l jD]$dZddlmZddlZddlmZmZddlm Z ddl Z ddl m ZddlmZddlmZmZmZmZmZmZdd lmZe r$ddlmZdd lmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)gd Z*ddZ+ddZ,ddZ- ddd Z.dd"Z/dd#Z0efdd%Z1ddd+Z2dd.Z3dd/Z4dd0Z5 ddd2Z6dd3Z7dd4Z8dd6Z9dd7Z: ddd<Z;dd>ZdFddGddLZ?ddOZ@ddQZAddUZBddYZCdd]ZDddaZE dddkZFddlZGddoZHddqZIddvZJddzZKdd|ZLdd~ZMefddZNdS)z9Utility functions for two- and three-dimensional vectors.) annotationsN)CallableSequence) TYPE_CHECKING)triangulate_float32)Rotation)DOWNOUTPIRIGHTTAUUP)adjacent_pairs) ManimFloatMatrixMN Point2D_ArrayPoint3D Point3DLikePoint3DLike_ArrayPointNDPointNDLike_ArrayVector2DVector2D_ArrayVector3D Vector3DLikeVector3DLike_Array)quaternion_multquaternion_from_angle_axisangle_axis_from_quaternionquaternion_conjugate rotate_vectorthick_diagonalrotation_matrixrotation_about_z z_to_vectorangle_of_vectorangle_between_vectors normalizeget_unit_normalcompass_directionsregular_vertices complex_to_R3 R3_to_complexcomplex_func_to_R3_funccenter_of_massmidpointfind_intersectionline_intersectionget_winding_numbershoelaceshoelace_directioncross2dearclip_triangulationcartesian_to_sphericalspherical_to_cartesianperpendicular_bisectorvfloatreturnc0tj||}|SN)npdot)r;vals P/home/agentuser/manim-venv/lib/python3.11/site-packages/manim/utils/space_ops.py norm_squaredrDEs1C Jv1rv2rctj|d|dz|d|dzz |d|dz|d|dzz |d|dz|d|dzz gS)Nrr@array)rFrGs rCcrossrMJs{ 8 qEBqEMBqEBqEM ) qEBqEMBqEBqEM ) qEBqEMBqEBqEM )   rEquatsSequence[float]%np.ndarray | list[float | np.ndarray]c.t|dkrgdS|d}|ddD]j}|\}}}}|\}}} } ||z||zz || zz || zz ||z||zz|| zz|| zz || z||zz||zz|| zz || z||zz|| zz||zz g}k|S)a(Gets the Hamilton product of the quaternions provided. For more information, check `this Wikipedia page `__. Returns ------- Union[np.ndarray, List[Union[float, np.ndarray]]] Returns a list of product of two quaternions. r)rIrrrrIN)len) rNresult next_quatw1x1y1z1w2x2y2z2s rCrrXs 5zzQ|| 1XF122Y  BB"BB Gb2g R '"r' 1 Gb2g R '"r' 1 Gb2g R '"r' 1 Gb2g R '"r' 1   MrEFangleaxis np.ndarrayaxis_normalizedbool list[float]c|st|}tj|dz gtj|dz |zS)aGets a quaternion from an angle and an axis. For more information, check `this Wikipedia page `__. Parameters ---------- angle The angle for the quaternion. axis The axis for the quaternion axis_normalized Checks whether the axis is normalized, by default False Returns ------- list[float] Gives back a quaternion from the angle and axis rJ)r(r@cossin)r]r^r`s rCrrssF.  F519   ; !2!2T!9 ;;rE quaternionct|ddtjgd}dtj|dz}|tdz kr t|z }||fS)zGets angle and axis from a quaternion. Parameters ---------- quaternion The quaternion from which we get the angle and axis. Returns ------- Sequence[float] Gives the angle and axis rINrIrr) fall_backrJr)r(r@rLarccosr )rfr^r]s rCrrsd Z^rx /B/B C C CD  *Q-(( (E sQwe  $;rEcRtj|}|ddxxdzcc<|S)zUsed for finding the conjugate of the quaternion Parameters ---------- quaternion The quaternion for which you want to find the conjugate for. Returns ------- np.ndarray The conjugate of the quaternion. rINrK)rfrSs rCr r s2Xj ! !F 122JJJ"JJJ MrEvectorct|dkrtdt|dkrtj|d}t |||zS)aFunction for rotating a vector. Parameters ---------- vector The vector to be rotated. angle The angle to be rotated by. axis The axis to be rotated, by default OUT Returns ------- np.ndarray The rotated vector with provided angle and axis. Raises ------ ValueError If vector is not of dimension 2 or 3. z(Vector must have the correct dimensions.rJr)rR ValueErrorr@appendr#)rmr]r^s rCr!r!sY0 6{{QCDDD 6{{a61%% 5$ ' '& 00rErJdimint thicknessrctj||||f}tj|}tj||z |kdS)Nuint8)r@arangerepeatreshape transposeabsastype)rrrt row_indices col_indicess rCr"r"sf)C..'',,44c3Z@@K,{++K F;, - - 9 A A' J JJrEquatlist[np.ndarray]cTtfdgdgdgdfDS)aConverts the quaternion, quat, to an equivalent rotation matrix representation. For more information, check `this page `_. Parameters ---------- quat The quaternion which is to be converted. Returns ------- List[np.ndarray] Gives back the Rotation matrix representation, returned as a 3-by-3 matrix or 3-by-3-by-N multidimensional array. cHg|]}tdg|ddS)rrIN)r).0basisrquat_invs rC z=rotation_matrix_transpose_from_quaternion..sD     qk5k844QRR8   rErh)rrIrrrrI)r )rrs`@rC)rotation_matrix_transpose_from_quaternionrs\ $D))H      II II II    rEcDtjt|Sr?)r@rzr)rs rCrotation_matrix_from_quaternionrs <A$GG H HHrEcttj|ddtjdkr/t |tj|dzjSt||jSNrJ)allr@rLzerosr$signTr#)r]r^s rCrotation_matrix_transposersg 28D>>"1" ! ,--<Q(8(8 899;; 5$ ' ' ))rE homogeneousctj|t|z}|s|St jd}||ddddf<|S)z3Rotation in R^3 about a specified axis of rotation.Nro)r from_rotvecr( as_matrixr@eye)r]r^rinhomogeneous_rotation_matrixr#s rCr#r#si %-$8 $%%ikk" ,,&))"?BQBrEctj|tj|}}tj|| dg||dggdgS)zReturns a rotation matrix for a given angle. Parameters ---------- angle Angle for the rotation matrix. Returns ------- np.ndarray Gives back the rotated matrix. rr)r@rdrerL)r]css rCr$r$sQ 6%=="&--qA 8 AJ 1I II   rEcht|}tt|t}t||}tj|dkr3ttt |}t|| }tj|||gjS)zt Returns some matrix in SO(3) which takes the z-axis to the (normalized) vector provided as an argument r) r(rMr r@linalgnormrrLr)rmaxis_zaxis_yaxis_xs rCr%r%'s v  F uVU++ , ,F 66 " "F y~~f""5V,,--''' 8VVV, - - //rESequence[float] | np.ndarrayct|tjrt|jdkr{|jddkrt dtj|jdtj}|d|_|d|_ tj |}|Stj t|dd}|S)zReturns polar coordinate theta when vector is projected on xy plane. Parameters ---------- vector The vector to find the angle for. Returns ------- float The angle of the vector projected. rIrrJz/Vector must have the correct dimensions. (2, n)dtypeN) isinstancer@ndarrayrRshaperpempty complex128realimagr]complex)rmc_vecval1rBs rCr&r&7s&"*%%#fl*;*;a*?*? <?Q  NOO Oa >>>AY AY huoo '6"1":.//C JrEc dtjtjt |t |z tjt |t |zz}|S)aReturns the angle between two vectors. This angle will always be between 0 and pi Parameters ---------- v1 The first vector. v2 The second vector. Returns ------- float The angle between the vectors. rJ)r@arctan2rrr()rFrGrBs rCr'r'Psg RZ y}}y}}455 y}}y}}455C JrEvectnp.ndarray | tuple[float]rinp.ndarray | Nonectj|}|dkrtj||z S|p tjt |SNr)r@rrrLrrR)rrirs rCr(r(hsN 9>>$  D axxx~~$$/BHSYY///rErLctj||z|}d||dk<tj||j||j}||z}|S)aNormalizes