.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/Interactive/plot_ipf_explorer.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_Interactive_plot_ipf_explorer.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_Interactive_plot_ipf_explorer.py:


Inverse Pole Figure (IPF) Explorer
==================================

An EBSD-style orientation explorer for a synthetic polycrystal:

* **Left panel** — IPF-Z orientation map, colored with the standard cubic
  IPF key (red = ⟨001⟩, green = ⟨011⟩, blue = ⟨111⟩).  Rendered as a
  true-color RGB image.
* **Right panel** — the *reduced 3-D inverse pole figure*: every grain's
  sample-Z direction, expressed in crystal coordinates and folded into the
  cubic fundamental sector, plotted as an IPF-colored point cloud on a
  shaded, wireframed unit sphere.

Drag the crosshair on the map: the grain's orientation is marked with a
highlighted dot on the sphere, and the sphere **rotates so that direction
faces you**.  Drag on the sphere to orbit freely; the next crosshair move
re-aims the camera.

.. GENERATED FROM PYTHON SOURCE LINES 20-126




.. raw:: html

    <div style="display:block;text-align:center;line-height:0;margin:12px 0;"><div id="sphx_glr_plot_ipf_explorer_001" class="awi-fig-wrap" data-awi-fig="sphx_glr_plot_ipf_explorer_001" style="display:inline-block;overflow:hidden;position:relative;width:684px;height:333px;"><iframe src="../../_static/viewer_widgets/sphx_glr_plot_ipf_explorer_001.html" data-awi-fig="sphx_glr_plot_ipf_explorer_001" frameborder="0" scrolling="no" style="width:896px;height:436px;border:none;overflow:hidden;display:block;transform-origin:top left;transform:scale(0.763393);position:absolute;top:0;left:0;"></iframe><div class="awi-badge" data-awi-badge="sphx_glr_plot_ipf_explorer_001"><button class="awi-badge-icon awi-activate-btn" data-awi-fig="sphx_glr_plot_ipf_explorer_001" title="Make interactive (boots Pyodide — may take ~10 s)">&#x26A1;</button></div></div><script>(function(){var wrap=document.getElementById('sphx_glr_plot_ipf_explorer_001'),ifr=wrap.querySelector('iframe'),nw=896,nh=436;function r(){var avail=wrap.parentElement?wrap.parentElement.offsetWidth:0;if(!avail)return;var s=Math.min(1,avail/nw);wrap.style.width=Math.round(nw*s)+'px';wrap.style.height=Math.round(nh*s)+'px';ifr.style.transform='scale('+s+')';}requestAnimationFrame(r);window.addEventListener('resize',r);})()</script></div>



