\iN%SrSSKJr SSKrSSKrS/rSrSrSr\ \ S'"S S \ 5r "S S \ 5r "S S\ 5rSrS\ 4Sjr"SS\"SS55r\"SSSSSS5rS\4SjrS\4Sjrg)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\rSrSrSrg) AffineError/N)__name__ __module__ __qualname____firstlineno____static_attributes__r R/var/www/html/kml_chatgpt/mouzaenv/lib/python3.13/site-packages/affine/__init__.pyrr/srrc\rSrSrSrSrg)TransformNotInvertibleError3z#The transform could not be invertedr Nr r r r __doc__rr rrrr3s-rrc\rSrSrSrSrg)UndefinedRotationError7z;The rotation angle could not be computed for this transformr Nrr rrrr7sErrcd^TRnTRnU4U4SjjnXl[X2S9$)zSpecial property decorator that caches the computed property value in the object's instance dict the first time it is accessed. cv>URU$![a T"U5=URU'nUs$f=fN)__dict__KeyError)selfnamevaluefuncs rgettercached_property..getterCsB ==& & *.t* 4DMM$ %L s #88)doc)r r func_nameproperty)r!rr$r"s` rcached_propertyr';s2 ==D ,,C F $$rdegcUS-nUS:XagUS:XagUS:Xag[R"U5n[R"U5[R"U54$)zReturn the cosine and sin for the given angle in degrees. With special-case handling of multiples of 90 for perfect right angles. gv@gV@)?gf@)rgp@)rr,)mathradianscossin)r(rads r cos_sin_degr2NsT +C d{   ,,s C 88C=$((3- ''rc\rSrSrSr\rS7S\S\S\S\S\S\S \S \S \4S jjr\ S\S\S\S\S\S\4 S j5r \ S5r \ S\S\4Sj5r \ S5r \ S8S\S\4Sjj5r\ S9S\4Sjj5r\ S5rS\4SjrS\4SjrSrSr\S\4Sj5r\S\4S j5r\S\4S!j5r\S"5r\S\4S#j5r\S\4S$j5r\S\4S%j5r\S\4S&j5r \S\4S'j5r!\S\4S(j5r"\S\4S)j5r#\S\4S*j5r$\S+5r%\4S,\S\4S-jjr&S\4S.jr'\'=r(=r)r*S/r+\+r,S0r-S1r.S2r/S:S3jr0S4r1\2Rfr3S5r4S6r5g);r_aDTwo 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 v[RUUS-US-US-US-US-US-US-US-U S-4 5$)zCreate a new object Parameters ---------- a, b, c, d, e, f : float Elements of an augmented affine transformation matrix. r+tuple__new__) clsr5r6r7r8r9r:r;r<r=s rrAAffine.__new__s\&}} CCCCCCCCC   rc *URXX1XVU5$)z{Use same coefficient order as GDAL's GetGeoTransform(). :param c, a, b, f, d, e: 6 floats ordered by GDAL. :rtype: Affine )rA)rBr7r5r6r:r8r9s r from_gdalAffine.from_gdals{{31q11rc[$)z/Return the identity transform. :rtype: Affine )identity)rBs rrHAffine.identitys rxoffyoffc @[RUSSUSSUSSS4 5$)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*r?)rBrJrKs r translationAffine.translations(}}S3T3T3S"QRRrc [U5S:Xa[US5=p#OUup#[RXSSSUSSSS4 5$)aCreate a scaling transform from a scalar or vector. :param scaling: The scaling factor. A scalar value will scale in both dimensions equally. A vector scaling value scales the dimensions independently. :type scaling: float or sequence :rtype: Affine rr*r+)lenfloatr@rA)rBscalingsxsys rscale Affine.scalesL w<1 GAJ' 'BFB}}SsCb#sC"MNNrx_angley_anglec [R"[R"U55n[R"[R"U55n[R USUSUSSSSS4 5$)zCreate 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.r@rA)rBrXrYmxmys rshear Affine.shearsVXXdll7+ , XXdll7+ ,}}S3CS#sC"MNNrNanglec [U5up4Uc[RXU*SXCSSSS4 5$UupV[RUUU*XUU-- Xd--UUXeU-- Xc-- SSS4 5$)amCreate 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+)r2r@rA)rBr`pivotcasapxpys rrotationAffine.rotationsU# ===B3RS#sC&PQ QFB==CbL27*bL27*   rc.