^ jKdZddlmZddlZddlZddlZdd Z Gd d ej Z Gd d ej Z Gddej Z Gddej ZGddej ZGddej ZdS)a-Matrix and Vector math. This module provides Vector and Matrix objects, including Vec2, Vec3, Vec4, Mat3, and Mat4. Most common matrix and vector operations are supported. Helper methods are included for rotating, scaling, and transforming. The :py:class:`~pyglet.matrix.Mat4` includes class methods for creating orthographic and perspective projection matrixes. Matrices behave just like they do in GLSL: they are specified in column-major order and multiply on the left of vectors, which are treated as columns. All objects are immutable and hashable. ) annotationsNnumfloatminimummaximumreturnc>tt|||S)z2Clamp a value between a minimum and maximum limit.)maxmin)rrrs F/home/agentuser/manim-venv/lib/python3.11/site-packages/pyglet/math.pyclampr s s3  ' * **ceZdZUdZdZded<dZded<dZdHd ZdHd Z dHd Z dHd Z dIdZ dIdZ dIdZdIdZdIdZdIdZdJdZdJdZdKdLdZdJdZdJdZdJdZdHdZdHd ZdMd#ZedNdOd'ZedNdPd)ZdQd*ZdQd+ZdQd,Z dRd/Z!dSd1Z"dTd3Z#dUd4Z$dVd6Z%dJd7Z&e'j(rDe'j)dWd:Z*e'j)dXd;Z*e'j)dYd<Z*e'j)dZd=Z*d[d>Z*d\d?Z+d]dCZ,d^dGZ-dS)_Vec2aA two-dimensional vector represented as an X Y coordinate pair. `Vec2` is an immutable 2D Vector, including most common operators. As an immutable type, all operations return a new object. .. note:: The Python ``len`` operator returns the number of elements in the vector. For the vector length, use the `length()` method. .. note:: Python's :py:func:`sum` requires the first item to be a ``Vec2``. After that, you can mix ``Vec2``-like :py:class:`tuple` and ``Vec2`` instances freely in the iterable. If you do not, you will see a :py:class:`TypeError` about being unable to add a :py:class:`tuple` and a :py:class:`int`. rxyc.|jdkp |jdkSNr)rrselfs r __bool__z Vec2.__bool__6sv}-# -rother"Vec2 | tuple[float, float] | floatrc t|d|dz|d|dzS#t$r%t|d|z|d|zcYSwxYwNrr TypeErrorrrs r __add__z Vec2.__add__9 Q%("DGeAh$6    Q%a5    -0,AAcp ||S#t$r}|dkr|cYd}~S|d}~wwxYwNr)r!rrrerrs r __radd__z Vec2.__radd__CsU <<&& &   zz I s 50505c t|d|dz |d|dz S#t$r%t|d|z |d|z cYSwxYwrrr s r __sub__z Vec2.__sub__Kr"r#c t|d|dz |d|dz S#t$r%t||dz ||dz cYSwxYwrrr s r __rsub__z Vec2.__rsub__Us a47"E!HtAw$6    Qa    r#scalar"float | Vec2 | tuple[float, float]c t|d|dz|d|dzS#t$r%t|d|z|d|zcYSwxYwrrrr-s r __mul__z Vec2.__mul___ Q&)#T!Wvay%8    Q& $q'F"2    r#c t|d|dz|d|dzS#t$r%t|d|z|d|zcYSwxYwrrr0s r __rmul__z Vec2.__rmul__ir2r#c t|d|dz |d|dz S#t$r%t|d|z |d|z cYSwxYwrrr0s r __truediv__zVec2.__truediv__sr2r#c t|d|dz |d|dz S#t$r%t||dz ||dz cYSwxYwrrr0s r __rtruediv__zVec2.__rtruediv__}s q DG#VAYa%8    a &47"2    r#c t|j|dz|j|dzS#t$r%t|d|z|d|zcYSwxYwr)rrrrr0s r __floordiv__zVec2.__floordiv__s &)#TVvay%8    Q6!47f#4    s+.,AAc t|d|dz|d|dzS#t$r%t||dz||dzcYSwxYwrrr0s r __rfloordiv__zVec2.__rfloordiv__s q T!W$fQi47&:    $q'!6T!W#4    r#cntt|dt|dSr)rabsrs r __abs__z Vec2.__abs__s&CQLL#d1g,,///rc>t|d |d Srrrs r __neg__z Vec2.__neg__sT!WHtAwh'''rNn_digits int | Nonec.tfd|DS)Nc38K|]}t|VdSNround.0vrCs r z!Vec2.__round__..-77QeAx((777777rrArrCs `r __round__zVec2.__round__#7777$77788rcttj|dtj|dSr)r_mathceilrs r __ceil__z Vec2.__ceil__s.EJtAw''DG)<)<===rcttj|dtj|dSr)rrSfloorrs r __floor__zVec2.