{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Strong", "__tag": 4048, "children": [ { "__type": "Text", "__tag": 4046, "value": "Array API Standard Support" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "as_euler", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.spatial.transform._rotation:Rotation.as_euler" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable " }, { "__type": "InlineCode", "__tag": 4051, "value": "SCIPY_ARRAY_API=1" }, { "__type": "Text", "__tag": 4046, "value": " and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. 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The returned angles are in the range:" } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "First angle belongs to [-180, 180] degrees (both inclusive)" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Third angle belongs to [-180, 180] degrees (both inclusive)" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Second angle belongs to:" } ] }, { "__type": "Blockquote", "__tag": 4059, "children": [ { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "[-90, 90] degrees if all axes are different (like xyz)" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "[0, 180] degrees if first and third axes are the same (like zxz)" } ] } ] } ] } ] } ] } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Represent as Euler angles." } ] } ], "title": [], "level": 0, "target": null }, "Receives": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Warnings": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Attributes": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Parameters": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "seq", "annotation": "string, length 3", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "3 characters belonging to the set {'X', 'Y', 'Z'} for intrinsic rotations, or {'x', 'y', 'z'} for extrinsic rotations " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": ". Adjacent axes cannot be the same. Extrinsic and intrinsic rotations cannot be mixed in one function call." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "degrees", "annotation": "boolean, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Returned angles are in degrees if this flag is True, else they are in radians. Default is False." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "suppress_warnings", "annotation": "boolean, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Disable warnings about gimbal lock. 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Once the axis sequence has been chosen, Euler angles define the angle of rotation around each respective axis " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The algorithm from " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "2" }, { "__type": "Text", "__tag": 4046, "value": " has been used to calculate Euler angles for the rotation about a given sequence of axes." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Euler angles suffer from the problem of gimbal lock " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "3" }, { "__type": "Text", "__tag": 4046, "value": ", where the representation loses a degree of freedom and it is not possible to determine the first and third angles uniquely. 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Note however that the returned angles still represent the correct rotation." } ] } ], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": "/scipy/spatial/transform/_rotation.py", "item_line": 1191, "item_type": "function", "aliases": [ "scipy.spatial.transform.Rotation.as_euler" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": "from scipy.spatial.transform import Rotation as R\nimport numpy as np\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nRepresent a single rotation:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "r = R.from_rotvec([0, 0, np.pi/2])\nr.as_euler('zxy', degrees=True)\nr.as_euler('zxy', degrees=True).shape\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nRepresent a stack of single rotation:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "r = R.from_rotvec([[0, 0, np.pi/2]])\nr.as_euler('zxy', degrees=True)\nr.as_euler('zxy', degrees=True).shape\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nRepresent multiple rotations in a single object:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "r = R.from_rotvec([\n[0, 0, np.pi/2],\n[0, -np.pi/3, 0],\n[np.pi/4, 0, 0]])\nr.as_euler('zxy', degrees=True)\nr.as_euler('zxy', degrees=True).shape\n", "execution_status": "success" } ], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "self", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "seq", "annotation": "str", "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "degrees", "annotation": "bool", "kind": "POSITIONAL_OR_KEYWORD", "default": "False" }, { "__type": "SigParam", "__tag": 4030, "name": "suppress_warnings", "annotation": "bool", "kind": "KEYWORD_ONLY", "default": "False" } ], "return_annotation": "Array", "target_name": "as_euler" }, "references": [ ".. [1] https://en.wikipedia.org/wiki/Euler_angles#Definition_by_intrinsic_rotations", ".. [2] Bernardes E, Viollet S (2022) Quaternion to Euler angles", " conversion: A direct, general and computationally efficient", " method. PLoS ONE 17(11): e0276302.", " https://doi.org/10.1371/journal.pone.0276302", ".. [3] https://en.wikipedia.org/wiki/Gimbal_lock#In_applied_mathematics" ], "qa": "scipy.spatial.transform._rotation:Rotation.as_euler", "arbitrary": [], "local_refs": [ "angles", "degrees", "seq", "suppress_warnings" ] }