_range, max_y_range])
    fig2.show()

interact(plot,formula=formula,RANGE_FROM=RANGE_FROM_SLIDER,RANGE_TO=RANGE_TO_SLIDER,N=N_slider,O_1_W_O_W_1_O=O_REDILS_1_W_O_W_1_SLIDER_O,O_2_W_O_W_2_O=O_REDILS_2_W_O_W_2_SLIDER_O);