__floor__.EKQ((%+d1g*>*>???rcttj|dtj|dSr)rrStruncrs r __trunc__zVec2.__trunc__rYrc t|d|dz|d|dzS#t$r%t|d|z|d|zcYSwxYwrrr s r __mod__z Vec2.__mod__r"r#c t|d|dz|d|dzS#t$r%t|d|z|d|zcYSwxYwrrr s r __pow__z Vec2.__pow__s Q58#T!Wa%8    Q5 $q'U"2    r#tuple[float, float]boolcb|ddz|ddzz|ddz|ddzzkSNrrr s r __lt__z Vec2.__lt__s7Aw!|d1gl*U1X]U1X]-JJJr?headinglengthcvt|tj|z|tj|zS)zCreate a new vector from the given heading and length. Args: heading: The desired heading, in radians length: The desired length of the vector rrScossin)rirjs r from_headingzVec2.from_headings2FUYw///%)G:L:L1LMMMranglecvt|tj|z|tj|zS)zCreate a new vector from the given polar coordinates. Args: angle: The angle, in radians. length: The desired length rl)rprjs r from_polarzVec2.from_polars2FUYu---v %8H8H/HIIIrcTtj|ddz|ddzzS)z>Calculate the length of the vector: ``sqrt(x ** 2 + y ** 2)``.rrerrSsqrtrs r rjz Vec2.lengths'z$q'Q,aA5666rcDtj|d|dS)a#Calculate the heading of the vector in radians. Shortcut for `atan2(y, x)` meaning it returns a value between -pi and pi. ``Vec2(1, 0)`` will have a heading of 0. Counter-clockwise is positive moving towards pi, and clockwise is negative moving towards -pi. rr)rSatan2rs r riz Vec2.headings{47DG,,,rc0|ddz|ddzzS)zCalculate the squared length of the vector. This is simply shortcut for `x ** 2 + y ** 2` and can be used for faster comparisons without the need for a square root. r@rrfrs r length_squaredzVec2.length_squareds Aw#~Q3..rVec2 | tuple[float, float]amountct|d||d|jz zz|d||d|dz zzS)aCreate a new Vec2 linearly interpolated between this vector and another Vec2. The equivalent in GLSL is `mix`. Args: other: Another Vec2 instance. amount: The amount of interpolation between this vector, and the other vector. This should be a value between 0.0 and 1.0. For example: 0.5 is the midway point between both vectors. rr)rrrrr|s r lerpz Vec2.lerpsNDGvqDF):;ghhhredgecrt|d|dkrdnd|d|dkrdndS)aA step function that returns 0.0 for a component if it is less than the edge, and 1.0 otherwise. This can be used enable and disable some behavior based on a condition. Example:: # First component is less than 1.0, second component is greater than 1.0 Vec2(0.5, 1.5).step((1.0, 1.0)) Vec2(1.0, 0.0) Args: edge: A Vec2 instance. rrrhrrA)rrs r stepz Vec2.stepsA47T!W,,CC#d1gQ>O>OssUXYYYrvectorc||dz}t|d||dzz |d||dzz S)zCreate a new Vec2 reflected (ricochet) from the given normalized vector. Args: vector: A normalized Vec2 or Vec2-like tuple. rerr)dotr)rrtwice_dot_values r reflectz Vec2.reflect sV((6**Q. Goq 1 1 Goq 1 1   rctj|}tj|}t||dz||dzz ||dz||dzzS)zCreate a new vector rotated by the angle. The length remains unchanged. Args: angle: The desired angle, in radians. rr)rSrnrmr)rrpscs r rotatez Vec2.rotates\ Ie   Ie  AQK!d1g+-q47{Qa[/HIIIrVec2 | tuple[int, int]cxtj|d|dz dz|d|dz dzzS)zCalculate the distance between this vector and another vector. Args: other: The point to calculate the distance to. rrerrtr s r distancez Vec2.distance"s> zE!HtAw.14%(T!W:LQR9RSTTTrctj|ddz|ddzzx}r"t|d|z |d|z S|SzReturn a normalized version of the vector. This simply means the vector will have a length of 1.0. If the vector has a length of 0, the original vector will be returned. rrer)rSrurrds