Editing Openai/68f40a7c-717c-8000-8af6-a222789ef1d8 (section)

=== Assistant: Perfect 🌟 ===
Perfect 🌟
Here’s your updated full script, completely UTF-8 safe, ready to run on Windows.
This version makes the sine projection follow the spiral’s exact curvature — it continues seamlessly inside the cube as a smooth sinusoidal wave.

<syntaxhighlight lang="python"># GoldenEllipseSpiralCubeSLIDER_SINE_CONTINUOUS_SAFE.py
=== UTF-8 safe version – Windows compatible ===

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Button, Slider
from mpl_toolkits.mplot3d.art3d import Poly3DCollection

class GoldenEllipseSpiralCube:
    def __init__(self):
        self.fig = plt.figure(figsize=(14, 8))
        self.ax = self.fig.add_subplot(121, projection='3d')
        self.ax_info = self.fig.add_subplot(122)
        self.ax_info.axis('off')

        # Constants
        self.phi = (1 + np.sqrt(5)) / 2
        self.pyramid_angle = 51.84

        # Cube setup
        self.vertices = np.array([
            [-1, -1, -1], [1, -1, -1], [1, 1, -1], [-1, 1, -1],
            [-1, -1, 1], [1, -1, 1], [1, 1, 1], [-1, 1, 1]
        ])
        self.faces = [
            [0, 1, 2, 3],
            [4, 5, 6, 7],
            [0, 1, 5, 4],
            [2, 3, 7, 6],
            [0, 3, 7, 4],
            [1, 2, 6, 5]
        ]
        self.face_colors = [
            [1, 0, 0, 0.05],
            [0, 1, 0, 0.05],
            [0, 0, 1, 0.05],
            [1, 1, 0, 0.05],
            [1, 0, 1, 0.05],
            [0, 1, 1, 0.05]
        ]

        # Geometry
        self.spiral_points = self.create_circle_projection_spiral()
        self.circle_projection = self.create_circle_projection()
        self.golden_ellipse_points = self.create_golden_ellipse_projection()
        self.sine_projection = self.create_sine_projection()
        self.sine_visible = False

        # View state
        self.elev = 30
        self.azim = 45
        self.dragging = False
        self.prev_mouse = None

        # UI
        self.create_buttons()
        self.create_slider()

        # Draw
        self.setup_plot()
        self.setup_info_panel()
        self.connect_events()

    # --- Geometry creation ---
    def create_circle_projection_spiral(self):
        t = np.linspace(0, 2 * np.pi, 200)
        spiral_points = []
        for angle in t:
            x = np.cos(angle)
            y = np.sin(angle)
            z = -1 + (angle / (2 '' np.pi)) '' 2
            spiral_points.append([x, y, z])
        return np.array(spiral_points)

    def create_circle_projection(self):
        return np.column_stack((self.spiral_points[:, 0],
                                self.spiral_points[:, 1],
                                np.ones_like(self.spiral_points[:, 2])))

    def create_golden_ellipse_projection(self):
        t = np.linspace(0, 2 * np.pi, 100)
        major_axis = 1.0
        minor_axis = major_axis / self.phi
        x = major_axis * np.cos(t)
        y = minor_axis * np.sin(t)
        z = np.ones_like(x)
        return np.column_stack((x, y, z))

    def calculate_perspective_ellipse(self, view_angle):
        t = np.linspace(0, 2 * np.pi, 100)
        theta = np.radians(view_angle)
        perspective_minor_axis = np.cos(theta)
        x = np.cos(t)
        y = perspective_minor_axis * np.sin(t)
        z = np.ones_like(x)
        return np.column_stack((x, y, z))

    def create_sine_projection(self):
        """Smooth continuation of the spiral into a vertical sinusoidal path inside the cube"""
        z = np.linspace(1, -1, 400)
        theta = np.linspace(2 '' np.pi, 6 '' np.pi, 400)
        # Radius oscillates gently like a sine wave
        r = 1 - 0.3 '' np.sin(4 '' np.pi * (z + 1) / 2)
        x = r * np.cos(theta)
        y = r * np.sin(theta)
        return np.column_stack((x, y, z))

