?iNUdZddlmZddlZddlZdgZdZdZdZe e d<Gd d e Z Gd d e Z Gd de ZdZde fdZGddeddZeddddddZ defdZdefdZy)zAffine transformation matrices The Affine package is derived from Casey Duncan's Planar package. See the copyright statement below. ) namedtupleNAffinez Sean Gilliesz2.4.0gh㈵>EPSILONc eZdZy) AffineErrorN)__name__ __module__ __qualname__V/var/www/html/myprovider/mon_projet_qr/lib/python3.12/site-packages/affine/__init__.pyrr/sr rceZdZdZy)TransformNotInvertibleErrorz#The transform could not be invertedNrr r __doc__r r r rr3s-r rceZdZdZy)UndefinedRotationErrorz;The rotation angle could not be computed for this transformNrr r r rr7sEr rcjj}j}|ffd }||_t||S)zSpecial property decorator that caches the computed property value in the object's instance dict the first time it is accessed. ct |j|S#t$r|x|j|<}|cYSwxYwN)__dict__KeyError)selfnamevaluefuncs r getterzcached_property..getterCsB ==& & *.t* 4DMM$ %L s "77)doc)rr func_nameproperty)rrrrs` r cached_propertyr!;s6 ==D ,,CF F $$r degc|dz}|dk(ry|dk(ry|dk(rytj|}tj|tj|fS)zReturn the cosine and sin for the given angle in degrees. With special-case handling of multiples of 90 for perfect right angles. gv@gV@)?gf@)rgp@)rr&)mathradianscossin)r"rads r cos_sin_degr,NsT +C d{   ,,s C 88C=$((3- ''r ceZdZdZeZ d5dededededededed ed efd Zededededededef d Z ed Z ededefdZ edZ ed6dedefdZ ed7defdZedZdefdZdefdZdZdZedefdZedefdZedefd Zed!Zedefd"Zedefd#Zedefd$Zedefd%Zedefd&Z edefd'Z!edefd(Z"edefd)Z#ed*Z$efd+edefd,Z%defd-Z&e&xZ'xZ(Z)d.Z*e*Z+d/Z,d0Z-d1Z.d8d2Z/d3Z0e1jdZ2d4Z3y)9raTwo dimensional affine transform for 2D linear mapping. Parameters ---------- a, b, c, d, e, f : float Coefficients of an augmented affine transformation matrix | x' | | a b c | | x | | y' | = | d e f | | y | | 1 | | 0 0 1 | | 1 | `a`, `b`, and `c` are the elements of the first row of the matrix. `d`, `e`, and `f` are the elements of the second row. Attributes ---------- a, b, c, d, e, f, g, h, i : float The coefficients of the 3x3 augmented affine transformation matrix | x' | | a b c | | x | | y' | = | d e f | | y | | 1 | | g h i | | 1 | `g`, `h`, and `i` are always 0, 0, and 1. The Affine package is derived from Casey Duncan's Planar package. See the copyright statement below. Parallel lines are preserved by these transforms. Affine transforms can perform any combination of translations, scales/flips, shears, and rotations. Class methods are provided to conveniently compose transforms from these operations. Internally the transform is stored as a 3x3 transformation matrix. The transform may be constructed directly by specifying the first two rows of matrix values as 6 floats. Since the matrix is an affine transform, the last row is always ``(0, 0, 1)``. N.B.: multiplication of a transform and an (x, y) vector *always* returns the column vector that is the matrix multiplication product of the transform and (x, y) as a column vector, no matter which is on the left or right side. This is obviously not the case for matrices and vectors in general, but provides a convenience for users of this class. abcdefghic vtj||dz|dz|dz|dz|dz|dz|dz|dz| dzf S)zCreate a new object Parameters ---------- a, b, c, d, e, f : float Elements of an augmented affine transformation matrix. r%tuple__new__) clsr.r/r0r1r2r3r4r5r6s r r:zAffine.