r normalizezVec2.normalize*sU  47a<$q'Q,677 71 2Q! T!Wq[11 1 rmin_valmax_valcdSrGrfrrrs r r z Vec2.clamp5 CrcdSrGrfrs r r z Vec2.clamp9rrcdSrGrfrs r r z Vec2.clamp>rrcdSrGrfrs r r z Vec2.clampBrrc |d|d}}n#t$r|}|}YnwxYw |d|d}}n#t$r|}|}YnwxYwtt|d||t|d||S)apRestrict the value of the X and Y components of the vector to be within the given values. If a single value is provided, it will be used for both X and Y. If a tuple or Vec2 is provided, the first value will be used for X and the second for Y. Args: min_val: The minimum value(s) max_val: The maximum value(s) rr)rrr )rrrmin_xmin_ymax_xmax_ys r r z Vec2.clampGs "1:wqz5EE   EEEE  "1:wqz5EE   EEEE  $q'5% ( (%Q*F*F   s$$9A  A cH|d|dz|d|dzzS)z?Calculate the dot product of this vector and another 2D vector.rrrfr s r rzVec2.dot`s'Awq!DGeAh$666rargs _typing.Anyintc tdNz"Vec types can be indexed directly.NotImplementedErrorrrs r indexz Vec2.indexd!"FGGGrattrsstrVec2 | Vec3 | Vec4c tttdt|}|fd|DS#tt t f$r}d|d}t||d}~wwxYw)Nrec3NK|]}d|V dS)xyNrrKrrs r rMz#Vec2.__getattr__..ks2BBqtDJJqMM2BBBBBBrz'Vec2' has no attribute: ''.rVec3Vec4len ValueErrorKeyErrorrAttributeErrorrr vec_classr'msgs` r __getattr__zVec2.__getattr__gs / Td33CJJ?I9BBBBEBBBC CHi0 / / /8u888C %%3 . /8<A.A))A.)rrrr)r-r.rr)rrrG)rCrDrr)rrarrb)rh)rirrjrrr)rprrjrrrrr)rr{r|rrr)rr{rr)rr{rr)rprrr)rrrr)rrrrrr)rr{rr{rr)rr{rrrr)rrrr{rr)rrrrrr)rr{rrrrrrrrrr).__name__ __module__ __qualname____doc__r__annotations__rrr!r(r*r,r1r4r6r8r:r<r?rBrPrUrXr\r^r`rg staticmethodrorrrjrirzrrrrrr_typing TYPE_CHECKINGoverloadr rrrrfrr rr s$ANNNNANNNN...0000((((99999>>>>@@@@@@@@KKKKNNNN\NJJJJ\J7777----//// i i i iZZZZ     JJJJUUUU                                    27777HHHH//////rrceZdZUdZdZded<dZded<dZded<dZdAd Z dAd Z dAd Z dAdZ dBdZ dBdZdBdZdCdZdCdZdCdZdDdZdDdZdEdFdZdDdZdDdZdDdZdAd ZdAd!ZdGd$ZedHd'ZdId)ZdJd*ZdJd+Z dKd,Z!dLd-Z"dMd/Z#dLd0Z$dDd1Z%e&j'rDe&j(dNd4Z)e&j(dOd5Z)e&j(dPd6Z)e&j(dQd7Z)dRd8Z)dSd<Z*dTd@Z+dS)Ura`A three-dimensional vector represented as X Y Z coordinates. `Vec3` is an immutable 3D Vector, including most common operators. As an immutable type, all operations return a new object. .. note:: The Python ``len`` operator returns the number of elements in the vector. For the vector length, use the `length()` method. rrrrzcD|jdkp|jdkp |jdkSrrrrrs r rz Vec3.__bool__s$v}># >3>rr)Vec3 | tuple[float, float, float] | floatrc t|d|dz|d|dz|d|dzS#t$r/t|d|z|d|z|d|zcYSwxYwNrrrerrr s r r!z Vec3.__add__ Q%("DGeAh$6Q%(8J    Q%a5$q'E/    =A6A98A9c |tjt|S#t$r}|dkr|cYd}~S|d}~wwxYwr%)r!rcastrrr&s r r(z Vec3.__radd__a << T5 9 9:: :   zz I  ,/ A AA AA c t|d|dz |d|dz |d|dz S#t$r/t|d|z |d|z |d|z cYSwxYwrrr s r r*z Vec3.__sub__rrc t|d|dz |d|dz |d|dz S#t$r/t||dz ||dz ||dz cYSwxYwrrr s r r,z Vec3.__rsub__ a47"E!HtAw$6a478J    Qa%$q'/    rr-)float | Vec3 | tuple[float, float, float]c t|d|dz|d|dz|d|dzS#t$r/t|d|z|d|z|d|zcYSwxYwrrr0s r r1z Vec3.__mul__ Q&)#T!Wvay%8$q'F1I:M    Q& $q'F"2DGf4D    rc t|d|dz|d|dz|d|dzS#t$r/t|d|z|d|z|d|zcYSwxYwrrr0s r r4z Vec3.__rmul__rrc t|d|dz |d|dz |d|dz S#t$r/t|d|z |d|z |d|z cYSwxYwrrr0s r r6zVec3.__truediv__rrc t|d|dz |d|dz |d|dz S#t$r/t||dz ||dz ||dz cYSwxYwrrr s r r8zVec3.__rtruediv__rrc t|d|dz|d|dz|d|dzS#t$r/t|d|z|d|z|d|zcYSwxYwrrr s r r:zVec3.