o GZŽh.ã@sØddlmZddlmZddlmZmZddlmZm Z m Z m Z ddl m ZddlmZddlmZddlZGd d „d eƒZGd d „d eƒZGd d„deƒZGdd„deƒZGdd„deƒZGdd„deƒZdd„ZdS)é)ÚBasic)Úsympify)ÚcosÚsin)ÚeyeÚ rot_axis1Ú rot_axis2Ú rot_axis3)ÚImmutableDenseMatrix)Úcacheit)ÚStrNc@seZdZdZdd„ZdS)ÚOrienterz/ Super-class for all orienter classes. cCó|jS)zV The rotation matrix corresponding to this orienter instance. )Ú_parent_orient©Úself©rúE/var/www/auris/lib/python3.10/site-packages/sympy/vector/orienters.pyÚrotation_matrixszOrienter.rotation_matrixN)Ú__name__Ú __module__Ú __qualname__Ú__doc__rrrrrr s r csLeZdZdZ‡fdd„Zdd„Zedd„ƒZedd „ƒZ ed d „ƒZ ‡Z S) Ú AxisOrienterz+ Class to denote an axis orienter. cs>t|tjjƒs tdƒ‚t|ƒ}tƒ |||¡}||_||_ |S)Nzaxis should be a Vector) Ú isinstanceÚsympyÚvectorZVectorÚ TypeErrorrÚsuperÚ__new__Ú_angleÚ_axis)ÚclsÚangleÚaxisÚobj©Ú __class__rrrszAxisOrienter.__new__cCódS)aá Axis rotation is a rotation about an arbitrary axis by some angle. The angle is supplied as a SymPy expr scalar, and the axis is supplied as a Vector. Parameters ========== angle : Expr The angle by which the new system is to be rotated axis : Vector The axis around which the rotation has to be performed Examples ======== >>> from sympy.vector import CoordSys3D >>> from sympy import symbols >>> q1 = symbols('q1') >>> N = CoordSys3D('N') >>> from sympy.vector import AxisOrienter >>> orienter = AxisOrienter(q1, N.i + 2 * N.j) >>> B = N.orient_new('B', (orienter, )) Nr)rr#r$rrrÚ__init__(szAxisOrienter.__init__cCs˜tj |j|¡ ¡}| |¡}|j}tdƒ||jt |ƒt d|d |dg|dd|d g|d |ddggƒt |ƒ||j}|j}|S)zø The rotation matrix corresponding to this orienter instance. Parameters ========== system : CoordSys3D The coordinate system wrt which the rotation matrix is to be computed éréé) rrZexpressr$Ú normalizeZ to_matrixr#rÚTrÚMatrixr)rÚsystemr$ÚthetaÚ parent_orientrrrrFs þþÿüzAxisOrienter.rotation_matrixcCr©N)r rrrrr#_ózAxisOrienter.anglecCrr3)r!rrrrr$cr4zAxisOrienter.axis) rrrrrr)r rÚpropertyr#r$Ú __classcell__rrr&rrs    rcsPeZdZdZ‡fdd„Zedd„ƒZedd„ƒZedd „ƒZed d „ƒZ ‡Z S) ÚThreeAngleOrienterz3 Super-class for Body and Space orienters. c s<t|tƒr|j}d}|}t|ƒ ¡}t|ƒdkstdƒ‚dd„|Dƒ}dd„|Dƒ}dd„|Dƒ}d |¡}||vr>td ƒ‚t|d ƒ}t|d ƒ}t|d ƒ} t |ƒ}t |ƒ}t |ƒ}|j rot ||ƒt ||ƒt | |ƒ} nt | |ƒt ||ƒt ||ƒ} | j } t ƒ ||||t|ƒ¡} || _|| _|| _|| _| | _| S) N) Z123Z231Z312Z132Z213Z321Z121Z131Z212Z232Z313Z323Úr*z%rot_order should be a str of length 3cSóg|]}| dd¡‘qS)ÚXÚ1©Úreplace©Ú.0ÚirrrÚ xóz.ThreeAngleOrienter.__new__..cSr9)ÚYÚ2r<r>rrrrAyrBcSr9)ÚZÚ3r<r>rrrrAzrBr8zInvalid rot_type parameterrr,r+)rr ÚnameÚstrÚupperÚlenrÚjoinÚintrÚ _in_orderÚ_rotr.rrÚ_angle1Ú_angle2Ú_angle3Ú _rot_orderr) r"Úangle1Úangle2Úangle3Ú rot_orderZapproved_ordersZoriginal_rot_orderZa1Za2Úa3r2r%r&rrrmsP       ÿþÿþÿzThreeAngleOrienter.__new__cCrr3)rOrrrrrS˜r4zThreeAngleOrienter.angle1cCrr3)rPrrrrrTœr4zThreeAngleOrienter.angle2cCrr3)rQrrrrrU r4zThreeAngleOrienter.angle3cCrr3)rRrrrrrV¤r4zThreeAngleOrienter.rot_order) rrrrrr5rSrTrUrVr6rrr&rr7hs +   r7c@ó$eZdZdZdZdd„Zdd„ZdS)Ú BodyOrienterz* Class to denote a body-orienter. TcCót |||||¡}|Sr3©r7r©r"rSrTrUrVr%rrrr°ó ÿzBodyOrienter.__new__cCr()a’ Body orientation takes this coordinate system through three successive simple rotations. Body fixed rotations include both Euler Angles and Tait-Bryan Angles, see https://en.wikipedia.org/wiki/Euler_angles. Parameters ========== angle1, angle2, angle3 : Expr Three successive angles to rotate the coordinate system by rotation_order : string String defining the order of axes for rotation Examples ======== >>> from sympy.vector import CoordSys3D, BodyOrienter >>> from sympy import symbols >>> q1, q2, q3 = symbols('q1 q2 q3') >>> N = CoordSys3D('N') A 'Body' fixed rotation is described by three angles and three body-fixed rotation axes. To orient a coordinate system D with respect to N, each sequential rotation is always about the orthogonal unit vectors