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

=== Assistant: Excellent — that image makes things crystal clear. ===
Excellent — that image makes things crystal clear.
Right now the sine curve’s starting radius doesn’t line up with the spiral’s last loop.
That’s why it “sticks out” instead of looking like a seamless continuation.

Let’s fix this so that:
# The sine wave starts exactly where the spiral ends (same x, y, z).
# The sine wave keeps the same rotation phase (so no sudden twist).
# It stays inside the cube (no overshoot).
# It transitions smoothly downward as a 3D sine variation.

===== Replace your current one with this version: =====

<syntaxhighlight lang="python">def create_sine_projection(self):
    """Smooth continuation of the spiral into a vertical sinusoidal pattern inside the cube"""
    # Get the endpoint of the spiral (start of sine)
    start = self.spiral_points[-1]
    x0, y0, z0 = start

    # Create z from top (1) to bottom (-1)
    z = np.linspace(z0, -1, 400)

    # Keep same angular direction as spiral continuation
    # Start where spiral left off (2π) and continue turning
    theta_start = np.arctan2(y0, x0)
    theta = np.linspace(theta_start, theta_start + 4 * np.pi, 400)

    # Compute sine-modulated radius that oscillates inward-outward slightly
    r_base = np.sqrt(x0'''2 + y0'''2)
    r = r_base '' (1 - 0.2 '' np.sin(4 '' np.pi '' (z - z0) / 2))

    # Convert back to Cartesian
    x = r * np.cos(theta)
    y = r * np.sin(theta)

    return np.column_stack((x, y, z))

</syntaxhighlight>

===== - The sine path starts from the exact (x, y, z) of the spiral’s end. =====
* It continues rotating in the same direction (theta_start ensures phase match).
* The radius modulates gently by a sine term, making it look alive yet contained.
* It stays fully inside [-1.5, 1.5]³ cube bounds.

Would you like me to show you how to make this appear as a smooth morphing transition (spiral → sine) when the button is pressed, instead of toggling instantly?
It would look like the spiral melts into the sine pattern.