__floordiv__ Q58#T!Wa%8$q'U1X:M    Q5 $q'U"2DGu4D    rc t|d|dz|d|dz|d|dzS#t$r/t||dz||dz||dzcYSwxYwrrr s r r<zVec3.__rfloordiv__s aDG#U1Xa%8%(d1g:M    a %47"2ET!W4D    rctt|dt|dt|dSr)rr>rs r r?z Vec3.__abs__s2CQLL#d1g,,DG ===rcNt|d |d |d Srrrs r rBz Vec3.__neg__s&T!WHtAwha111rNrCrDc.tfd|DS)Nc38K|]}t|VdSrGrHrJs r rMz!Vec3.__round__..rNrrrOs `r rPzVec3.__round__rQrcttj|dtj|dtj|dSr)rrSrTrs r rUz Vec3.__ceil__s>EJtAw''DG)<)Q>QRRRrcttj|dtj|dtj|dSr)rrSrWrs r rXzVec3.__floor__?EKQ((%+d1g*>*> DQRG@T@TUUUrcttj|dtj|dtj|dSr)rrSr[rs r r\zVec3.__trunc__rrc t|d|dz|d|dz|d|dzS#t$r/t|d|z|d|z|d|zcYSwxYwrrr s r r^z Vec3.__mod__rrc t|d|dz|d|dz|d|dzS#t$r/t|d|z|d|z|d|zcYSwxYwrrr s r r`z Vec3.__pow__rr!Vec3 | tuple[float, float, float]rbc|ddz|ddzz|ddzz|ddz|ddzz|ddzzkSrdrfr s r rgz Vec3.__lt__ sXAw!|d1gl*T!W\9E!HMERSHXYM#>>>rcltj|ddz|ddzz|ddzzS)zGCalculate the length of the vector: ``sqrt(x ** 2 + y ** 2 + z ** 2)``.rrerrtrs r rjz Vec3.lengths4z$q'Q,aA5Q1 DEEErcH|ddz|ddzz|ddzzS)zCalculate the squared length of the vector. This is simply shortcut for `x ** 2 + y ** 2 + z ** 2` and can be used for faster comparisons without the need for a square root. rrerrfrs r rzzVec3.length_squared#s, Aw!|d1gl*T!W\99rct|j|dz|j|dzz |j|dz|j|dzz |j|dz|j|dzz S)zCalculate the cross product of this vector and another 3D vector. Args: other: Another Vec3 or tuple of 3 floats. rerr)rrrrr s r crossz Vec3.cross+sp  VeAh 46E!H#4 5 VeAh 46E!H#4 5 VeAh 46E!H#4 5   rcf|j|dz|j|dzz|j|dzzS)zCalculate the dot product of this vector and another 3D vector. Args: other: Another Vec3 or tuple of 3 floats. rrrerr s r rzVec3.dot7s5 va 46E!H#44tva7HHHralphact|j||d|jz zz|j||d|jz zz|j||d|jz zzS)aCreate a new Vec3 linearly interpolated between this vector and another Vec3-like. Args: other: Another Vec3 instance or tuple of 3 floats. alpha: The amount of interpolation between this vector, and the other vector. This should be a value between 0.0 and 1.0. For example: 0.5 is the midway point between both vectors. rrre)rrrr)rrrs r rz Vec3.lerp?sd FeuQx$&01 2 FeuQx$&01 2 FeuQx$&01 2   rctj|d|jz dz|d|jz dzz|d|jz dzzS)zCalculate the distance between this vector and another 3D vector. Args: other: The point to calculate the distance to. rrer)rSrurrrr s r rz Vec3.distanceNsT zE!Htv-!3qDF9Jq8PQV[\]V^aeagVglmUmnooorc tj|ddz|ddzz|ddzz}t|j|z |j|z |j|z S#t $r|cYSwxYwr)rSrurrrrZeroDivisionErrorrs r rzVec3.normalizeVs   47a<$q'Q,6aAEFFA DFQJ ;; ;    KKK sAA A/.A/rrcdSrGrfrs r r z Vec3.clampcrrcdSrGrfrs r r z Vec3.clampgrrcdSrGrfrs r r z Vec3.clamplrrcdSrGrfrs r r z Vec3.clampprrc b |d|d|d}}}n#t$r |}|}|}YnwxYw |d|d|d}}}n#t$r |}|}|}YnwxYwtt|d||t|d||t|d||S)aRestrict the value of the X, Y and Z components of the vector to be within the given values. If a single value is provided, it will be used for all components. If a tuple or Vec3 is provided, the first value will be used for X, the second for Y, and the third for Z. Args: min_val: The minimum value(s) max_val: The maximum value(s) rrre)rrr ) rrrrrmin_zrrmax_zs r r z Vec3.clampus ")!*gaj'!*%5EE   EEEEE  ")!*gaj'!*%5EE   EEEEE   $q'5% ( (%Q*F*FdSTgW\^cHdHd   s..A AArrrc tdrrrs r rz Vec3.indexrrrrrc tttdt|}|fd|DS#tt t f$r}d|d}t||d}~wwxYw)Nrc3NK|]}d|V dS)xyzNrrs r rMz#Vec3.