.. raw:: html

    <script type="text/x-python" data-fig-id="sphx_glr_plot_ipf_explorer_001" data-fig-index="0" data-src-file="plot_ipf_explorer" data-src="&quot;\&quot;\&quot;\&quot;\nInverse Pole Figure (IPF) Explorer\n==================================\n\nAn EBSD-style orientation explorer for a synthetic polycrystal:\n\n* **Left panel** \u2014 IPF-Z orientation map, colored with the standard cubic\n  IPF key (red = \u27e8001\u27e9, green = \u27e8011\u27e9, blue = \u27e8111\u27e9).  Rendered as a\n  true-color RGB image.\n* **Right panel** \u2014 the *reduced 3-D inverse pole figure*: every grain&#x27;s\n  sample-Z direction, expressed in crystal coordinates and folded into the\n  cubic fundamental sector, plotted as an IPF-colored point cloud on a\n  shaded, wireframed unit sphere.\n\nDrag the crosshair on the map: the grain&#x27;s orientation is marked with a\nhighlighted dot on the sphere, and the sphere **rotates so that direction\nfaces you**.  Drag on the sphere to orbit freely; the next crosshair move\nre-aims the camera.\n\&quot;\&quot;\&quot;\n\nimport numpy as np\nimport anyplotlib as apl\n\nrng = np.random.default_rng(42)\n\n# \u2500\u2500 1. Synthetic polycrystal: nearest-seed grain map \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\nH = W = 192\nN_GRAINS = 60\n\nseeds = rng.uniform(0, [H, W], size=(N_GRAINS, 2))\nyy, xx = np.mgrid[0:H, 0:W]\nd2 = (yy[..., None] - seeds[:, 0]) ** 2 + (xx[..., None] - seeds[:, 1]) ** 2\ngrain_id = np.argmin(d2, axis=-1)                       # (H, W) labels\n\n\n# \u2500\u2500 2. Random orientation per grain (uniform rotations via quaternions) \u2500\u2500\u2500\u2500\u2500\ndef random_rotations(n):\n    \&quot;\&quot;\&quot;Uniform random rotation matrices, shape (n, 3, 3) (Shoemake method).\&quot;\&quot;\&quot;\n    u1, u2, u3 = rng.random((3, n))\n    q = np.stack([\n        np.sqrt(1 - u1) * np.sin(2 * np.pi * u2),\n        np.sqrt(1 - u1) * np.cos(2 * np.pi * u2),\n        np.sqrt(u1) * np.sin(2 * np.pi * u3),\n        np.sqrt(u1) * np.cos(2 * np.pi * u3),\n    ], axis=1)                                          # (n, 4) unit quats\n    x, y, z, w = q.T\n    return np.stack([\n        np.stack([1 - 2 * (y * y + z * z), 2 * (x * y - z * w), 2 * (x * z + y * w)], -1),\n        np.stack([2 * (x * y + z * w), 1 - 2 * (x * x + z * z), 2 * (y * z - x * w)], -1),\n        np.stack([2 * (x * z - y * w), 2 * (y * z + x * w), 1 - 2 * (x * x + y * y)], -1),\n    ], axis=1)\n\n\nrotations = random_rotations(N_GRAINS)\n\n# Sample-Z expressed in each grain&#x27;s crystal frame: d = R\u1d40 \u00b7 \u1e91\ndirs = rotations[:, 2, :]                               # row 2 of R == R\u1d40\u00b7\u1e91\n\n# \u2500\u2500 3. Reduce to the cubic fundamental sector and IPF-color \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n# For cubic symmetry, sorting |components| ascending lands every direction\n# in the standard 001\u2013011\u2013111 stereographic triangle.\nreduced = np.sort(np.abs(dirs), axis=1)                 # (a \u2264 b \u2264 c)\na, b, c = reduced.T\n\n# Classic IPF key: distance to each triangle corner \u2192 R, G, B\nrgb = np.stack([c - b, b - a, a], axis=1)\nrgb /= rgb.max(axis=1, keepdims=True) + 1e-12           # vivid normalisation\ngrain_rgb_u8 = (rgb * 255).astype(np.uint8)             # (N_GRAINS, 3)\n\nipf_map = grain_rgb_u8[grain_id]                        # (H, W, 3) true-color\n\n\n# \u2500\u2500 4. Figure: RGB map + reduced 3-D IPF point cloud \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\nfig, (ax_map, ax_ipf) = apl.subplots(\n    1, 2, figsize=(880, 420),\n    help=\&quot;Drag the crosshair: the sphere rotates to face that grain&#x27;s\\n\&quot;\n         \&quot;crystal direction.  Drag the sphere to orbit freely.\&quot;)\n\nvmap = ax_map.imshow(ipf_map)                           # (H, W, 3) \u2192 RGB\nvmap.set_title(\&quot;IPF-Z orientation map\&quot;)\ncross = vmap.add_widget(\&quot;crosshair\&quot;, cx=W // 2, cy=H // 2, color=\&quot;#ffffff\&quot;)\n\n# reduced directions live on the unit sphere \u2192 fix bounds to keep the\n# origin centred and the geometry origin-true\nvipf = ax_ipf.scatter3d(\n    reduced[:, 0], reduced[:, 1], reduced[:, 2],\n    colors=grain_rgb_u8, point_size=6,\n    x_label=\&quot;[100]\&quot;, y_label=\&quot;[010]\&quot;, z_label=\&quot;[001]\&quot;,\n    bounds=((-1, 1),) * 3, zoom=1.4,\n)\nvipf.set_title(\&quot;Reduced 3D IPF (cubic fundamental sector)\&quot;)\n# Shaded unit sphere with lat/long wireframe behind the direction vectors\nvipf.set_sphere(1.0)\n\n\n# \u2500\u2500 5. Crosshair \u2192 highlight + rotate-to-face \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\ndef face_camera(v):\n    \&quot;\&quot;\&quot;(azimuth\u00b0, elevation\u00b0) that aim the camera straight down *v*.\n\n    With the turntable camera, the view faces unit vector ``v`` when\n    ``el = asin(vz)`` and ``az = atan2(vx, -vy)``.\n    \&quot;\&quot;\&quot;\n    vx, vy, vz = v\n    el = np.degrees(np.arcsin(np.clip(vz, -1.0, 1.0)))\n    az = np.degrees(np.arctan2(vx, -vy))\n    return az, el\n\n\ndef show_orientation(gid: int) -&gt; None:\n    v = reduced[gid]\n    vipf.set_highlight(*v, color=\&quot;#ffffff\&quot;, size=8)\n    az, el = face_camera(v)\n    vipf.set_view(azimuth=az, elevation=el)\n\n\n@cross.add_event_handler(\&quot;pointer_move\&quot;)\ndef on_move(event):\n    ix = int(np.clip(round(cross.cx), 0, W - 1))\n    iy = int(np.clip(round(cross.cy), 0, H - 1))\n    show_orientation(int(grain_id[iy, ix]))\n\n\nshow_orientation(int(grain_id[H // 2, W // 2]))\n\nfig  # Interactive\n&quot;"></script>






.. code-block:: Python


    import numpy as np
    import anyplotlib as apl

    rng = np.random.default_rng(42)

