.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples\piecewise_geodesic.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_piecewise_geodesic.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_piecewise_geodesic.py:


Piecewise Geodesic Example
==========================

Compute and visualize a piecewise geodesic curve on the unit sphere.

.. GENERATED FROM PYTHON SOURCE LINES 7-116



.. image-sg:: /auto_examples/images/sphx_glr_piecewise_geodesic_001.png
   :alt: Piecewise Geodesic on Sphere
   :srcset: /auto_examples/images/sphx_glr_piecewise_geodesic_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import numpy as np
    import plotly.graph_objects as go
    import plotly.io as pio
    from spheresmooth import piecewise_geodesic

    # -------------------------------------------------------------
    # Example setup
    # -------------------------------------------------------------
    c = 1/np.sqrt(3)
    control_points = np.array([
        [ c,  c,  c],
        [ c,  c, -c],
        [-c,  c,  c],
        [-c,  c, -c]
    ])
    knots = np.array([1, 2, 3, 3.5])

    t = np.linspace(0, 4, 300)
    curve = piecewise_geodesic(t, control_points, knots)

    # -------------------------------------------------------------
    # Sphere mesh
    # -------------------------------------------------------------
    u = np.linspace(0, 2*np.pi, 60)
    v = np.linspace(0, np.pi, 30)
    x = np.outer(np.cos(u), np.sin(v))
    y = np.outer(np.sin(u), np.sin(v))
    z = np.outer(np.ones_like(u), np.cos(v))

    # -------------------------------------------------------------
    # Plot
    # -------------------------------------------------------------
    fig = go.Figure()

    # Sphere surface
    fig.add_surface(
        x=x, y=y, z=z,
        opacity=0.1,
        colorscale="Greys",
        showscale=False
    )

    # Control points
    fig.add_trace(go.Scatter3d(
        x=control_points[:, 0],
        y=control_points[:, 1],
        z=control_points[:, 2],
        mode='markers',
        marker=dict(size=5, color='blue', opacity=1),
        name='Control Points' 
    ))

    # Geodesic path
    fig.add_trace(go.Scatter3d(
        x=curve[:, 0],
        y=curve[:, 1],
        z=curve[:, 2],
        mode='lines',
        line=dict(color='red', width=6),
        name='Piecewise Geodesic' 
    ))

    # Optional: lat/long grid 
    lat_values = np.linspace(-60, 60, 8)
    for lat in lat_values:
        phi = np.radians(lat)
        ugrid = np.linspace(0, 2*np.pi, 200)
        fig.add_trace(go.Scatter3d(
            x=np.cos(ugrid) * np.cos(phi),
            y=np.sin(ugrid) * np.cos(phi),
            z=np.full_like(ugrid, np.sin(phi)),
            mode='lines',
            line=dict(color='gray', width=1),
            showlegend=False
        ))

    lon_values = np.linspace(0, 330, 12)
    for lon in lon_values:
        lam = np.radians(lon)
        vgrid = np.linspace(-np.pi/2, np.pi/2, 200)
        fig.add_trace(go.Scatter3d(
            x=np.cos(vgrid) * np.cos(lam),
            y=np.cos(vgrid) * np.sin(lam),
            z=np.sin(vgrid),
            mode='lines',
            line=dict(color='gray', width=1),
            showlegend=False
        ))

    fig.update_layout(
        title="Piecewise Geodesic on the Sphere",
        scene=dict(
            xaxis=dict(visible=False),
            yaxis=dict(visible=False),
            zaxis=dict(visible=False),
            aspectmode="data"
        )
    )

    import matplotlib.pyplot as plt
    import matplotlib.image as mpimg

    img = mpimg.imread("piecewise_geodesic_example.png")

    plt.figure(figsize=(6, 6))
    plt.imshow(img)
    plt.axis("off")
    plt.title("Piecewise Geodesic on Sphere")
    plt.show()

.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.260 seconds)


.. _sphx_glr_download_auto_examples_piecewise_geodesic.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: piecewise_geodesic.ipynb <piecewise_geodesic.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: piecewise_geodesic.py <piecewise_geodesic.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: piecewise_geodesic.zip <piecewise_geodesic.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_