__getattr__..s2CCtEKKNN3CCCCCCrz'Vec3' has no attribute: 'rrrs` r rzVec3.__getattr__s / Td33CJJ?I9CCCCUCCCD DHi0 / / /8u888C %%3 . /r)rrrr)r-rrr)rrrr)rrrG)rCrDrr)rrrrb)rrrrrr)rrar)rrrr)rrrr)rrrrrr)rrrrrr)rrrrrr)rrrrrr)rrrrrr)rrrrrrrr),rrrrrrrrrr!r(r*r,r1r4r6r8r:r<r?rBrPrUrXr\r^r`rg classmethodrrrjrzrrrrrrrrr rrrfrr rrqsANNNNANNNNANNNN???>>>>222299999SSSSVVVVVVVVjjjj   [ ????FFFF::::     IIII     pppp                                        8HHHH//////rrceZdZUdZdZded<dZded<dZded<dZded<dZ d@d Z dAdZ d@dZ d@dZ dBdZdBdZdBdZdBdZdBdZdBdZdCdZdCdZdDdEdZdCdZdCd ZdCd!ZdFd#ZdFd$ZdGd'ZdHd(ZdHd)ZdId+ZdJd,Z dCd-Z!e"j#rDe"j$dKd0Z%e"j$dLd2Z%e"j$dMd3Z%e"j$dNd4Z%dOd6Z%dJd7Z&dPd;Z'dQd?Z(dS)Rra`A four-dimensional vector represented as X Y Z W coordinates. `Vec4` is an immutable 4D Vector, including most common operators. As an immutable type, all operations return a new object. .. note:: The Python ``len` operator returns the number of elements in the vector. For the vector length, use the `length()` method. rrrrrwcZ|jdkp |jdkp|jdkp |jdkSrrrrrrs r rz Vec4.__bool__s/v}O# O3O$&C-Orr0Vec4 | tuple[float, float, float, float] | floatrc , t|d|dz|d|dz|d|dz|d|dzS#t$r9t||dz||dz||dz||dzcYSwxYwNrrrerrrr s r r!z Vec4.__add__ a47"E!HtAw$6a478JERSHW[\]W^L^    Qa%$q'/54PQ7?    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This is simply shortcut for `x ** 2 + y ** 2 + z ** 2 + w ** 2` and can be used for faster comparisons without the need for a square root. rrerrrfrs r rzzVec4.length_squared@s9 Aw!|d1gl*T!W\9DGqLHHrr|c t|j||j|jz zz|j||j|jz zz|j||j|jz zz|j||j|jz zzS)aqCreate a new Vec4 linearly interpolated between this vector and another Vec4. Args: other: Another Vec4 instance. amount: The amount of interpolation between this vector, and the other vector. This should be a value between 0.0 and 1.0. For example: 0.5 is the midway point between both vectors. r.r~s r rz Vec4.lerpHsv Ff$& 01 2 Ff$& 01 2 Ff$& 01 2 Ff$& 01 2    rctj|j|jz dz|j|jz dzz|j|jz dzz|j|jz dzzS)zCalculate the distance between this vector and another 4D vector. Args: other: The point to calculate the distance to. re)rSrurrrrr s r rz Vec4.distanceXsm zg1 $$& Q& ($& Q& ($& Q& (   rctj|ddz|ddzz|ddzz|ddzzx}r6t|d|z |d|z |d|z |d|z S|S)zReturns a normalized version of the vector meaning a version that has length 1. This means that the vector will have the same direction, but a length of 1.0. If the vector has a length of 0, the original vector will be returned. rrerr)rSrurrs r rzVec4.normalizees  47a<$q'Q,6aAEQST TUU U1 LQ! T!Wq[$q'A+tAw{KK K rrrcdSrGrfrs r r z Vec4.clampprr!tuple[float, float, float, float]cdSrGrfrs r r z Vec4.clamptrrcdSrGrfrs r r z Vec4.clampyrrcdSrGrfrs r r z Vec4.clamp}rr)float | tuple[float, float, float, float]c  |d|d|d|df\}}}}n#t$r |}|}|}|}YnwxYw |d|d|d|df\}}} } n#t$r |}|}|} |} YnwxYwtt|d||t|d||t|d|| t|d|| S)aRestrict the value of the X, Y, Z and W components of the vector to be within the given values. The minimum and maximum values can be a single value that will be applied to all components, or a tuple of 4 values that will be applied to each component respectively. Args: min_val: The minimum value(s) max_val: The maximum value(s) rrrer)rrr ) rrrrrrmin_wrrrmax_ws r r z Vec4.clamps$ )0WQZWUVZ)W &E5%   EEEEEE    )0WQZ'!