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        {
          "__type": "Parameters",
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          "children": [
            {
              "__type": "DocParam",
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              "name": "transform",
              "annotation": "`RigidTransform` instance",
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                {
                  "__type": "Paragraph",
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                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Rigid transform objects with the same leading dimensions as the input."
                    }
                  ]
                }
              ]
            }
          ]
        }
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    },
    "Summary": {
      "__type": "Section",
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          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
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              "value": "Initialize from exponential coordinates of transform."
            }
          ]
        }
      ],
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    },
    "Receives": {
      "__type": "Section",
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    "Parameters": {
      "__type": "Section",
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          "__type": "Parameters",
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            {
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              "name": "exp_coords",
              "annotation": "array_like, shape (..., 6)",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Exponential coordinate vectors. Each exp_coords[..., :] represents a 6D exponential coordinate vector with the expected order of components "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "[rx, ry, rz, vx, vy, vz]"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". The first 3 components encode rotation and the last 3 encode translation."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
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          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "This implements the exponential map that converts 6-dimensional real vectors to SE(3)."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "An exponential coordinate vector consists of 6 elements "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "[rx, ry, rz, vx, vy, vz]"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". The first 3 encode rotation (and form a rotation vector used in "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "Rotation.from_rotvec",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.spatial.transform._rotation:Rotation.from_rotvec"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ") and the last 3 encode translation (and form a translation vector for pure translations). The exponential mapping can be expressed as matrix exponential "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "T = exp(tau)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", where "
            },
            {
              "__type": "InlineCode",
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              "value": "T"
            },
            {
              "__type": "Text",
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              "value": " is a 4x4 matrix representing a rigid transform and "
            },
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              "__type": "InlineCode",
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              "value": "tau"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is a 4x4 matrix formed from the elements of an exponential coordinate vector      "
            }
          ]
        },
        {
          "__type": "Code",
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          "value": "tau = [  0 -rz  ry vx]\n      [ rz   0 -rx vy]\n      [-ry  rx   0 vz]\n      [  0   0   0  0]",
          "execution_status": null,
          "out": ""
        }
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    "Raises",
    "Warns",
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  "item_file": "build-install/usr/lib/python3.14/site-packages/scipy/spatial/transform/_rigid_transform.py",
  "item_line": 757,
  "item_type": "staticmethod",
  "aliases": [
    "scipy.spatial.transform.RigidTransform.from_exp_coords"
  ],
  "example_section_data": {
    "__type": "Section",
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    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "from scipy.spatial.transform import RigidTransform as Tf\nimport numpy as np\n",
        "execution_status": "success",
        "out": ""
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nCreating from a single 6d vector of exponential coordinates:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "tf = Tf.from_exp_coords([\n    -2.01041204, -0.52983629, 0.65773501,\n    0.10386614, 0.05855009, 0.54959179])\n",
        "execution_status": "success",
        "out": ""
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "tf.as_matrix()\n",
        "execution_status": "failure",
        "out": "array([[ 0.76407,  0.10505, -0.63653, -0.1021 ],\n       [ 0.59956, -0.47987,  0.6405 ,  0.40159],\n       [-0.23817, -0.87103, -0.42964,  0.19638],\n       [ 0.     ,  0.     ,  0.     ,  1.     ]])\n"
      },
      {
        "__type": "Code",
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        "value": "tf.single\n",
        "execution_status": "success",
        "out": "True\n"
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        "value": "\nA vector of zeros represents the identity transform:\n\n"
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      {
        "__type": "Code",
        "__tag": 4050,
        "value": "tf = Tf.from_exp_coords(np.zeros(6))\ntf.as_matrix()\n",
        "execution_status": "success",
        "out": "array([[1., 0., 0., 0.],\n       [0., 1., 0., 0.],\n       [0., 0., 1., 0.],\n       [0., 0., 0., 1.]])\n"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nThe last three numbers encode translation. If the first three numbers\nare zero, the last three components can be interpreted as the\ntranslation:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "tf_trans = Tf.from_exp_coords([0, 0, 0, 4.3, -2, 3.4])\n",
        "execution_status": "success",
        "out": ""
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "tf_trans.translation\n",
        "execution_status": "failure",
        "out": "array([ 4.3, -2. ,  3.4])\n"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nThe first three numbers encode rotation as a rotation vector:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "tf_rot = Tf.from_exp_coords([0.5, 0.3, 0.1, 0, 0, 0])\ntf_rot.rotation.as_rotvec()\n",
        "execution_status": "success",
        "out": "array([0.5, 0.3, 0.1])\n"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nCombining translation and rotation preserves the rotation vector,\nbut changes the last three components as they encode translation and\nrotation:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "(tf_trans * tf_rot).as_exp_coords()\n",
        "execution_status": "failure",
        "out": "array([ 0.5    ,  0.3    ,  0.1    ,  3.64306, -1.2588 ,  4.46109])\n"
      }
    ],
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  "signature": {
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        "__type": "SigParam",
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        "name": "exp_coords",
        "annotation": "ArrayLike",
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      }
    ],
    "return_annotation": "RigidTransform",
    "target_name": "from_exp_coords"
  },
  "references": null,
  "qa": "scipy.spatial.transform._rigid_transform:RigidTransform.from_exp_coords",
  "arbitrary": [],
  "local_refs": [
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  ]
}