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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 a set of size 180 degrees, given by: " }, { "__type": "InlineCode", "__tag": 4051, "value": "[-abs(lambda), 180 - abs(lambda)]" }, { "__type": "Text", "__tag": 4046, "value": ", where " }, { "__type": "InlineCode", "__tag": 4051, "value": "lambda" }, { "__type": "Text", "__tag": 4046, "value": " is the angle between the first and third axes." } ] } ] } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Represent as Davenport 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": "axes", "annotation": "array_like, shape (..., [1 or 2 or 3], 3) or (..., 3)", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Axis of rotation, if one dimensional. 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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": 1292, "item_type": "function", "aliases": [ "scipy.spatial.transform.Rotation.as_davenport" ], "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": "\nDavenport angles are a generalization of Euler angles, when we use the\ncanonical basis axes:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "ex = [1, 0, 0]\ney = [0, 1, 0]\nez = [0, 0, 1]\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_davenport([ez, ex, ey], 'extrinsic', degrees=True)\nr.as_euler('zxy', degrees=True)\nr.as_davenport([ez, ex, ey], 'extrinsic', 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_davenport([ez, ex, ey], 'extrinsic', degrees=True)\nr.as_davenport([ez, ex, ey], 'extrinsic', 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, 90],\n[45, 0, 0]], degrees=True)\nr.as_davenport([ez, ex, ey], 'extrinsic', degrees=True)\nr.as_davenport([ez, ex, ey], 'extrinsic', 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": "axes", "annotation": "ArrayLike", "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "order", "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_davenport" }, "references": [ ".. [1] Shuster, Malcolm & Markley, Landis. (2003). Generalization of", " the Euler Angles. Journal of the Astronautical Sciences. 51. 123-132.", " 10.1007/BF03546304.", ".. [2] Bernardes E, Viollet S (2022) Quaternion to Euler angles", " conversion: A direct, general and computationally efficient method.", " PLoS ONE 17(11): e0276302. 10.1371/journal.pone.0276302", ".. [3] https://en.wikipedia.org/wiki/Gimbal_lock#In_applied_mathematics" ], "qa": "scipy.spatial.transform._rotation:Rotation.as_davenport", "arbitrary": [], "local_refs": [ "angles", "axes", "degrees", "order", "suppress_warnings" ] }