an array with the provided axis. Parameters ---------- array The array which has to be normalized. axis The axis to be normalized to. Returns ------- np.ndarray Array which has been normalized according to the axis. rIr)r@sqrtsumrxrry)rLr^norms buffed_normss rCnormalize_along_axisrrsj GUU]''-- . .EE%1*9UEK$566>>u{KKL \E LrEư>tolctj|}tj|}ttj|ttj|}}|dkr|dkrtS||z }nT|dkr||z }nH||z ||z } }t || } tjt| } | |kr| | z S|}t|d|kr t|d|krtStj|d |dz|d |dz|d|dz|d|dzzg} tjt| } | | z S)aGets the unit normal of the vectors. Parameters ---------- v1 The first vector. v2 The second vector tol [description], by default 1e-6 Returns ------- np.ndarray The normal of the two vectors. grrIrJ) r@asarraymaxr{r rMrrDrL) rFrGrnp_v1np_v2div1div2uu1u2cpcp_norms rCr)r)sn" JrNNE JrNNERVE]]##S%7%7$D s{{ 3;;K DL  DLut|B 2r]]',r**++ S==<   1Q4yy33qt99s??  AaD51Q4.s'LLLa]:q5y99LLLrE)r r@rLrange)rrr]s `@rCr*r*s= !GE 8LLLLL588LLL M MMrErI)radius start_anglerr float | Nonetuple[np.ndarray, float]c||dzdkrdn tdz }tt|z|}t||}||fS)a@Generates regularly spaced vertices around a circle centered at the origin. Parameters ---------- n The number of vertices radius The radius of the circle that the vertices are placed on. start_angle The angle the vertices start at. If unspecified, for even ``n`` values, ``0`` will be used. For odd ``n`` values, 90 degrees is used. Returns ------- vertices : :class:`numpy.ndarray` The regularly spaced vertices. start_angle : :class:`float` The angle the vertices start at. NrJrr)r r!r r*)rrr start_vectorverticess rCr+r+sP0q5A::aa37  ==L!!\22H [  rE complex_numrcDtj|j|jdfSr)r@rLrr)rs rCr,r,s 8[%{'7; < <z)complex_func_to_R3_func..s!]<< a0@0@#A#ABBrEr)rs`rCr.r.s C B B BBrEpointsrrc ltj|dtjt|S)zGets the center of mass of the points in space. Parameters ---------- points The points to find the center of mass from. Returns ------- np.ndarray The center of mass of the points. r)r@averageonesrR)rs rCr/r/s( :faV!5!5 6 66rEpoint1point2float | np.ndarrayc$t||gS)zGets the midpoint of two points. Parameters ---------- point1 The first point. point2 The second point. Returns ------- Union[float, np.ndarray] The midpoint of the points )r/)rrs rCr0r0s$ 66* + ++rEline1Sequence[np.ndarray]line2clttj||gdddddfdrt dd||fD}d|D\}}t ||\}}}|dkrt dtj||z ||z dgS) a9Returns the intersection point of two lines, each defined by a pair of distinct points lying on the line. Parameters ---------- line1 A list of two points that determine the first line. line2 A list of two points that determine the second line. Returns ------- np.ndarray The intersection points of the two lines which are intersecting. Raises ------ ValueError Error is produced if the two lines don't intersect with each other or if the coordinates don't lie on the xy-plane. NrJrlzCoords must be in the xy-plane.c3K|]9}tjtj|ddddfddV:dS)NrJ))rr)rrIrI)constant_values)r@padrLris rC z$line_intersection..Dsa  rx{{111bqb5!