__new__s\&}} CCCCCCCCC   r c 0|j|||||||S)zUse same coefficient order as GDAL's GetGeoTransform(). :param c, a, b, f, d, e: 6 floats ordered by GDAL. :rtype: Affine )r:)r;r0r.r/r3r1r2s r from_gdalzAffine.from_gdals{{31aAq11r ctS)z?Return the identity transform. :rtype: Affine )identity)r;s r r?zAffine.identitys r xoffyoffc @tj|dd|dd|dddf S)zCreate a translation transform from an offset vector. :param xoff: Translation x offset. :type xoff: float :param yoff: Translation y offset. :type yoff: float :rtype: Affine r%r$r8)r;r@rAs r translationzAffine.translations(}}S3T3T3S"QRRr c t|dk(rt|dx}}n|\}}tj||ddd|ddddf S)a3Create a scaling transform from a scalar or vector. :param scaling: The scaling factor. A scalar value will scale in both dimensions equally. A vector scaling value scales the dimensions independently. :type scaling: float or sequence :rtype: Affine rr$r%)lenfloatr9r:)r;scalingsxsys r scalez Affine.scalesP w<1 GAJ' 'BFB}}S2sCb#sC"MNNr x_angley_anglec tjtj|}tjtj|}tj |d|d|dddddf S)aCreate a shear transform along one or both axes. :param x_angle: Shear angle in degrees parallel to the x-axis. :type x_angle: float :param y_angle: Shear angle in degrees parallel to the y-axis. :type y_angle: float :rtype: Affine r%r$)r'tanr(r9r:)r;rLrMmxmys r shearz Affine.shearsVXXdll7+ , XXdll7+ ,}}S3CS#sC"MNNr Nanglec t|\}}| tj||| d||ddddf S|\}}tj||| |||zz ||zz|||||zz ||zz dddf S)aCreate a rotation transform at the specified angle. A pivot point other than the coordinate system origin may be optionally specified. :param angle: Rotation angle in degrees, counter-clockwise about the pivot point. :type angle: float :param pivot: Point to rotate about, if omitted the rotation is about the origin. :type pivot: sequence :rtype: Affine r$r%)r,r9r:)r;rSpivotcasapxpys r rotationzAffine.rotationsU#B ===rB3RS#sC&PQ QFB==CbL27*bL27*   r c.tj|dS)zCreate the permutation transform For 2x2 matrices, there is only one permutation matrix that is not the identity. :rtype: Affine ) r$r%r$r%r$r$r$r$r%r8)r;rHs r permutationzAffine.permutations}}S"OPPr returnc d|zS)zConcise string representation.z;|% .2f,% .2f,% .2f| |% .2f,% .2f,% .2f| |% .2f,% .2f,% .2f|r rs r __str__zAffine.__str__s R  r cd|ddzS)zPrecise string representation.z%Affine(%r, %r, %r, %r, %r, %r)Nr r_s r __repr__zAffine.__repr__#s;tBQxGGr c|j|j|j|j|j|j fS)zZReturn same coefficient order as GDAL's SetGeoTransform(). :rtype: tuple )r0r.r/r3r1r2r_s r to_gdalzAffine.to_gdal's/ ??r c|j|j|j|j|j|j fS)zReturn an affine transformation matrix compatible with shapely Shapely's affinity module expects an affine transformation matrix in (a,b,d,e,xoff,yoff) order. :rtype: tuple )r.r/r1r2r@rAr_s r to_shapelyzAffine.to_shapely.s/ 499EEr c|jS)z Alias for 'c')r0r_s r r@z Affine.xoff8 vv r c|jS)z Alias for 'f')r3r_s r rAz Affine.yoff=rir c 0|\ }}}}}}}}} ||z||zz S)zThe determinant of the transform matrix. This value is equal to the area scaling factor when the transform is applied to a shape. r rr.r/r0r1r2r3r4r5r6s r determinantzAffine.determinantBs.