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<EFBFBD><EFBFBD>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='<00>&<26><15>&A<16>&N<14>&O<16>&%<1D>&<26>$<24>&<26><><EFBFBD>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26><><EFBFBD>&<26>$<24>&%<1D>&O<16>&N<14>&A<16>&<26><15>&'
)

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='<00>&O<16>&<26>$<24>&%<1D>&<26><><EFBFBD>&<26>%<25>&<26><15><15>&df<15>&N<00>&<26><15>&%<1D>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&%<1D>&<26><15>&N<00>&df<15>&<26><15><15>&<26>%<25>&<26><><EFBFBD>&%<1D>&<26>$<24>&O<16>&'
)

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='<00>&<26>$<24>&$'<27>&<26>%<25>&<26><15><15>&df<15>&N<00>&<26><15>&%<1D>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&%<1D>&<26><15>&N<00>&df<15>&<26><15><15>&<26>%<25>&$'<27>&<26>$<24>&'
)

N_slider = widgets.IntSlider(
    min=1,
    max=16,
    value=8,
    layout=widgets.Layout(width='100%'),
    readout_format='.256f',
    description='<00>&%<1D>&<26><15><15>&<26><15>&<26>$<24>&<26><07>&<26>%<25>&%<1D>&<26><15><15>&<26>&<26>&O<16>&N<14>&N<00>&<26>%<25>&$'<27>&N<00>&<26><><EFBFBD>&<26>$<24>&km<14>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&km<14>&<26>$<24>&<26><><EFBFBD>&N<00>&$'<27>&<26>%<25>&N<00>&N<14>&O<16>&<26>&<26>&<26><15><15>&%<1D>&<26>%<25>&<26><07>&<26>$<24>&<26><15>&<26><15><15>&%<1D>&'
)

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='<00>&<26><00>&<26>%<25>&<26><15><15>&A<16>&<26>&<26>&<26><15>&<26><><EFBFBD>&%<1D>&<26><15>&<26><15>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26><15>&<26><15>&%<1D>&<26><><EFBFBD>&<26><15>&<26>&<26>&A<16>&<26><15><15>&<26>%<25>&<26><00>&'
)

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='<00>&<26><><EFBFBD>&<26>%<25>&<26><15><15>&A<16>&<26>&<26>&<26><15>&<26><><EFBFBD>&%<1D>&<26><15>&<26><15>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26>%<25>&<26><15>&<26><15>&%<1D>&<26><><EFBFBD>&<26><15>&<26>&<26>&A<16>&<26><15><15>&<26>%<25>&<26><><EFBFBD>&'
)

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);