hVSSKJr SSKJrJrJrJrJr SSKrSSK r SSK Jr SSKJ r JrJr SSKJr SSKJrJrJrJrJrJr \(aSSKJr S /rS S jr"S S 5rg) ) annotations)SequenceIterableIterator TYPE_CHECKINGOptionalN)sincostan)chain)Vec3X_AXISY_AXISZ_AXISNULLVECVec2)UVecMatrix44cDUVs/sHn[U5PM sn$s snfNfloat)itemsvs F/var/www/html/env/lib/python3.13/site-packages/ezdxf/math/_matrix44.pyfloatsrs# $eE!He $$ $sc\rSrSr%SrSrS\S'\R"/SQ\RS9r Sr S8S jr S9S jr \S:S j5rS;S jrSSjrS?Sjr\r\S@Sj5r\R0SASj5r\S@Sj5r\S@Sj5r\S@Sj5r\SBSj5r\SBSj5r\SCSDSjj5r\SESj5r \SFSj5r!\SFSj5r"\SFSj5r#\SGSj5r$\SHSj5r%\SISJS jj5r&\SKS!j5r'\SLS"j5r(\SMS#j5r)\\*\+\,\-4SNS$jj5r.SOS%jr/SPS&jr0SQS'jr1SRS(jr2SRS)jr3SRS*jr4SSS+jr5SSS,jr6STS-jr7SUSTS.jjr8\8r9SVS/jr:SWS0jr;SXS1jr<SUSVS2jjr=SYS3jr>SYS4jr?\?r@SZS5jrAS[S6jrBSZS7jrCSrDg)\r!atAn optimized 4x4 `transformation matrix`_. The utility functions for constructing transformations and transforming vectors and points assumes that vectors are stored as row vectors, meaning when multiplied, transformations are applied left to right (e.g. vAB transforms v by A then by B). Matrix44 initialization: - ``Matrix44()`` returns the identity matrix. - ``Matrix44(values)`` values is an iterable with the 16 components of the matrix. - ``Matrix44(row1, row2, row3, row4)`` four rows, each row with four values. .. _transformation matrix: https://en.wikipedia.org/wiki/Transformation_matrix _matrixznpt.NDArray[np.float64]r!)?r#r#r#r"r#r#r#r#r"r#r#r#r#r"dtypec[U5nUS:Xa$[RR5UlO{US:Xa,[ R "US[ RS9UlOIUS:Xa8[ R "[[U65[ RS9UlO [S5eURRS:wa [S5eg) z Matrix44() is the identity matrix. Matrix44(values) values is an iterable with the 16 components of the matrix. Matrix44(row1, row2, row3, row4) four rows, each row with four values. rr r$zFInvalid count of arguments (4 row vectors or one list with 16 values).)zInvalid matrix countN) lenr _identitycopyr!nparrayfloat64listr ValueErrorshape)selfargsnargss r__init__Matrix44.__init__BsD  A:#--224DL aZ88DG2::>DL aZ88D$6bjjIDL(  <<   &34 4 'cb^SmSSRU4SjUR555-$)zReturns the representation string of the matrix in row-major order: ``Matrix44((col0, col1, col2, col3), (...), (...), (...))`` c8SSRSU55-$)Nz(%s), c38# UHn[U5v M g7fr)str).0values r 8Matrix44.__repr__..format_row..`s%BcUc%jjcs)join)rows r format_row%Matrix44.__repr__..format_row_sDII%Bc%BBB Br7z Matrix44(%s)r:c34># UH nT"U5v M g7fr)r=rBrCs rr?$Matrix44.__repr__..bs)Q[c*S//[s)rArows)r2rCs @r__repr__Matrix44.__repr__Zs+  C )QTYY[)Q QQQr7c TURnUSUSSUSUSSUSUSS4 $) zReturns a 2D transformation as a row-major matrix in a linear array (tuple). A more correct transformation could be implemented like so: https://stackoverflow.com/questions/10629737/convert-3d-4x4-rotation-matrix-into-2d rr r#r' r"r r2ms rget_2d_transformationMatrix44.get_2d_transformationds> LLtQqT3!adC2"sBBr7c[U5S:wa [S5e[5nURnUSUS'USUS'USUS'USUS'USUS 'USUS 'U$) zReturns the :class:`Matrix44` class for an affine 2D (3x3) transformation matrix defined by 6 float values: m11, m12, m21, m22, m31, m32. zFFirst 2 columns of a 3x3 matrix required: m11, m12, m21, m22, m31, m32rr r'rLrMrN)r)r0rr!) componentsm44rPs rfrom_2d_transformationMatrix44.from_2d_transformationns z?a X j KK!