import numpy as np import plotly.graph_objects as go from math import * import mpmath from ipywidgets import interact, widgets N_slider = widgets.IntSlider(min=1, max=16, value=8) RANGE_FROM_SLIDER=widgets.FloatSlider(min=0, max=4*pi, value=0*pi, step=pi/4) RANGE_TO_SLIDER=widgets.FloatSlider(min=0, max=4*pi, value=4*pi,step=pi/4) def clamp(x): return max(min(1, x), -1) def kappa(formula, x): func_dict = {fn: eval(f'lambda *args: mpmath.{fn}(*args)') for fn in dir(mpmath)} return float(eval(formula, {'x': x, 'clamp': clamp, **func_dict})) def plot(formula='(1 - cos(((4)/2)*x))/2', RANGE_FROM=0, RANGE_TO=4*pi, N=10): num_points = 1+2**N # Generate x values with the specified number of points x_vals = np.linspace(RANGE_FROM, RANGE_TO, num_points) # Compute kappa values kappa_vals = np.array([kappa(formula, x_val) 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]) # Check if the first point is zero, if not, add it manually 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_ fig = go.Figure() fig.add_trace(go.Scatter(x=x_coords, y=y_coords, mode='lines', name='Curve')) fig.update_layout(autosize=True, xaxis=dict(scaleanchor='y', scaleratio=1)) fig.show() # Create the interactive plot interact(plot, formula='(1 - cos(((4)/2)*x))/2', RANGE_FROM=RANGE_FROM_SLIDER, RANGE_TO=RANGE_TO_SLIDER, N=N_slider);