    # ── 1. Synthetic polycrystal: nearest-seed grain map ────────────────────────
    H = W = 192
    N_GRAINS = 60

    seeds = rng.uniform(0, [H, W], size=(N_GRAINS, 2))
    yy, xx = np.mgrid[0:H, 0:W]
    d2 = (yy[..., None] - seeds[:, 0]) ** 2 + (xx[..., None] - seeds[:, 1]) ** 2
    grain_id = np.argmin(d2, axis=-1)                       # (H, W) labels


    # ── 2. Random orientation per grain (uniform rotations via quaternions) ─────
    def random_rotations(n):
        """Uniform random rotation matrices, shape (n, 3, 3) (Shoemake method)."""
        u1, u2, u3 = rng.random((3, n))
        q = np.stack([
            np.sqrt(1 - u1) * np.sin(2 * np.pi * u2),
            np.sqrt(1 - u1) * np.cos(2 * np.pi * u2),
            np.sqrt(u1) * np.sin(2 * np.pi * u3),
            np.sqrt(u1) * np.cos(2 * np.pi * u3),
        ], axis=1)                                          # (n, 4) unit quats
        x, y, z, w = q.T
        return np.stack([
            np.stack([1 - 2 * (y * y + z * z), 2 * (x * y - z * w), 2 * (x * z + y * w)], -1),
            np.stack([2 * (x * y + z * w), 1 - 2 * (x * x + z * z), 2 * (y * z - x * w)], -1),
            np.stack([2 * (x * z - y * w), 2 * (y * z + x * w), 1 - 2 * (x * x + y * y)], -1),
        ], axis=1)


    rotations = random_rotations(N_GRAINS)

    # Sample-Z expressed in each grain's crystal frame: d = Rᵀ · ẑ
    dirs = rotations[:, 2, :]                               # row 2 of R == Rᵀ·ẑ

    # ── 3. Reduce to the cubic fundamental sector and IPF-color ────────────────
    # For cubic symmetry, sorting |components| ascending lands every direction
    # in the standard 001–011–111 stereographic triangle.
    reduced = np.sort(np.abs(dirs), axis=1)                 # (a ≤ b ≤ c)
    a, b, c = reduced.T

    # Classic IPF key: distance to each triangle corner → R, G, B
    rgb = np.stack([c - b, b - a, a], axis=1)
    rgb /= rgb.max(axis=1, keepdims=True) + 1e-12           # vivid normalisation
    grain_rgb_u8 = (rgb * 255).astype(np.uint8)             # (N_GRAINS, 3)

    ipf_map = grain_rgb_u8[grain_id]                        # (H, W, 3) true-color


    # ── 4. Figure: RGB map + reduced 3-D IPF point cloud ───────────────────────
    fig, (ax_map, ax_ipf) = apl.subplots(
        1, 2, figsize=(880, 420),
        help="Drag the crosshair: the sphere rotates to face that grain's\n"
             "crystal direction.  Drag the sphere to orbit freely.")

    vmap = ax_map.imshow(ipf_map)                           # (H, W, 3) → RGB
    vmap.set_title("IPF-Z orientation map")
    cross = vmap.add_widget("crosshair", cx=W // 2, cy=H // 2, color="#ffffff")

    # reduced directions live on the unit sphere → fix bounds to keep the
    # origin centred and the geometry origin-true
    vipf = ax_ipf.scatter3d(
        reduced[:, 0], reduced[:, 1], reduced[:, 2],
        colors=grain_rgb_u8, point_size=6,
        x_label="[100]", y_label="[010]", z_label="[001]",
        bounds=((-1, 1),) * 3, zoom=1.4,
    )
    vipf.set_title("Reduced 3D IPF (cubic fundamental sector)")
    # Shaded unit sphere with lat/long wireframe behind the direction vectors
    vipf.set_sphere(1.0)


    # ── 5. Crosshair → highlight + rotate-to-face ───────────────────────────────
    def face_camera(v):
        """(azimuth°, elevation°) that aim the camera straight down *v*.

        With the turntable camera, the view faces unit vector ``v`` when
        ``el = asin(vz)`` and ``az = atan2(vx, -vy)``.
        """
        vx, vy, vz = v
        el = np.degrees(np.arcsin(np.clip(vz, -1.0, 1.0)))
        az = np.degrees(np.arctan2(vx, -vy))
        return az, el


    def show_orientation(gid: int) -> None:
        v = reduced[gid]
        vipf.set_highlight(*v, color="#ffffff", size=8)
        az, el = face_camera(v)
        vipf.set_view(azimuth=az, elevation=el)


    @cross.add_event_handler("pointer_move")
    def on_move(event):
        ix = int(np.clip(round(cross.cx), 0, W - 1))
        iy = int(np.clip(round(cross.cy), 0, H - 1))
        show_orientation(int(grain_id[iy, ix]))


    show_orientation(int(grain_id[H // 2, W // 2]))

    fig  # Interactive


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

   **Total running time of the script:** (0 minutes 0.699 seconds)


.. _sphx_glr_download_auto_examples_Interactive_plot_ipf_explorer.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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