}!!}!!}!!}!1 "1 " r7c|SUs=::aS:a"O OUS-n[URX"S-5$[SU35e)zJGet row as list of four float values. Args: row: row index [0 .. 3] rr'invalid row index: )tupler! IndexError)r2rBindexs rget_rowMatrix44.get_rowsC vDLLV!4 523%89 9r7cSUs=::aS:a&O O#URnX!X!S-X!S-X!S-4$[SU35e)zRReturns a column as a tuple of four floats. Args: col: column index [0 .. 3] rr'rMr\r!r^)r2colrPs rget_colMatrix44.get_colsN  >23%89 9r7cSUs=::aS:aRO OOURnUupEpg[U5X1'[U5X1S-'[U5X1S-'[U5X1S-'g[SU35e)zoSets the values in a column. Args: col: column index [0 .. 3] values: iterable of four column values rr'rgrMr\N)r!rr^)r2rircrPabcds rset_colMatrix44.set_colsl )rrrrabsdot)r2rrrs r is_orthogonalMatrix44.is_orthogonalsWW    WW    WW    r Ot # (BFF2J4' (BFF2J4' r7NcUcUnUcUnU"[U5SSSS[U5SSSS[U5SSSSS/5nU$)zqReturns a scaling transformation matrix. If `sy` is ``None``, `sy` = `sx`, and if `sz` is ``None`` `sz` = `sx`. r#r"r)clssxsyszrPs rscaleMatrix44.scales^ :B :B  "Ir2r b 2r E"Ir B   r7chU"SSSSSSSSSSSS[U5[U5[U5S/5$)zAReturns a translation matrix for translation vector (dx, dy, dz).r"r#r)rdxdydzs r translateMatrix44.translatesF B B B "IuRy%)R    r7c^[U5n[U5nU"SSSSSX#SSU*USSSSS/5$)zYReturns a rotation matrix about the x-axis. Args: angle: rotation angle in radians r"r#r r ranglecos_asin_as rx_rotateMatrix44.x_rotatesLE E  B b r B    r7c`[U5n[U5nU"USU*SSSSSUSUSSSSS/5$)zYReturns a rotation matrix about the y-axis. Args: angle: rotation angle in radians r#r"rrs ry_rotateMatrix44.y_rotate$sNE E  2vr B 2ub B    r7c^[U5n[U5nU"X#SSU*USSSSSSSSSS/5$)zYReturns a rotation matrix about the z-axis. Args: angle: rotation angle in radians r#r"rrs rz_rotateMatrix44.z_rotate7sLE E  "b FE2r B B    r7cH[U5n[U5nSU- n[U5R5upgnU"Xf-U-U-Xv-U-X--Xh-U-Xt-- SXg-U-X-- Xw-U-U-Xx-U-Xd--SXh-U-Xt--Xx-U-Xd-- X-U-U-SSSSS/5$)zReturns a rotation matrix about an arbitrary `axis`. Args: axis: rotation axis as ``(x, y, z)`` tuple or :class:`Vec3` object angle: rotation angle in radians r"r#)r r rr) raxisrrosomcxyzs r axis_rotateMatrix44.axis_rotateJs J JAgt*&&(a ECK!OQUS[150!%#+2Er ECK!% q!%#+2Er ECK!% qu!4aeckAor B    r7c[U5n[U5n[U5n[U5n[U5n[U5n XW-n XG-n U"Xh-X-XI--U *U-XY--SU*U -U *U -XH--X-XX--SXu*U-XF-SSSSS/5$)zReturns a rotation matrix for rotation about each axis. Args: angle_x: rotation angle about x-axis in radians angle_y: rotation angle about y-axis in radians angle_z: rotation angle about z-axis in radians r#r"r) rangle_xangle_yangle_zcxrcyrczrsxsycxsys r xyz_rotateMatrix44.xyz_rotate`s\ \ \ \ \ \ww GTY(4%"*rw*> C"Htebj27*DI,? b"'2 B    r7c[R"U5n[R"U5nU"SUSSUSSSSSSSSSSS/5$)zReturns a translation matrix for shear mapping (visually similar to slanting) in the xy-plane. Args: angle_x: slanting angle in x direction in radians angle_y: slanting angle in y direction in radians r"r#)mathr )rrrtxtys rshear_xyMatrix44.shear_xy|sVXXg  XXg  B B B B    r7cU"SU-X!- - SSSSSU-X4- - SSX!-X!