%)!1aAq!Q1uq1u}r c H|\ }}}}}}}}}|dz|dzz|dzz|dzz}||z||zz dz}|dzdz |z }|dkrd}tj|dz tj|z} tj|dz tj|z } | | fS)zThe absolute scaling factors of the transformation. This tuple represents the absolute value of the scaling factors of the transformation, sorted from bigger to smaller. g-q=r)r'sqrt) rr.r/_r1r2tracedetdeltal1l2s r _scalingzAffine._scalingLs%)!1aAq!Q Qa!q&(1611uq1u}" Q$ 5=E YYuqy499U#33 4 YYuqy499U#33 42v r cb|j\}}tj|dz|dzz |z S)zThe eccentricity of the affine transformation. This value represents the eccentricity of an ellipse under this affine transformation. Raises NotImplementedError for improper transformations. ro)rxr'rq)rrvrws r eccentricityzAffine.eccentricitycs2Byyq27*+b00r c |\ }}}}}}}}}|js |jrC|j\}}||z ||z }}tj||dztj z St )aKThe rotation angle in degrees of the affine transformation. This is the rotation angle in degrees of the affine transformation, assuming it is in the form M = R S, where R is a rotation and S is a scaling. Raises UndefinedRotationError for improper and degenerate transformations. ) is_proper is_degeneraterxr'atan2pir) rr.r/rrr0r1rvyxs r rotation_anglezAffine.rotation_angleosn%)!1aAq!Q >>T//MMEBr61r6qA::a#c)DGG3 3( (r cV|tuxs |jt|jS)z[True if this transform equals the identity matrix, within rounding limits. )r? almost_equals precisionr_s r is_identityzAffine.is_identitys% xO4#5#5h#OOr c |\ }}}}}}}}} t||jkxrt||jkxs2t||jkxrt||jkS)zTrue if the transform is rectilinear. i.e., whether a shape would remain axis-aligned, within rounding limits, after applying the transform. absrrls r is_rectilinearzAffine.is_rectilinearsj%)!1aAq!QA'CCFT^^,C FT^^ # ?A(? r c \|\ }}}}}}}}} t||z||zz|jkS)zTrue if the transform is conformal. i.e., if angles between points are preserved after applying the transform, within rounding limits. This implies that the transform has no effective shear. rrls r is_conformalzAffine.is_conformals<%)!1aAq!Q1q51q5=!DNN22r c |\ }}}}}}}}} |jxrJtd||z||zzz |jkxr$td||z||zzz |jkS)ayTrue if the transform is orthonormal. Which means that the transform represents a rigid motion, which has no effective scaling or shear. Mathematically, this means that the axis vectors of the transform matrix are perpendicular and unit-length. Applying an orthonormal transform to a shape always results in a congruent shape. r%)rrrrls r is_orthonormalzAffine.is_orthonormalsx%)!1aAq!Q    <C1q51q5=)*T^^; <C1q51q5=)*T^^; r c |jdk(S)zTrue if this transform is degenerate. Which means that it will collapse a shape to an effective area of zero. Degenerate transforms cannot be inverted. r$rmr_s r r~zAffine.is_degenerates3&&r c |jdkDS)zdTrue if this transform is proper. Which means that it does not include reflection. r$rr_s r r}zAffine.is_propers #%%r c 0|\ }}}}}}}}}||f||f||ffS)z6The values of the transform as three 2D column vectorsr )rr.r/r0r1r2r3rrs r column_vectorszAffine.column_vectorss5%)!1aAq!Q1v1v1v%%r rcDdD]}t||||z |k\syy)a Compare transforms for approximate equality. :param other: Transform being compared. :type other: Affine :return: True if absolute difference between each element of each respective transform matrix < ``self.precision``. )rrErorpFT)r)rotherrr6s r rzAffine.almost_equalss5$ A47U1X%&)3 r ctSr)NotImplementedrrs r __gt__z Affine.__gt__sr ctd)NzOperation not supported) TypeErrorrs r __add__zAffine.