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        "value": "\nA `Rotation` instance can be initialized in any of the above formats and\nconverted to any of the others. The underlying object is independent of the\nrepresentation used for initialization.\n\nConsider a counter-clockwise rotation of 90 degrees about the z-axis. This\ncorresponds to the following quaternion (in scalar-last format):\n\n"
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        "value": "r = R.from_quat([0, 0, np.sin(np.pi/4), np.cos(np.pi/4)])\n",
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        "value": "\nThe rotation can be expressed in any of the other formats:\n\n"
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        "value": "r.as_matrix()\nr.as_rotvec()\nr.as_euler('zyx', degrees=True)\n",
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        "value": "\nThe same rotation can be initialized using a rotation matrix:\n\n"
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        "value": "r = R.from_matrix([[0, -1, 0],\n                   [1, 0, 0],\n                   [0, 0, 1]])\n",
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        "value": "r.as_quat()\nr.as_rotvec()\nr.as_euler('zyx', degrees=True)\n",
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        "value": "\nThe rotation vector corresponding to this rotation is given by:\n\n"
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        "value": "r = R.from_rotvec(np.pi/2 * np.array([0, 0, 1]))\n",
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        "value": "\nThe ``from_euler`` method is quite flexible in the range of input formats\nit supports. Here we initialize a single rotation about a single axis:\n\n"
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        "value": "r = R.from_euler('z', 90, degrees=True)\n",
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        "value": "\nIt is also possible to initialize multiple rotations in a single instance\nusing any of the ``from_...`` functions. Here we initialize a stack of 3\nrotations using the ``from_euler`` method:\n\n"
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        "value": "r = R.from_euler('zyx', [\n[90, 0, 0],\n[0, 45, 0],\n[45, 60, 30]], degrees=True)\n",
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        "value": "\nMultiple rotations can be composed using the ``*`` operator:\n\n"
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        "value": "r1 = R.from_euler('z', 90, degrees=True)\nr2 = R.from_rotvec([np.pi/4, 0, 0])\nv = [1, 2, 3]\n",
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        "value": "r3 = r2 * r1 # Note the order\n",
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        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "def plot_rotated_axes(ax, r, name=None, offset=(0, 0, 0), scale=1):\n    colors = (\"#FF6666\", \"#005533\", \"#1199EE\")  # Colorblind-safe RGB\n    loc = np.array([offset, offset])\n    for i, (axis, c) in enumerate(zip((ax.xaxis, ax.yaxis, ax.zaxis),\n                                      colors)):\n        axlabel = axis.axis_name\n        axis.set_label_text(axlabel)\n        axis.label.set_color(c)\n        axis.line.set_color(c)\n        axis.set_tick_params(colors=c)\n        line = np.zeros((2, 3))\n        line[1, i] = scale\n        line_rot = r.apply(line)\n        line_plot = line_rot + loc\n        ax.plot(line_plot[:, 0], line_plot[:, 1], line_plot[:, 2], c)\n        text_loc = line[1]*1.2\n        text_loc_rot = r.apply(text_loc)\n        text_plot = text_loc_rot + loc[0]\n        ax.text(*text_plot, axlabel.upper(), color=c,\n                va=\"center\", ha=\"center\")\n    ax.text(*offset, name, color=\"k\", va=\"center\", ha=\"center\",\n            bbox={\"fc\": \"w\", \"alpha\": 0.8, \"boxstyle\": \"circle\"})\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nCreate three rotations - the identity and two Euler rotations using\nintrinsic and extrinsic conventions:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "r0 = R.identity()\nr1 = R.from_euler(\"ZYX\", [90, -30, 0], degrees=True)  # intrinsic\nr2 = R.from_euler(\"zyx\", [90, -30, 0], degrees=True)  # extrinsic\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nAdd all three rotations to a single plot:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "ax = plt.figure().add_subplot(projection=\"3d\", proj_type=\"ortho\")\nplot_rotated_axes(ax, r0, name=\"r0\", offset=(0, 0, 0))\nplot_rotated_axes(ax, r1, name=\"r1\", offset=(3, 0, 0))\nplot_rotated_axes(ax, r2, name=\"r2\", offset=(6, 0, 0))\n_ = ax.annotate(\n    \"r0: Identity Rotation\\n\"\n    \"r1: Intrinsic Euler Rotation (ZYX)\\n\"\n    \"r2: Extrinsic Euler Rotation (zyx)\",\n    xy=(0.6, 0.7), xycoords=\"axes fraction\", ha=\"left\"\n)\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "ax.set(xlim=(-1.25, 7.25), ylim=(-1.25, 1.25), zlim=(-1.25, 1.25))\nax.set(xticks=range(-1, 8), yticks=[-1, 0, 1], zticks=[-1, 0, 1])\n",
        "execution_status": "failure"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "ax.set_aspect(\"equal\", adjustable=\"box\")\nax.figure.set_size_inches(6, 5)\nplt.tight_layout()\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nShow the plot:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "plt.show()\n",
        "execution_status": "success"
      },
      {
        "__type": "Figure",
        "__tag": 4024,
        "value": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "scipy",
          "version": "1.17.1",
          "kind": "assets",
          "path": "fig-929483627434c532.png"
        }
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nThese examples serve as an overview into the `Rotation` class and highlight\nmajor functionalities. For more thorough examples of the range of input and\noutput formats supported, consult the individual method's examples."
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "Slerp",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.spatial.transform._rotation:Slerp"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    }
  ],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "quat",
        "annotation": "ArrayLike",
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "normalize",
        "annotation": "bool",
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "True"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "copy",
        "annotation": "bool",
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "True"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "scalar_first",
        "annotation": "bool",
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "Rotation"
  },
  "references": null,
  "qa": "scipy.spatial.transform._rotation:Rotation",
  "arbitrary": [],
  "local_refs": [
    "__getitem__",
    "__len__",
    "__mul__",
    "__pow__",
    "align_vectors",
    "apply",
    "approx_equal",
    "as_davenport",
    "as_euler",
    "as_matrix",
    "as_mrp",
    "as_quat",
    "as_rotvec",
    "concatenate",
    "create_group",
    "from_davenport",
    "from_euler",
    "from_matrix",
    "from_mrp",
    "from_quat",
    "from_rotvec",
    "identity",
    "inv",
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  ]
}