*gVWj)X &E5%   EEEEEE    $q'5% ( (%Q*F*F $q'5% ( (%Q*F*F   s#&;;#A##A87A8c|j|jz|j|jzz|j|jzz|j|jzzS)zCalculate the dot product of this vector and another 4D vector. Args: other: Another Vec4 instance. rr s r rzVec4.dots? v$&57"22TVeg5EEQVQXHXXXrrrrc tdrrrs r rz Vec4.indexrrrrrc tttdt|}|fd|DS#tt t f$r}d|d}t||d}~wwxYw)Nrc3NK|]}d|V dS)xyzwNrrs r rMz#Vec4.__getattr__..s2DDtFLLOO4DDDDDDrz'Vec4' has no attribute: 'rrrs` r rzVec4.__getattr__s / Td33CJJ?I9DDDDeDDDE EHi0 / / /8u888C %%3 . /r)rrrr)rrrr)r-r$rr)rrrG)rCrDrr)rr5rr)rr8rrbr)rr8r|rrr)rr8rr)rrrrrr)rr@rr@rr)rr@rrrr)rrrr@rr)rrDrrDrrrr))rrrrrrrrrrr!r(r*r,r1r4r6r8r:r<r?rBrPrUrXr\r^r`rgrjrzrrrrrrr rrrrfrr rrs]ANNNNANNNNANNNNANNNNPPPLLLL888899999hhhhllllllllOOOOUUUUIIII                                             DYYYYHHHH//////rrc@eZdZUdZdZded<dZded<dZded<dZded<dZ ded <dZ ded <dZ ded <dZ ded <dZ ded <d,dZd-dZd.dZd,dZd/dZd/dZd0dZd0dZd0dZd1d2d!Zd3d$Zejd4d&Zejd/d'Zd5d)Zd6d+ZdS)7Mat3aA 3x3 Matrix. `Mat3` is an immutable 3x3 Matrix, which includes most common operators. A Matrix can be created with a list or tuple of 9 values. If no values are provided, an "identity matrix" will be created (1.0 on the main diagonal). 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This includes class methods for creating orthogonal and perspective projection matrixes, which can be used directly by OpenGL. You can create a Matrix with 16 initial values (floats), or no values at all. If no values are provided, an "identity matrix" will be created (1.0 on the main diagonal). ``Mat4`` objects are immutable, so all operations will return a new Mat4 object. Note: Matrix multiplication is performed using the "@" operator. rhrrOrrPrrrQrRrSrTrUjklmnripr type[Mat4]leftrightbottomtopz_nearz_farrc||z }||z }||z } d|z } d|z } d| z } ||z |z } ||z |z }||z | z }|| dddd| dddd| d| ||dS)a Create a Mat4 orthographic projection matrix for use with OpenGL. Given left, right, bottom, top values, and near/far z planes, create a 4x4 Projection Matrix. This is useful for setting :py:attr:`~pyglet.window.Window.projection`. ryrrhrf)rrrrrrrwidthheightdepths_xs_ys_zt_xt_yt_zs r orthogonal_projectionzMat4.orthogonal_projection_s vEkFlUFl o%f o&%'s3S#S#S#S#'' 'r<aspectfovc|tj|tjzdz z}| }| }||z }||z } ||z } ||z | z } d|z|z| z } d|z|z } | |z } d|z| z }|| dddd|dddd| ddd| dS)aCreate a Mat4 perspective projection matrix for use with OpenGL. Given a desired aspect ratio, near/far planes, and fov (field of view), create a 4x4 Projection Matrix. This is useful for setting :py:attr:`~pyglet.window.Window.projection`. ihrer)rStanpi)rrrrrxy_maxy_minx_minrrrqqnrrTs r perspective_projectionzMat4.perspective_projectionys%)C%(NS$8999%fn  % %Z& 5 ( J  J J s1aAaAaBaQ   rrprrc>|||S)zCreate a rotation matrix from an angle and Vec3. Args: angle: The desired angle, in radians. vector: A Vec3 indicating the direction. )r)rrprs r from_rotationzMat4.from_rotationssuu||E6***rcT||jdddd|jdddd|jdddddS)z"Create a scale matrix from a Vec3.rrhrrrs r from_scalezMat4.from_scalesAs68S#s#sVXsS#'' 'rcT|dddddddddddd|j|j|jdS)z(Create a translation matrix from a Vec3.rhrrrs r