+ i.^RIHt^RIHt^RIHtHt^RIHtH t H t H t ^RI H t^RIHt^RIHt^RIt!R R ]4t!R R ]4t!R R]4t!RR]4t!RR]4t!RR]4tRtR#))Basic)sympify)cossin)eye rot_axis1 rot_axis2 rot_axis3)ImmutableDenseMatrix)cacheit)StrNc*a]tRt^ toRtRtRtVtR#)Orienterz' Super-class for all orienter classes. c VP#)z> The rotation matrix corresponding to this orienter instance. )_parent_orientselfs&T/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/vector/orienters.pyrotation_matrixOrienter.rotation_matrixs """N)__name__ __module__ __qualname____firstlineno____doc__r__static_attributes____classdictcell__ __classdict__s@rrr s##rrclaa]tRt^toRtV3RltRt]R4t] R4t ] R4t Rt Vt V;t#) AxisOrienterz# Class to denote an axis orienter. c<\V\PP4'g \ R4h\ V4p\ SV`WV4pWnW#n V#)zaxis should be a Vector) isinstancesympyvectorVector TypeErrorrsuper__new___angle_axis)clsangleaxisobj __class__s&&& rr+AxisOrienter.__new__sN$ 3 34456 6goc$/   rc R#)aI 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/r0s&&&r__init__AxisOrienter.__init__(s8 rc \PPVPV4P 4pVP V4pVP p\^4W"P,, \V4,\^V^,)V^,.V^,^V^,).V^,)V^,^..4\V4,,W"P,,pVPpV#)z The rotation matrix corresponding to this orienter instance. Parameters ========== system : CoordSys3D The coordinate system wrt which the rotation matrix is to be computed ) r&r'expressr0 normalize to_matrixr/rTrMatrixr)rsystemr0theta parent_orients&& rrAxisOrienter.rotation_matrixFs||##DIIv6@@B~~f% a&4&&=0CJ>!d1gXtAw!7"&q'1tAwh!7#'7(DGQ!7!9:>> 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') Nrrrlrmrnros&&&&&rr5BodyOrienter.__init__sn rrN rrrrrrfr+r5rrr s@rrrs I 7 7 rrc4a]tRt^toRtRtRtRtRtVt R#) SpaceOrienterz# Class to denote a space-orienter. Fc4\PWW#V4pV#rBrrs&&&&& rr+SpaceOrienter.__new__rrc R#)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, )) Nrrs&&&&&rr5SpaceOrienter.__init__s` rrNrr s@rrrs I 0 0 rrc|aa]tRtRtoRtV3RltRt]R4t]R4t ]R4t ]R4t R t Vt V;t#) QuaternionOrienteri.z( Class to denote a quaternion-orienter. c b<\V4p\V4p\V4p\V4p\V^,V^,,V^,, V^,, ^W#,W,, ,^W,W$,,,.^W#,W,,,V^,V^,, V^,,V^,, ^W4,W,, ,.^W$,W,, ,^W,W4,,,V^,V^,, V^,, V^,,..4pVPp\SV`WW#V4pWnW&nW6nWFnWVn V#)) rr<r;r*r+_q0_q1_q2_q3r)r.q0q1q2q3r?r1r2s&&&&& rr+QuaternionOrienter.__new__3s_ R[ R[ R[ R["'B!G"3bAg"="$'#*"#rw'8"9"#rw'8"9";#$rw'8"9"$'B!G"3"$'#*,.!G#4"#rw'8"9";#$rw'8"9"#rw'8"9"$'B!G"3"$'#*,.!G#4"5 !6 7 & gocrr2* rc R#)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, )) Nrrs&&&&&rr5QuaternionOrienter.__init__OsJ rcVP#rB)rrs&rrQuaternionOrienter.q0v xxrcVP#rB)rrs&rrQuaternionOrienter.q1zrrcVP#rB)rrs&rrQuaternionOrienter.q2~rrcVP#rB)rrs&rrQuaternionOrienter.q3rrr)rrrrrr+r5rFrrrrrrrGrHs@@rrr.sj8% NrrcV^8Xd\\V4P4#V^8Xd\\V4P4#V^8Xd\\ V4P4#R#)z)DCM for simple axis 1, 2 or 3 rotations. N)r<rr;r r )r0r/s&&rrgrgs^ qyi&(()) i&(()) i&(()) r)sympy.core.basicrsympy.core.sympifyr(sympy.functions.elementary.trigonometricrrsympy.matrices.denserrr r sympy.matrices.immutabler r<sympy.core.cacher sympy.core.symbolr sympy.vectorr&rr#rJrrrrgrrrrsz"&?GGC$! #u #M8M`>>BC %C L< &< ~VVr*r