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

===== 🧩 GoldenEllipseSpiralCubeSLIDER_SINE_MORPH_SAFE_XYZ_v2.py =====

<syntaxhighlight lang="python"># -''- coding: utf-8 -''-
"""
GoldenEllipseSpiralCubeSLIDER_SINE_MORPH_SAFE_XYZ_v2.py
Fully UTF-8 safe, includes live XYZ coordinate display (4 decimal precision)
and smooth sine morph inside the cube.
"""

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

class GoldenEllipseSpiralCube:
    def __init__(self):
        # --- Figure layout ---
        self.fig = plt.figure(figsize=(16, 10))
        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  # Golden ratio
        self.pyramid_angle = 51.84       # Great Pyramid slope angle (degrees)

        # --- Cube geometry ---
        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]
        ]

        # --- Colors ---
        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.sine_points = self.create_sine_projection()
        self.morph_t = 0.0  # Morph progress [0-1]

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

        # --- Build ---
        self.create_buttons()
        self.setup_plot()
        self.setup_info_panel()
        self.create_xyz_display()
        self.connect_events()

    # ===============================================================
    #   GEOMETRY CREATION
    # ===============================================================

    def create_circle_projection_spiral(self):
        """3D spiral inside cube (perfect circle projection)"""
        t = np.linspace(0, 2 * np.pi, 200)
        x = np.cos(t)
        y = np.sin(t)
        z = -1 + (t / (2 '' np.pi)) '' 2
        return np.column_stack((x, y, z))

    def create_sine_projection(self):
        """Sine wave inside cube aligned with the spiral path"""
        t = np.linspace(0, 2 * np.pi, 200)
        x = np.cos(t)
        y = np.sin(t) '' np.sin(3 '' t)  # morphable sine variation
        z = -1 + (t / (2 '' np.pi)) '' 2
        return np.column_stack((x, y, z))

    def interpolate_points(self):
        """Morph between spiral and sine"""
        return (1 - self.morph_t) '' self.spiral_points + self.morph_t '' self.sine_points

    # ===============================================================
    #   DISPLAY SETUP
    # ===============================================================

    def create_buttons(self):
        """Bottom control buttons"""
        self.ax_reset = plt.axes([0.25, 0.02, 0.12, 0.04])
        self.ax_morph = plt.axes([0.39, 0.02, 0.12, 0.04])
        self.ax_pyramid = plt.axes([0.53, 0.02, 0.15, 0.04])
        self.ax_xyz = plt.axes([0.70, 0.02, 0.15, 0.04])

        self.button_reset = Button(self.ax_reset, 'Default View')
        self.button_morph = Button(self.ax_morph, 'Toggle Sine Morph')
        self.button_pyramid = Button(self.ax_pyramid, 'Pyramid Angle View')
        self.button_xyz = Button(self.ax_xyz, 'Toggle XYZ Window')

        self.button_reset.on_clicked(self.reset_view)
        self.button_morph.on_clicked(self.toggle_sine_morph)
        self.button_pyramid.on_clicked(self.reset_to_pyramid_view)
        self.button_xyz.on_clicked(self.toggle_xyz_display)

    def setup_plot(self):
        """Initial 3D plot"""
        self.ax.clear()

        # Draw cube
        for i, face in enumerate(self.faces):
            poly = Poly3DCollection([self.vertices[face]], alpha=0.05)
            poly.set_facecolor(self.face_colors[i])
            poly.set_edgecolor('gray')
            poly.set_linewidth(0.5)
            self.ax.add_collection3d(poly)

        # Draw spiral/sine
        points = self.interpolate_points()
        self.ax.plot3D(points[:, 0], points[:, 1], points[:, 2],
                       color='black', linewidth=3)

        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.view_init(elev=self.elev, azim=self.azim)
        self.ax.set_title('Golden Ellipse Spiral Cube', fontsize=14, fontweight='bold')
        self.fig.canvas.draw_idle()

    def setup_info_panel(self):
        """Right-hand legend"""
        self.ax_info.clear()
        self.ax_info.axis('off')

        text = (
            "LEGEND:\n"
            "Black line: Spiral/Sine Morph\n"
            "Cube: Transparent structure\n\n"
            "BUTTONS:\n"
            "Default View - Reset camera\n"
            "Toggle Sine Morph - Morph spiral to sine\n"
            "Pyramid Angle View - Set view to 51.84°\n"
            "Toggle XYZ Window - Show/Hide live coordinates"
        )

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

    # ===============================================================
    #   XYZ DISPLAY
    # ===============================================================

    def create_xyz_display(self):
        """Small window with XYZ coordinates"""
        self.ax_text = self.fig.add_axes([0.02, 0.8, 0.2, 0.15])
        self.ax_text.axis('off')
        self.text_box = self.ax_text.text(0, 1, "X: +0.0000\nY: +0.0000\nZ: +0.0000",
                                          fontfamily='monospace',
                                          fontsize=10,
                                          verticalalignment='top',
                                          bbox=dict(boxstyle="round,pad=0.3",
                                                    facecolor='white',
                                                    alpha=0.8))
        self.xyz_visible = True

    def toggle_xyz_display(self, event=None):
        """Show/hide XYZ window"""
        self.xyz_visible = not self.xyz_visible
        self.ax_text.set_visible(self.xyz_visible)
        self.fig.canvas.draw_idle()

    def update_xyz_display(self, point):
        """Update coordinates in real time"""
        if not self.xyz_visible:
            return
        x, y, z = point
        self.text_box.set_text(f"X: {x:+.4f}\nY: {y:+.4f}\nZ: {z:+.4f}")
        self.fig.canvas.draw_idle()

    # ===============================================================
    #   EVENTS
    # ===============================================================

    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:
            scale = 1.1 if event.step > 0 else 0.9
            self.ax.set_xlim(np.array(self.ax.get_xlim()) * scale)
            self.ax.set_ylim(np.array(self.ax.get_ylim()) * scale)
            self.ax.set_zlim(np.array(self.ax.get_zlim()) * scale)
            self.fig.canvas.draw_idle()

    # ===============================================================
    #   VIEW CONTROLS
    # ===============================================================

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

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

    def toggle_sine_morph(self, event=None):
        """Smoothly morph between spiral and sine"""
        target = 1.0 if self.morph_t < 0.5 else 0.0
        steps = 30
        for i in range(steps + 1):
            self.morph_t = self.morph_t + (target - self.morph_t) * 0.1
            self.setup_plot()
            self.update_xyz_display(self.interpolate_points()[-1])
            plt.pause(0.03)
        self.morph_t = target
        self.setup_plot()
        self.update_xyz_display(self.interpolate_points()[-1])

    # ===============================================================

    def show(self):
        """Display"""
        print("Golden Ellipse Spiral Cube - with sine morph and XYZ display")
        plt.show()

=== =============================================================== ===
=== RUN ===
=== =============================================================== ===

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

</syntaxhighlight>