from_translationzMat4.from_translationsAs3S#S#S#8VXvx66 6rpositiontargetupc||z }|}||}||}||j|j|j d|j|j|j d|j|j|j d|| || ||dS)aCreate a viewing matrix that points toward a target. This method takes three Vec3s, describing the viewer's position, where they are looking, and the upward axis (typically positive on the Y axis). The resulting Mat4 can be used as the projection matrix. Args: position: The location of the viewer in the scene. target: The point that the viewer is looking towards. up: A vector pointing "up" in the scene, typically `Vec3(0.0, 1.0, 0.0)`. rrh)rrrrrr)rrrrrRurs r look_atz Mat4.look_atsh  ) ) + + LLNN GGAJJ " " GGAJJs13acT33acT33acT3EE(OO#aeeHoo%5quuXMM Mrrrtuplec||ddS)zGet a specific row as a tuple.Nrrfrrs r rowzMat4.rowsEH1H~rc(||dz|dzdzS)z!Get a specific column as a tuple.rrfrs r columnz Mat4.columnsEAIuqy1},--rctd|Dstd|\}}}tj|}tj|}d|z }||z||z||z} } } || |zz} d| |zz||zz} d| |zz||zz }d| |zz||zz }|| |zz}d| |zz||zz}d| |zz||zz}d| |zz||zz }|| |zz}|t | | |d|||d|||dddddzS)z)Get a rotation Matrix on x, y, or z axis.c3<K|]}t|dkVdS)rN)r>)rKrs r rMzMat4.rotate..s,//13q66Q;//////rzvector must be normalized (<=1)rr)allrrSrmrnr)rrprrrrrrttemp_xtemp_ytemp_zrarbrcrerfrgrirjrks r rz Mat4.rotates[/////// @>?? ?1a Ie   Ie   E!"QAq1u !^ !^a!e # !^a!e # !^a!e # !^ !^a!e # !^a!e # !^a!e # !^d2r2q"b"aRQ1aQRSSSSrct|}|dxx|dzcc<|dxx|dzcc<|dxx|dzcc<t|S)z&Get a scale Matrix on x, y, or z axis.rr re)listr)rrtemps r r\z Mat4.scaleseDzz Q6!9 Q6!9 RF1IT{rc<|tddddddddddddg |dRzS)z0Get a translation Matrix along x, y, and z axis.rrr)rrs r r`zMat4.translates8d1aAq!Q1aAJJJJJJJrcntg|ddd|ddd|ddd|dddRS)zGet a transpose of this Matrix.rNrrrerrrs r transposezMat4.transposesMGT!$Q$ZG$qt!t*GtADqDzGDAJGGGGrrct|tstdtdt||DS)Nz Can only add to other Mat4 typesc3&K|] \}}||zV dSrGrfrhs r rMzMat4.__add__..rjrrlrrrmr s r r!z Mat4.__add__rnrct|tstdtdt||DS)Nz'Can only subtract from other Mat4 typesc3&K|] \}}||z V dSrGrfrhs r rMzMat4.__sub__..rjrrr s r r*z Mat4.__sub__rqrc|SrGrfrs r rsz Mat4.__pos__rtrc(td|DS)Nc3K|]}| VdSrGrfrws r rMzMat4.__neg__..rxrrrs r rBz Mat4.__neg__ryrc|\}}}}}}}}} } } } } }}}| |z| |zz }| |z| |zz }| |z| |zz }| |z| | zz }| |z| | zz }| |z| | zz }||z||zz }||z||zz }||z||zz }|| z|| zz }|| z|| zz }|| z|| zz }||z|| zz }||z|| zz }|| z|| zz }|| z|| zz } ||z|| zz }!|| z|| zz }"|||z||zz ||zzz|||z||zz ||zzzz |||z||zz ||zzzz|||z||zz ||zzzz }#|#dkrtjd|Sd|#z }$|$ }%t|$||z||zz ||zzz|%||z||zz ||zzz|$||z||zz ||zzz|%||z||zz ||zzz|%||z||zz ||zzz|$||z||zz ||zzz|%||z||zz ||zzz|$||z||zz || zzz|$||z||zz ||zzz|%||z||zz ||zzz|$||z||zz ||!zzz|%||z||zz ||"zzz|%||z||zz ||zzz|$||z||zz ||zzz|%||z||zz ||!zzz|$||z|| zz ||"zzzS)Nrr{r)r|r}r)&rr~rra14rrra24rrra34a41a42a43a44rOrPrrrQrRrSrTrUrrrrrrirrrrpdetndets& r rzMat4.__invert__ sY]VS#sCc3S#sCcSV #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic ! #Ic !cAga'#'12cAga'#'123cAga'#'123cAga'#'123 !88 NK L L LK3wuDC!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78C!GcAg-a78:: :rrrDc.tfd|DS)Nc38K|]}t|VdSrGrHrs r rMz!Mat4.__round__..>rrrrs `r rPzMat4.__round__=rrrc$d}t|rrrs r r1z Mat4.__mul__@rrrcdSrGrfr s r rzMat4.__matmul__DrrcdSrGrfr s r rzMat4.