#3QGGGrEc3(K|] }t|VdSr?)rMrs rCrz$line_intersection..Hs&..!E1I......rErz>The lines are parallel, there is no unique intersection point.)anyr@rLryrprM)rrpaddedxyzs rCr2r2's0 28UEN # #AAAqqq!G , 4 4R 8 899<:;;;F/.v...LE5E5!!GAq!Avv L    8QUAE1% & &&rEh㈵>p0srv0srp1sv1s threshold list[Point3D]cg}t||||dD]m\}}}} t| t|| } ttj|| |} ||tj||z | | z |zzgz }n|S)a' Return the intersection of a line passing through p0 in direction v0 with one passing through p1 in direction v1 (or array of intersections from arrays of such points/directions). For 3d values, it returns the point on the ray p0 + v0 * t closest to the ray p1 + v1 * t Tstrict)ziprMrr@rA) rrrrrrSp0v0p1rFnormaldenoms rCr1r1SsFc3S>>>>>BBr5R==))BF2v&& 222rBw//%7"<<== MrEcd}t|D]C\}}t|t|z }|tztztz }||z }D|tz }|S)a!Determine the number of times a polygon winds around the origin. The orientation is measured mathematically positively, i.e., counterclockwise. Parameters ---------- points The vertices of the polygon being queried. Examples -------- >>> from manim import Square, UP, get_winding_number >>> polygon = Square() >>> get_winding_number(polygon.get_vertices()) np.float64(1.0) >>> polygon.shift(2 * UP) Square >>> get_winding_number(polygon.get_vertices()) np.float64(0.0) r)rr&r r )r total_angler p2d_anglerBs rCr3r3ksl.K ((B!"%%(;(;;bLC'2-w s"C JrEx_yrc`|dddf}|dddf}tj||}|S)zx2D implementation of the shoelace formula. Returns ------- :class:`float` Returns signed area. NrrI)r@ trapezoid)rrrrBs rCr4r4s< AAAqD A AAAqD Aa##C JrEstrc4t|}|dkrdndS)z Uses the area determined by the shoelace method to determine whether the input set of points is directed clockwise or counterclockwise. Returns ------- :class:`str` Either ``"CW"`` or ``"CCW"``. rCWCCW)r4)rareas rCr5r5s! C==D!8844&rEaVector2D | Vector2D_Arrayb$ManimFloat | npt.NDArray[ManimFloat]ct|jdkr3|dddf|dddfz|dddf|dddfzz S|d|dz|d|dzz S)aCompute the determinant(s) of the passed vector (sequences). Parameters ---------- a A vector or a sequence of vectors. b A vector or a sequence of vectors. Returns ------- Sequence[float] | float The determinant or sequence of determinants of the first two components of the specified vectors. Examples -------- .. code-block:: pycon >>> cross2d(np.array([1, 2]), np.array([3, 4])) np.int64(-2) >>> cross2d( ... np.array([[1, 2, 0], [1, 0, 0]]), ... np.array([[3, 4, 0], [0, 1, 0]]), ... ) array([-2, 1]) rJNrrI)rRr)rrs rCr6r6sB 17||qAw111a4 1QQQT7Qqqq!tW#444tad{QqTAaD[((rEverts ring_endslistc dtdg||dD}|dd}|dd}i|rfd||fD\}}t|d|t|dzt|fd   t| fd  t|fd    < <t fd |Dd}|+||||ntd|g}d} |D]?} |t| dz| || | } @gd ttt|zdz D]S} vr(  g| n |  dkrnTtddftj tgtj } fd| DS)a|Returns a list of indices giving a triangulation of a polygon, potentially with holes. Parameters ---------- verts verts is a numpy array of points. ring_ends ring_ends is a list of indices indicating where the ends of new paths are. Returns ------- list A list of indices giving a triangulation of a polygon. cNg|]"\}}tt||#Sr)rr)re0e1s rCrz)earclip_triangulation..s9    &BU2r]]   rErFrNrIc 3pK|]0}ttfdtj|V1dS)c |vSr?r)rloop_connectionss rCrz1earclip_triangulation...s a'77rEN)rfilteritchain)r ring_groupr&s rCrz(earclip_triangulation..sh    8777Hj)          rErJc4t|z Sr?rD)r tmp_j_vertrs rCrz'earclip_triangulation..s|E!Hz4I'J'JrE)keyc@t|z Sr?r,)jrrs rCrz'earclip_triangulation..