g. ddlmZddlmZddlmZmZddlmZm Z m Z m Z ddl m ZddlmZddlmZddlZGd d eZGd d eZGd deZGddeZGddeZGddeZdZdS))Basic)sympify)cossin)eye rot_axis1 rot_axis2 rot_axis3)ImmutableDenseMatrix)cacheit)StrNceZdZdZdZdS)Orienterz/ Super-class for all orienter classes. c|jS)zV The rotation matrix corresponding to this orienter instance. )_parent_orientselfs R/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/vector/orienters.pyrotation_matrixzOrienter.rotation_matrixs ""N)__name__ __module__ __qualname____doc__rrrrr s-#####rrcjeZdZdZfdZdZedZedZ edZ xZ S) AxisOrienterz+ Class to denote an axis orienter. ct|tjjst dt |}t |||}||_||_ |S)Nzaxis should be a Vector) isinstancesympyvectorVector TypeErrorrsuper__new___angle_axis)clsangleaxisobj __class__s rr%zAxisOrienter.__new__s`$ 344 7566 6ggooc5$//   rcdS)a Axis rotation is a rotation about an arbitrary axis by some angle. The angle is supplied as a SymPy expr scalar, and the axis is supplied as a Vector. Parameters ========== angle : Expr The angle by which the new system is to be rotated axis : Vector The axis around which the rotation has to be performed Examples ======== >>> from sympy.vector import CoordSys3D >>> from sympy import symbols >>> q1 = symbols('q1') >>> N = CoordSys3D('N') >>> from sympy.vector import AxisOrienter >>> orienter = AxisOrienter(q1, N.i + 2 * N.j) >>> B = N.orient_new('B', (orienter, )) Nr)rr)r*s r__init__zAxisOrienter.__init__(s 8 rctj|j|}||}|j}td||jzz t|ztd|d |dg|dd|d g|d |ddggt|zz||jzz}|j}|S)z The rotation matrix corresponding to this orienter instance. Parameters ========== system : CoordSys3D The coordinate system wrt which the rotation matrix is to be computed r) r r!expressr* normalize to_matrixr)rTrMatrixr)rsystemr*theta parent_orients rrzAxisOrienter.rotation_matrixFs|##DIv66@@BB~~f%% a&&4$&=0CJJ>!d1gXtAw!7"&q'1tAwh!7#'7(DGQ!7!9::z.ThreeAngleOrienter.__new__..x&<<.yrZrc:g|]}|ddS)Z3rTrVs rrYz.ThreeAngleOrienter.__new__..zrZrrPzInvalid rot_type parameterrr2r1)rr namestrupperlenr#joinintr _in_order_rotr6r$r%_angle1_angle2_angle3 _rot_orderr) r(angle1angle2angle3 rot_orderapproved_ordersoriginal_rot_ordera1a2a3r:r+r,s rr%zThreeAngleOrienter.__new__ms i % % '!I-' NN((** I!##CDD D<<)<<< <<)<<< <<)<<< GGI&& O + +899 9 1   1   1   = /!"f--!"f--.!"f--.MM""f--!"f--.!"f--.M& ggoo Y99   +* rc|jSr<)rirs rrmzThreeAngleOrienter.angle1 |rc|jSr<)rjrs rrnzThreeAngleOrienter.angle2rwrc|jSr<)rkrs rrozThreeAngleOrienter.angle3rwrc|jSr<)rlrs rrpzThreeAngleOrienter.rot_orders r) rrrrr%r>rmrnrorpr?r@s@rrBrBhs)))))VXXXXrrBc"eZdZdZdZdZdZdS) BodyOrienterz* Class to denote a body-orienter. TcBt|||||}|Sr<rBr%r(rmrnrorpr+s rr%zBodyOrienter.__new__' ((fff)244 rcdS)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') Nrrrmrnrorps rr.zBodyOrienter.__init__s n rNrrrrrgr%r.rrrr|r|sCI 7 7 7 7 7 rr|c"eZdZdZdZdZdZdS) SpaceOrienterz+ Class to denote a space-orienter. FcBt|||||}|Sr<r~rs rr%zSpaceOrienter.__new__rrcdS)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 rr.zSpaceOrienter.__init__s ` rNrrrrrrsCI 0 0 0 0 0 rrceZdZdZfdZdZedZedZedZ edZ xZ S)QuaternionOrienterz0 Class to denote a quaternion-orienter. c bt|}t|}t|}t|}t|dz|dzz|dzz |dzz d||z||zz zd||z||zzzgd||z||zzz|dz|dzz |dzz|dzz d||z||zz zgd||z||zz zd||z||zzz|dz|dzz |dzz |dzzgg}|j}t|||||}||_||_||_||_||_ |S)Nr1) rr7r6r$r%_q0_q1_q2_q3r)r(q0q1q2q3r:r+r,s rr%zQuaternionOrienter.__new__3s R[[ R[[ R[[ R[["'B!G"3bAg"="$'#*"#rBwb'8"9"#rBwb'8"9";#$rBwb'8"9"$'B!G"3"$'#*,.!G#4"#rBwb'8"9";#$rBwb'8"9"#rBwb'8"9"$'B!G"3"$'#*,.!G#4"5 !6 7 7 & ggooc2r2r22* rcdS)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 rr.zQuaternionOrienter.__init__Os J rc|jSr<)rrs rrzQuaternionOrienter.q0v xrc|jSr<)rrs rrzQuaternionOrienter.q1zrrc|jSr<)rrs rrzQuaternionOrienter.q2~rrc|jSr<)rrs rrzQuaternionOrienter.q3rr) rrrrr%r.r>rrrrr?r@s@rrr.s8% % % NXXXXrrc|dkr!tt|jS|dkr!tt|jS|dkr!tt |jSdS)z)DCM for simple axis 1, 2 or 3 rotations. r2r1r0N)r7rr6r r )r*r)s rrhrhso qyyi&&())) i&&())) i&&())) r)sympy.core.basicrsympy.core.sympifyr(sympy.functions.elementary.trigonometricrrsympy.matrices.denserrr r sympy.matrices.immutabler r7sympy.core.cacher sympy.core.symbolr sympy.vectorr rrrBr|rrrhrrrrs""""""&&&&&&????????GGGGGGGGGGGGCCCCCC$$$$$$!!!!!! # # # # #u # # #MMMMM8MMM`>>>>>>>>BC C C C C %C C C L< < < < < &< < < ~VVVVVVVVr*****r