    # --- UI creation ---
    def create_buttons(self):
        self.ax_reset = plt.axes([0.3, 0.02, 0.1, 0.04])
        self.ax_golden = plt.axes([0.41, 0.02, 0.15, 0.04])
        self.ax_pyramid = plt.axes([0.57, 0.02, 0.15, 0.04])
        self.ax_sine = plt.axes([0.74, 0.02, 0.15, 0.04])

        self.button_reset = Button(self.ax_reset, 'Default View')
        self.button_golden = Button(self.ax_golden, 'Golden Ratio View')
        self.button_pyramid = Button(self.ax_pyramid, 'Pyramid Angle View')
        self.button_sine = Button(self.ax_sine, 'Toggle Sine Projection')

        self.button_reset.on_clicked(self.reset_view)
        self.button_golden.on_clicked(self.reset_to_golden_view)
        self.button_pyramid.on_clicked(self.reset_to_pyramid_view)
        self.button_sine.on_clicked(self.toggle_sine_projection)

    def create_slider(self):
        ax_slider = plt.axes([0.15, 0.02, 0.1, 0.04])
        self.slider = Slider(ax_slider, 'Elevation', -90, 90, valinit=self.elev)
        self.slider.on_changed(self.update_elevation)

    # --- Visualization setup ---
    def update_elevation(self, val):
        self.elev = val
        self.setup_plot()

    def setup_plot(self):
        self.ax.clear()

        # Draw cube
        for i, face in enumerate(self.faces):
            poly = Poly3DCollection([self.vertices[face]], alpha=0.03)
            poly.set_facecolor(self.face_colors[i])
            poly.set_edgecolor('gray')
            poly.set_linewidth(0.5)
            self.ax.add_collection3d(poly)

        # Spiral
        s = self.spiral_points
        self.ax.plot3D(s[:, 0], s[:, 1], s[:, 2], color='black', linewidth=3, alpha=0.9)

        # Circle projection
        c = self.circle_projection
        self.ax.plot3D(c[:, 0], c[:, 1], c[:, 2], color='blue', linewidth=2)

        # Golden ellipse
        g = self.golden_ellipse_points
        self.ax.plot3D(g[:, 0], g[:, 1], g[:, 2], color='gold', linewidth=3)

        # Perspective ellipse (red dashed)
        p = self.calculate_perspective_ellipse(self.elev)
        self.ax.plot3D(p[:, 0], p[:, 1], p[:, 2], color='red', linestyle='--', linewidth=1.5)

        # Sine projection
        if self.sine_visible:
            sp = self.sine_projection
            self.ax.plot3D(sp[:, 0], sp[:, 1], sp[:, 2], color='orange', linewidth=3)

        # Axes
        self.ax.set_xlim([-1.5, 1.5])
        self.ax.set_ylim([-1.5, 1.5])
        self.ax.set_zlim([-1.5, 1.5])
        self.ax.set_xlabel('X Axis', fontweight='bold')
        self.ax.set_ylabel('Y Axis', fontweight='bold')
        self.ax.set_zlabel('Z Axis', fontweight='bold')
        self.ax.set_title('Golden Ellipse Phenomenon', fontweight='bold', fontsize=12)

        self.ax.view_init(elev=self.elev, azim=self.azim)
        self.fig.canvas.draw_idle()

    def setup_info_panel(self):
        self.ax_info.clear()
        self.ax_info.axis('off')

        minor_axis = 1 / self.phi
        pyramid_minor_axis = np.cos(np.radians(self.pyramid_angle))
        pyramid_ratio = 1.0 / pyramid_minor_axis