|E!HuQx4G'H'HrEc@t|z Sr?r,)rr0rs rCrz'earclip_triangulation..r1rEc3TK|]"}|dcxkr |dknn|V#dS)rrlNr)rringr0s rCrz(earclip_triangulation..sL H HdQ10G0G0G0GtBx0G0G0G0G0GT0G0G0G0G H HrEzCould not find a ring to attachrc g|] }| Srr)rmiindicess rCrz)earclip_triangulation..(s / / /BGBK / / /rE)rr0rRminnextremoverq Exceptionextendrearcutr@rLuint32)rrringsattached_ringsdetached_ringsi_rangej_rangenew_ringafterend0end1_ meta_indicesrr7r0r&r-s` @@@@@rCr7r7s*  *-qo9oyQV*W*W*W   E2A2YN122YN $?      .~>    eGAJ/ws7||q?P7Q1RSS JJJJJ K K K HHHHH I I I HHHHH I I I  H H H Hn H H H$      ! !( + + +  ! !( + + + +=>> >I $?NE D U4!8T**+++ TG A 3u::I.2 3 3     #A NNAq6 " " "aAA NN1   aA 66 E %! ,bhG ~RY.W.W.WXXL / / / /, / / //rEvecc"tj|}|dkrtjdS|}tj|d|z }tj|d|d}tj|||gS)zReturns an array of numbers corresponding to each polar coordinate value (distance, phi, theta). Parameters ---------- vec A numpy array or a sequence of floats ``[x, y, z]``. rrorJrI)r@rrrrjrrL)rJrrphithetas rCr8r8+sy 9>>#  D qyyx{{ A )CFQJ  C Js1vs1v & &E 8QsO $ $$rE sphericalc|\}}}tj|tj|ztj|z|tj|ztj|z|tj|zgS)aReturns a numpy array ``[x, y, z]`` based on the spherical coordinates given. Parameters ---------- spherical A list of three floats that correspond to the following: r - The distance between the point and the origin. theta - The azimuthal angle of the point to the positive x-axis. phi - The vertical angle of the point to the positive z-axis. )r@rLrdre)rOrLrNrMs rCr9r9=sqMAuc 8 u s + u s + s O   rEline norm_vectorc||d}|d}t||z |}t||}||z||z gS)aReturns a list of two points that correspond to the ends of the perpendicular bisector of the two points given. Parameters ---------- line a list of two numpy array points (corresponding to the ends of a line). norm_vector the vector perpendicular to both the line given and the perpendicular bisector. Returns ------- list A list of two numpy array points that correspond to the ends of the perpendicular bisector rrI)rMr0)rQrRr r directionms rCr:r:VsK. aB aBb2g{++IRA M1y= ))rE)r;r<r=r<)rFrrGrr=r)rNrOr=rP)F)r]r<r^r_r`rar=rb)rfrOr=rO)rfrOr=r_)rmrr]r<r^rr=r)rJ)rrrsrtrsr=r)rr_r=r)rr_r=r_)r]r<r^rr=r_)r]r<r^rrrar=r_)r]r<r=r_)rmr_r=r_)rmrr=r<)rFr_rGr_r=r<r?)rrrirr=r_)rLr_r^r_r=r_)r)rFrrGrrr<r=r)rrsrr_r=r_)rrsrr<rrr=r)rrr=r_)rrOr=r_)rrr=r)rrr=r)rrOrrOr=r)rrrrr=r_)r) rrrrrrrrrr<r=r)rrr=r<)rrr=r<)rrr=r)rrrrr=r)rr_rrr=r)rJrr=r_)rOrOr=r_)rQrrRrr=r)O__doc__ __future__r itertoolsr(collections.abcrrtypingrnumpyr@ mapbox_earcutrr=scipy.spatial.transformrmanim.constantsr r r r r rmanim.utils.iterablesr numpy.typingnpt manim.typingrrrrrrrrrrrrr__all__rDrMrrrr r!r"rrrr#r$r%r&r'r(rr)r*r+r,r-r.r/r0r2r1r3r4r5r6r7r8r9r:rrErCrds??""""""........ 777777,,,,,,9999999999999999000000    D <"<<<<<8(&>A11111>KKKKK 6IIII****". 0 0 0 0 22EI00000,22222p!"ENNNNN( !d!!!!!!B====CCCC 7 7 7 7 ,,,,*)')')')'b 0@     ' ' ' '$)$)$)$)NZ0Z0Z0Z0z%%%%$6 *******rE