__matmul__GrrcL |\}}}}}}}} } } } } }}}}|\}}}}}}}}}}}}}}} }!t||z||zz| |zz||zz||z||zz| |zz||zz||z||zz| |zz||zz||z| |zz| |zz||zz||z||zz| |zz||zz||z||zz| |zz||zz||z||zz| |zz||zz||z| |zz| |zz||zz||z||zz| |zz||zz||z||zz| |zz||zz||z||zz| |zz||zz||z| |zz| |zz||zz||z||zz| | zz||!zz||z||zz| | zz||!zz||z||zz| | zz||!zz||z| |zz| | zz||!zzS#t$r|\}"}#}$}%|\}}}}}}}} } } } } }}}}t|"|z|#|zz|$| zz|%|zz|"|z|#|zz|$| zz|%|zz|"|z|#|zz|$| zz|%|zz|"|z|#| zz|$| zz|%|zzcYSwxYwrG)rrr)&rrr~rrr rrrr rrrrrrrrrrrb14rrrb24rrrb34b41b42b43b44rrrrs& r rzMat4.__matmul__Js ]a ZCc3S#sCc3SRUWZ]b ZCc3S#sCc3SRUWZc C#I%c 1C#I=sSy3QT9?TWZ]`W`?`cfilcl?lc C#I%c 1C#I=sSy3QT9?TWZ]`W`?`cfilcl?lc C#I%c 1C#I=sSy3QT9?TWZ]`W`?`cfilcl?lc C#I%c 1C#I=sSy3QT9?TWZ]`W`?`cfilcl?lc C#I%c 1C#I=sSy3QT9?TWZ]`W`?`cfilcl?lc C#I%c 1C#I=sSy3QT9?TWZ]`W`?`cfilcl?lc C#I%c 1C#I=sSy3QT9?TWZ]`W`?`cfilcl?lc C#I%c 1C#I=sSy3QT9?TWZ]`W`?`cfilcl?l      JAq!Q]a ZCc3S#sCc3SRUWZC!c'!AG+a#g5C!c'!AG+a#g5C!c'!AG+a#g5C!c'!AG+a#g5     sFFB H#"H#rc t|jj|ddd|ddd|ddd|ddS)Nrrr rrs r rz Mat4.__repr__isX.)l4!9llD1IllTRSTVRVZll_cdfgidi_jlllrN)rrrrrrrrrrrrrrrr)r) rrrrrrrrrrrr)rprrrrr)rrrrrr) rrrrrrrrrr)rrrr)rrrrrr)rrrr)rrDrr)rrrr)rrrrr)-rrrrrOrrPrrrQrRrSrTrUrrrrrrirrrrrrrrrrrr\r`rr!r*rsrBrrPr1rrrrrfrr rr;s)  ANNNNANNNNANNNNANNNNANNNNANNNNANNNNANNNNANNNNANNNNANNNNANNNNANNNNANNNNANNNNANNNN'''['2    [ 4+++[+'''['666[6MMM[M.....TTTT6KKKKHHHH;;;; ;;;; ))))2:2:2:2:h8888'''' 2222 2222>mmmmmmrrceZdZUdZdZded<dZded<dZded<dZded<e dd Z e ddZ d dZ d!dZ d"dZd#dZd$dZd#dZd%dZd%dZd&dZd%dZd#dZd%dZdS)' QuaternionzhQuaternion. Quaternions are 4-dimensional complex numbers, useful for describing 3D rotations. rhrrrrrrmatrNrctrGrrr*s r from_mat3zQuaternion.from_mat3x!!rrctrGrr,s r from_mat4zQuaternion.from_mat4|r.rc|j}|j}|j}|j}d|dz|dzzdzz }d||z||zz z}d||z||zzz}d||z||zzz}d|dz|dzzdzz } d||z||zz z} d||z||zz z} d||z||zzz} d|dz|dzzdzz } t |||d|| | d| | | dddddS)z:Calculate a 4x4 transform matrix which applies a rotation.rrerrh)rrrrrrrrrrrOrPrrQrRrSrUrrs r to_mat4zQuaternion.to_mat4s# F F F F A1! ! QQ  QQ  QQ  A1! ! QQ  QQ  QQ  A1! !Aq!S!Q31ac3SQQQrc l|j}|j}|j}|j}d|dz|dzzdzz }d||z||zz z}d||z||zzz}d||z||zzz}d|dz|dzzdzz } d||z||zz z} d||z||zz z} d||z||zzz} d|dz|dzzdzz } t ||||| | | | | f S)zCreate a 3x3 rotation matrix.rre)rrrrrNr2s r to_mat3zQuaternion.to_mat3s F F F F A1! ! QQ  QQ  QQ  A1! ! 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This operation: #. leaves the :py:attr:`.w` component alone #. inverts the sign of the :py:attr:`.x`, :py:attr:`.y`, and :py:attr:`.z` components )r)rrrrrs r conjugatezQuaternion.conjugates&$&46'DF7TVG<<rr-cv|j|z|j|z}}|j|z|j|z}}t ||||SrG)rrrrr))rr-rrrrs r r1zQuaternion.__mul__s@v1v1!Q1%%%rc||zSrGrfr s r r6zQuaternion.__truediv__suu}rc\|d||z zSNr)r8rrs r rzQuaternion.__invert__s&~~1txx~~#566rc|jt|dd}}|jt|dd}}||z||z }||z||zz||z}t |g|RSrC)rrrrr))rrrOrrPrLr-rs r rzQuaternion.__matmul__svtT!""X1weABBi(1Qq!QQ+&*6****rN)r*rNrr))r*rrr)r'rr)rr))rr)rr)rr)rr))r-rrr))rrrrrrrrrrr-r0r3r5rjr8rrr!r*r1r6rrrfrr r)r)ms ANNNNANNNNANNNNANNNN"""[""""["RRRR622226IIII====---- J J J J6666 6666 &&&& 7777++++++rr))rrrrrrrr)r __future__rmathrStypingrwarningsr|r NamedTuplerrrrNrr)rfrr rJs  &#"""""++++ N/N/N/N/N/7 N/N/N/b j/j/j/j/j/7 j/j/j/Z X/X/X/X/X/7 X/X/X/vYYYYY7 YYYDomomomomom7 omomomd E+E+E+E+E+#E+E+E+E+E+r