[RUS5$)zCreate the permutation transform For 2x2 matrices, there is only one permutation matrix that is not the identity. :rtype: Affine ) r*r+r*r+r*r*r*r*r+r?)rBrSs r permutationAffine.permutations}}S"OPPrreturnc SU-$)zConcise string representation.z;|% .2f,% .2f,% .2f| |% .2f,% .2f,% .2f| |% .2f,% .2f,% .2f|r rs r__str__Affine.__str__s R  rcSUSS-$)zPrecise string representation.z%Affine(%r, %r, %r, %r, %r, %r)Nr rns r__repr__Affine.__repr__#s;tBQxGGrcURURURURURUR 4$)zJReturn same coefficient order as GDAL's SetGeoTransform(). :rtype: tuple )r7r5r6r:r8r9rns rto_gdalAffine.to_gdal's/ ??rcURURURURURUR 4$)zReturn an affine transformation matrix compatible with shapely Shapely's affinity module expects an affine transformation matrix in (a,b,d,e,xoff,yoff) order. :rtype: tuple )r5r6r8r9rJrKrns r to_shapelyAffine.to_shapely.s/ 499EErcUR$)z Alias for 'c')r7rns rrJ Affine.xoff8 vv rcUR$)z Alias for 'f')r:rns rrK Affine.yoff=r}rc $Uu pp4pVpxn X-X$-- $)zThe determinant of the transform matrix. This value is equal to the area scaling factor when the transform is applied to a shape. r rr5r6r7r8r9r:r;r<r=s r determinantAffine.determinantBs"%)!aA!uqu}rc HUu pp4n nUS-US--US--US--nX-X$-- S-nUS-S- U- nUS:aSn[R"US- [R"U5-5n [R"US- [R"U5- 5n X4$)zThe absolute scaling factors of the transformation. This tuple represents the absolute value of the scaling factors of the transformation, sorted from bigger to smaller. g-q=r)r-sqrt) rr5r6_r8r9tracedetdeltal1l2s r_scalingAffine._scalingLs%)!aAq!Q Qa!q&(161uqu}" Q$ 5=E YYuqy499U#33 4 YYuqy499U#33 4v rcbURup[R"US-US-- 5U- $)zThe eccentricity of the affine transformation. This value represents the eccentricity of an ellipse under this affine transformation. Raises NotImplementedError for improper transformations. r)rr-r)rrrs r eccentricityAffine.eccentricitycs0yyq27*+b00rc Uu pp4n nUR(dUR(a?URupcXF- X- p[R"Xx5S-[R - $[ e)aThe rotation angle in degrees of the affine transformation. This is the rotation angle in degrees of the affine transformation, assuming it is in the form M = R S, where R is a rotation and S is a scaling. Raises UndefinedRotationError for improper and degenerate transformations. ) is_proper is_degeneraterr-atan2pir) rr5r6rr7r8ryxs rrotation_angleAffine.rotation_angleos`%)!aAq!Q >>T//MMEB616q::a#c)DGG3 3( (rc`U[L=(d UR[UR5$)zKTrue if this transform equals the identity matrix, within rounding limits. )rH almost_equals precisionrns r is_identityAffine.is_identitys% xO4#5#5h#OOrc Uu pp4pVpxn [U5UR:=(a [U5UR:=(d7 [U5UR:=(a [U5UR:$)zTrue if the transform is rectilinear. i.e., whether a shape would remain axis-aligned, within rounding limits, after applying the transform. absrrs ris_rectilinearAffine.is_rectilinearsb%)!aA!A'CCFT^^,C FT^^ # ?A(? rc PUu pp4pVpxn [X-XE--5UR:$)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. rrs r is_conformalAffine.is_conformals0%)!aA!1515=!DNN22rc Uu pp4pVpxn UR=(aK [SX-XD--- 5UR:=(a" [SX"-XU--- 5UR:$)aITrue if the transform is orthonormal. Which means that the transform represents a rigid motion, which has no effective scaling or shear. Mathematically, this means that the axis vectors of the transform matrix are perpendicular and unit-length. Applying an orthonormal transform to a shape always results in a congruent shape. r+)rrrrs ris_orthonormalAffine.is_orthonormalsh%)!aA!    <C1515=)*T^^; <C1515=)*T^^; rc URS:H$)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*rrns rrAffine.is_degenerates3&&rc URS:$)zTTrue if this transform is proper. Which means that it does not include reflection. r*rrns rrAffine.is_propers #%%rc $Uu pp4pV nX4X%4X644$)z6The values of the transform as three 2D column vectorsr )rr5r6r7r8r9r:rs rcolumn_vectorsAffine.column_vectorss)%)!aA!Qvvv%%rrcFSHn[XX- 5U:dM g g)zCompare 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``. )rrPrrFT)r)rotherrr=s rrAffine.almost_equalss,$A47UX%&)3$rc[$r)NotImplementedrrs r__gt__ Affine.__gt__src[S5e)NzOperation not supported) TypeErrorrs r__add__Affine.__add__s122rc zUu p#pEpg n[U[5(abUu ppp n[RURX)-X<--X*-X=--X+-X>--U-XY-Xl--XZ-Xm--X[-Xn--U-SSS4 5$UunnX-UU--U-X-UU--U-4$![ [ 4a [s$f=f)ahMultiplication 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+) isinstancerr@rA __class__ ValueErrorrr)rrrdsbscsdsesfroaobocodoeofvxvys r__mul__Affine.__mul__s+/'1a eV $ $.3 +BBBAq!==Gbg%Gbg%Gbg%*Gbg%Gbg%Gbg%*    &B"r')B."r'0AB0FGG * &%% &sB!!B:9B:c[R"S[SS9 [U[5(aeUR U5$)a4Right 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 3.0r) stacklevel)warningswarnDeprecationWarningrrrrs r__rmul__Affine.__rmul__s=  D  eV,,,,||E""rc[U[5(d[U[5(aURU5$[$r)rrr@rrrs r__imul__Affine.__imul__s0 eV $ $ 5%(@(@<<& &! !rc U[LaFU[:wa;Uu p#pEpg n[U5H"un upX-X--U-X-X--U-4X'M$ ggg)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)rH enumerate) rseqrdrrrrrrr=rrs r itransformAffine.itransform"sg x DH$4.2 +BBBAq!&s^ 6A&16/B."0DE,%5 rc UR(a [S5eSUR- nUu p#pEpg nXa-n U*U-n U*U-n X!-n [R UR XU*U -Xz-- XU*U -X|-- SSS4 5$)zmReturn the inverse transform. :raises: :except:`TransformNotInvertible` if the transform is degenerate. z"Cannot invert degenerate transformr+r*)rrrr@rAr) ridetrdrrrrrrrarbrdres r __invert__Affine.__invert__.s   -.RS ST%%%*.'1a YS4ZS4Z Y}} NN bS2X'"rBG1CS#s S  rcURURURURURUR 4$)zPickle protocol support Notes ----- Normal unpickling creates a situation where __new__ receives all 9 elements rather than the 6 that are required for the constructor. This method ensures that only the 6 are provided. )r5r6r7r8r9r:rns r__getnewargs__Affine.__getnewargs__Cs/vvtvvtvvtvvtvvtvv==rr )r*r*r+)rrr)rlN)6r r r r rrrrRrA classmethodrErHrMrVr^rgrjstrrorsrvryr&rJrKr'rrrrboolrrrrrrrrr__ge____lt____le__r__iadd__rrrrrr@__hash__rrr rrrr_sD-^I                          D2%2E2e22%2E22 Su SE S S O O OE O O O U  D Q Q H#H@FeeU, 1e 1 1)))$PTPP       3d33   't''&4&&&& 7> e $ t &%F%Vf 3H"&H#*" F &~~H >r) r5r6r7r8r9r:r;r<r=rPsc 2[US5(d [S5eUR5n[U5S:wa[ S[U5-5eSU5up#pEpg[ R [X$XcXWSSS/ 5nU[RSS5-$) 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 stringrrz!Expected 6 coefficients, found %dc38# UHn[U5v M g7fr)rR).0rs r loadsw..cs1&Qa&sr*r+g) hasattrrrrQrr@rArrM) rcoeffsr5r8r6r9r7r:centers rloadswrUs 1g  344 WWYF 6{a# UHn[[TU55v M g7fr)reprgetattr)rrrs rrdumpsw..qs F~!T'&!,--~s"%adbecf)rrMjoinlist)objrs @rdumpswr hs:6%%c3/ /F 99FtH~F F MMr)r collectionsrr-r__all__ __author__ __version__rrR__annotations__ Exceptionrrrr'r2rrHrrr r rrrsD#  *    ) .+.F[F%&(U("m>Z"O Pm>` !Q1a # 3c3& N3 Nr