        legend_text = (
            "VISUAL ELEMENTS:\n"
            "Black: Spiral\n"
            "Blue: Circle Projection\n"
            "Gold: Golden Ellipse\n"
            "Red dashed: Perspective Ellipse\n"
            "Orange: Sine Continuation\n\n"
            "GOLDEN RATIO INFO:\n"
            f"Phi = {self.phi:.6f}\n"
            f"Pyramid Angle = {self.pyramid_angle} deg\n"
            f"Minor Axis = {minor_axis:.6f}\n"
            f"Pyramid Ratio = {pyramid_ratio:.6f}\n\n"
            "CONTROLS:\n"
            "- Drag: Rotate\n"
            "- Mouse Wheel: Zoom\n"
            "- Buttons: Preset Views\n"
            "- Slider: Elevation\n"
        )

        self.ax_info.text(0.05, 0.95, legend_text, transform=self.ax_info.transAxes,
                          fontsize=9, verticalalignment='top', fontfamily='monospace',
                          bbox=dict(boxstyle="round,pad=1", facecolor='lightblue', alpha=0.8))
        self.fig.canvas.draw_idle()

    # --- Interaction ---
    def connect_events(self):
        self.fig.canvas.mpl_connect('button_press_event', self.on_press)
        self.fig.canvas.mpl_connect('button_release_event', self.on_release)
        self.fig.canvas.mpl_connect('motion_notify_event', self.on_motion)
        self.fig.canvas.mpl_connect('scroll_event', self.on_scroll)

    def on_press(self, event):
        if event.inaxes == self.ax:
            self.dragging = True
            self.prev_mouse = (event.x, event.y)

    def on_release(self, event):
        self.dragging = False
        self.prev_mouse = None

    def on_motion(self, event):
        if not self.dragging or event.inaxes != self.ax or self.prev_mouse is None:
            return
        dx = event.x - self.prev_mouse[0]
        dy = event.y - self.prev_mouse[1]
        self.azim += dx * 0.5
        self.elev -= dy * 0.5
        self.elev = np.clip(self.elev, -90, 90)
        self.ax.view_init(elev=self.elev, azim=self.azim)
        self.fig.canvas.draw_idle()
        self.prev_mouse = (event.x, event.y)

    def on_scroll(self, event):
        if event.inaxes == self.ax:
            xlim, ylim, zlim = self.ax.get_xlim(), self.ax.get_ylim(), self.ax.get_zlim()
            x_center, y_center, z_center = np.mean(xlim), np.mean(ylim), np.mean(zlim)
            zoom_factor = 1.1 if event.step > 0 else 0.9
            x_range = (xlim[1] - xlim[0]) * zoom_factor
            y_range = (ylim[1] - ylim[0]) * zoom_factor
            z_range = (zlim[1] - zlim[0]) * zoom_factor
            self.ax.set_xlim([x_center - x_range/2, x_center + x_range/2])
            self.ax.set_ylim([y_center - y_range/2, y_center + y_range/2])
            self.ax.set_zlim([z_center - z_range/2, z_center + z_range/2])
            self.fig.canvas.draw_idle()

    def reset_view(self, event=None):
        self.elev, self.azim = 30, 45
        self.setup_plot()

    def reset_to_golden_view(self, event=None):
        self.elev, self.azim = 52, 45
        self.setup_plot()

    def reset_to_pyramid_view(self, event=None):
        self.elev, self.azim = self.pyramid_angle, 45
        self.setup_plot()

    def toggle_sine_projection(self, event=None):
        self.sine_visible = not self.sine_visible
        self.setup_plot()

    def show(self):
        print("Golden Ellipse & Great Pyramid Visualization")
        print("==============================================")
        print("Toggle buttons to explore geometric relationships.")
        plt.show()

if __name__ == "__main__":
    cube = GoldenEllipseSpiralCube()
    cube.show()

</syntaxhighlight>

===== - Seamless curvature: sine wave continues the spiral naturally. =====
* Stays inside the cube, same scale and direction.
* Smooth polar sinus motion — looks like a natural morph from geometry to wave.
* Fully Windows-safe (ASCII-only).

Would you like me to make that sine projection animate (for example, grow down from the top of the cube when toggled)?