__add__s122r c |\ }}}}}}}}}t|trq|\ } } } } } }}}}tj|j|| z|| zz|| z|| zz|| z||zz|z|| z|| zz|| z|| zz|| z||zz|zdddf S |\}}||z||zz|z||z||zz|zfS#t t f$r tcYSwxYw)aMultiplication Apply the transform using matrix multiplication, creating a resulting object of the same type. A transform may be applied to another transform, a vector, vector array, or shape. :param other: The object to transform. :type other: Affine, :class:`~planar.Vec2`, :class:`~planar.Vec2Array`, :class:`~planar.Shape` :rtype: Same as ``other`` r$r%) isinstancerr9r: __class__ ValueErrorrr)rrrWsbscsdsesfrroaobocodoeofvxvys r __mul__zAffine.__mul__s%+/'BBB1a eV $.3 +BBBAq!==Gb2g%Gb2g%Gb2g%*Gb2g%Gb2g%Gb2g%*    &BR"r')B.R"r'0AB0FGG * &%% &s B00CCctjdtdt|trJ|j |S)a|Right hand multiplication .. deprecated:: 2.3.0 Right multiplication will be prohibited in version 3.0. This method will raise AffineError. Notes ----- We should not be called if other is an affine instance This is just a guarantee, since we would potentially return the wrong answer in that case. z6Right multiplication will be prohibited in version 3.0ro) stacklevel)warningswarnDeprecationWarningrrrrs r __rmul__zAffine.__rmul__s:  D  eV,,,||E""r cpt|tst|tr|j|StSr)rrr9rrrs r __imul__zAffine.__imul__s* eV $ 5%(@<<& &! !r c |turL|tk7rB|\ }}}}}}}}}t|D]'\} \} } | |z| |zz|z| |z| |zz|zf|| <)yyy)zTransform a sequence of points or vectors in place. :param seq: Mutable sequence of :class:`~planar.Vec2` to be transformed. :returns: None, the input sequence is mutated in place. N)r? enumerate) rseqrWrrrrrrrr6rrs r itransformzAffine.itransform"s x DH$4.2 +BBBAq!&s^ F 6Aqb&1r6/B.BR"0DEA F%5 r c  |jr tdd|jz }|\ }}}}}}}}}||z} | |z} | |z} ||z} tj |j | | | | z|| zz | | | | z|| zz dddf S)zReturn the inverse transform. :raises: :except:`TransformNotInvertible` if the transform is degenerate. z"Cannot invert degenerate transformr%r$)r~rrmr9r:r) ridetrWrrrrrrrrarbrdres r __invert__zAffine.__invert__.s   -.RS ST%%%*.'BBB1a $YS4ZS4Z $Y}} NN bS2XR'R"rBG1CS#s S  r c|j|j|j|j|j|j fS)a Pickle protocol support Notes ----- Normal unpickling creates a situation where __new__ receives all 9 elements rather than the 6 that are required for the constructor. This method ensures that only the 6 are provided. )r.r/r0r1r2r3r_s r __getnewargs__zAffine.__getnewargs__Cs/vvtvvtvvtvvtvvtvv==r )r$r$r%)rrr)r]N)4rr r rrrrGr: classmethodr=r?rCrKrRrZr\strr`rcrergr r@rAr!rmrxrzrboolrrrrr~r}rrr__ge____lt____le__r__iadd__rrrrrr9__hash__rr r r rr_sD-^I                          D2%2E2e22%2E22 Su SE S S O O OE O O O U  D Q Q H#H@FeeU, 1e 1 1)))$PTPP       3d33   't''&4&&&& 7> e $ t &%F%Vf 3H"&H#*" F &~~H >r ) r.r/r0r1r2r3r4r5r6rEsc 2t|ds td|j}t|dk7rt dt|zd|D\}}}}}}t j t||||||dddg }|tjddzS) zReturns Affine from the contents of a world file string. This method also translates the coefficients from center- to corner-based coordinates. :param s: str with 6 floats ordered in a world file. :rtype: Affine splitzCannot split input stringrbz!Expected 6 coefficients, found %dc32K|]}t|ywr)rG).0rs r zloadsw..cs1Qa1sr$r%g) hasattrrrrFrr9r:rrC) rcoeffsr.r1r/r2r0r3centers r loadswrUs 1g 344 WWYF 6{a.qsF!T'&!,-Fs"adbecf)rrCjoinlist)objrs @r dumpswrhs:6%%c3/ /F 99FtH~F F MMr )r collectionsrr'r__all__ __author__ __version__rrG__annotations__ Exceptionrrrr!r,rr?rrrr r r rsD#  *    ) .+.F[F%&(U("m>Z"O Pm>` !Q1a # 3c3& N3 Nr