fixed to D. For example, a '123' rotation will specify rotations about N.i, then D.j, then D.k. (Initially, D.i is same as N.i) Therefore, >>> body_orienter = BodyOrienter(q1, q2, q3, '123') >>> D = N.orient_new('D', (body_orienter, )) is same as >>> from sympy.vector import AxisOrienter >>> axis_orienter1 = AxisOrienter(q1, N.i) >>> D = N.orient_new('D', (axis_orienter1, )) >>> axis_orienter2 = AxisOrienter(q2, D.j) >>> D = D.orient_new('D', (axis_orienter2, )) >>> axis_orienter3 = AxisOrienter(q3, D.k) >>> D = D.orient_new('D', (axis_orienter3, )) Acceptable rotation orders are of length 3, expressed in XYZ or 123, and cannot have a rotation about about an axis twice in a row. >>> body_orienter1 = BodyOrienter(q1, q2, q3, '123') >>> body_orienter2 = BodyOrienter(q1, q2, 0, 'ZXZ') >>> body_orienter3 = BodyOrienter(0, 0, 0, 'XYX') Nr©rrSrTrUrVrrrr)µs7zBodyOrienter.__init__N©rrrrrMrr)rrrrrY©ó  rYc@rX)Ú SpaceOrienterz+ Class to denote a space-orienter. FcCrZr3r[r\rrrrör]zSpaceOrienter.__new__cCr()a¢ Space rotation is similar to Body rotation, but the rotations are applied in the opposite order. Parameters ========== angle1, angle2, angle3 : Expr Three successive angles to rotate the coordinate system by rotation_order : string String defining the order of axes for rotation See Also ======== BodyOrienter : Orienter to orient systems wrt Euler angles. Examples ======== >>> from sympy.vector import CoordSys3D, SpaceOrienter >>> from sympy import symbols >>> q1, q2, q3 = symbols('q1 q2 q3') >>> N = CoordSys3D('N') To orient a coordinate system D with respect to N, each sequential rotation is always about N's orthogonal unit vectors. For example, a '123' rotation will specify rotations about N.i, then N.j, then N.k. Therefore, >>> space_orienter = SpaceOrienter(q1, q2, q3, '312') >>> D = N.orient_new('D', (space_orienter, )) is same as >>> from sympy.vector import AxisOrienter >>> axis_orienter1 = AxisOrienter(q1, N.i) >>> B = N.orient_new('B', (axis_orienter1, )) >>> axis_orienter2 = AxisOrienter(q2, N.j) >>> C = B.orient_new('C', (axis_orienter2, )) >>> axis_orienter3 = AxisOrienter(q3, N.k) >>> D = C.orient_new('C', (axis_orienter3, )) Nrr^rrrr)ûs0zSpaceOrienter.__init__Nr_rrrrraïr`racsXeZdZdZ‡fdd„Zdd„Zedd„ƒZedd „ƒZed d „ƒZ ed d „ƒZ ‡Z S)ÚQuaternionOrienterz0 Class to denote a quaternion-orienter. cs0t|ƒ}t|ƒ}t|ƒ}t|ƒ}t|d|d|d|dd||||d||||gd|||||d|d|d|dd||||gd||||d|||||d|d|d|dggƒ}|j}tƒ |||||¡}||_||_||_||_||_ |S)Nr+) rr/r.rrÚ_q0Ú_q1Ú_q2Ú_q3r)r"Úq0Úq1Úq2Úq3r2r%r&rrr3sFÿýÿÿýÿÿþø zQuaternionOrienter.__new__cCr()a¨ Quaternion orientation orients the new CoordSys3D with Quaternions, defined as a finite rotation about lambda, a unit vector, by some amount theta. This orientation is described by four parameters: q0 = cos(theta/2) q1 = lambda_x sin(theta/2) q2 = lambda_y sin(theta/2) q3 = lambda_z sin(theta/2) Quaternion does not take in a rotation order. Parameters ========== q0, q1, q2, q3 : Expr The quaternions to rotate the coordinate system by Examples ======== >>> from sympy.vector import CoordSys3D >>> from sympy import symbols >>> q0, q1, q2, q3 = symbols('q0 q1 q2 q3') >>> N = CoordSys3D('N') >>> from sympy.vector import QuaternionOrienter >>> q_orienter = QuaternionOrienter(q0, q1, q2, q3) >>> B = N.orient_new('B', (q_orienter, )) Nrr^rrrr)Os%zQuaternionOrienter.__init__cCrr3)rcrrrrrgvr4zQuaternionOrienter.q0cCrr3)rdrrrrrhzr4zQuaternionOrienter.q1cCrr3)rerrrrri~r4zQuaternionOrienter.q2cCrr3)rfrrrrrj‚r4zQuaternionOrienter.q3) rrrrrr)r5rgrhrirjr6rrr&rrb.s '   rbcCsF|dkr tt|ƒjƒS|dkrtt|ƒjƒS|dkr!tt|ƒjƒSdS)z)DCM for simple axis 1, 2 or 3 rotations. r,r+r*N)r/rr.rr )r$r#rrrrN‡sÿrN)Zsympy.core.basicrZsympy.core.sympifyrZ(sympy.functions.elementary.trigonometricrrZsympy.matrices.denserrrr Zsympy.matrices.immutabler r/Zsympy.core.cacher Zsympy.core.symbolr Z sympy.vectorrr rr7rYrarbrNrrrrÚs     PAF? Y