- - X4-X4- - Xe-Xe- - *SSSSU-U-Xe- - *S/5$)a<Returns a matrix for a 2D projection. Args: left: Coordinate of left of screen right: Coordinate of right of screen top: Coordinate of the top of the screen bottom: Coordinate of the bottom of the screen near: Coordinate of the near clipping plane far: Coordinate of the far clipping plane @r#grF)rleftrighttopbottomnearfars rperspective_projectionMatrix44.perspective_projections, $Y5< ("b" ds|,b" \el +cls|-Lzcj) *C rCx$3:67    r7chU[US- 5-nU*U-nXR-nU*nUn URXgXX45$)zReturns a matrix for a 2D projection. Args: fov: The field of view (in radians) aspect: The aspect ratio of the screen (width / height) near: Coordinate of the near clipping plane far: Coordinate of the far clipping plane r)r r) rfovaspectrrvrangerrrrs rperspective_projection_fov#Matrix44.perspective_projection_fovsJC#I&w))$vDNNr7c4[5nUHnX-nM U$)zrBris r __setitem__Matrix44.__setitem__sK # UHnTRU5v M g7fr)r`r=r_r2s rr? Matrix44.rows..> U##!rr rUrVrFrus`rrH Matrix44.rows>>>r7c^U4SjS5$)z!Iterate over columns as 4-tuples.c3F># UHnTRU5v M g7fr)rjrs rr?#Matrix44.columns.. rrrrFrus`rcolumnsMatrix44.columnsrr7cURn[U5up4n[X2S-XBS--XRS--US-X2S-XBS--XRS--US-X2S -XBS --XRS --US -5$) zReturns a transformed vertex.rr'rgrMr rL rNrUrT ryrz)r2vectorrPrrrs r transformMatrix44.transform"s LLv,a !HqQ4x !d( *QrU 2 !HqQ4x !d( *QrU 2 !HqQ4x !e) +ae 3  r7cURn[U5upEn[XCS-XSS--XcS--XCS-XSS--XcS--XCS-XSS--XcS --5nU(aUR5$U$) z;Returns a transformed direction vector without translation.rr'rgr rLrrUrTrr!rr)r2r rrPrrrrs rtransform_directionMatrix44.transform_direction.s LLv,a  !HqQ4x !d( * !HqQ4x !d( * !HqQ4x !e) +  !*q{{}0q0r7c## URup#pEpgppppnnUHWn[U5unnn[UU-UU--UU --U-UU-UU--UU --U-UU-UU--UU --U-5v MY g7f)z,Returns an iterable of transformed vertices.Nrz)r2vectorsm0rrm3m4m5m6m7m8m9m10m11m12m13m14m15r rrrs rtransform_verticesMatrix44.transform_vertices=s LL  B B C c3F6lGAq!BR!b&(3.BR!b&(3.BR!c')C/ sA5A7c## URnUSnUSnUSnUSnUSnUSnUHHn [U 5n U Rn U Rn [X-X--U-X-X--U-5v MJ g7f)aFast transformation of 2D points. For 3D input points the z-axis will be ignored. This only works reliable if only 2D transformations have been applied to the 4x4 matrix! Profiling results - speed gains over :meth:`transform_vertices`: - pure Python code: ~1.6x - Python with C-extensions: less than 1.1x - PyPy 3.8: ~4.3x But speed isn't everything, returning the processed input points as :class:`Vec2` instances is another advantage. .. versionadded:: 1.1 rr r'rLrMrNN)r!rrr) r2pointsrPr)rr+r,r3r4pntrrrs rfast_2d_transformMatrix44.fast_2d_transformQs" LL qT qT qT qTeeCS AAAqv,afqvo.CD D sA:A<c US:Xa9[R"UR5[RS9nSUlOFUS:Xa5[R"UR [RS9nSUlO [ S5e[R"[R"USS2SU24[R"URSS 454S S 9U5nUSS2SU24R5USS2SU24'g) a Transforms a numpy array inplace, the argument `ndim` defines the dimensions to transform, this allows 2D/3D transformation on arrays with more columns e.g. a polyline array which stores points as (x, y, start_width, end_width, bulge) values. .. versionadded:: 1.1 rUr$)rVrVrV)r'r'zndim has to be 2 or 3Nrr )r) r,r-rQr.r1r!r0r concatenateonesr+)r2r-ndimrPrs rtransform_array_inplace Matrix44.transform_array_inplaceos 19335RZZHAAG QYRZZ8AAG45 5 II NNE!UdU(ORWWekk!na5H-IJQR SUV AuuH+**,a$hr7c # # URt p4pVpxpppUHgn[U5unnn[UU-UU--UU --UU-UU--UU --UU-UU --UU --5nU(aUR5OUv Mi g7f)zKReturns an iterable of transformed direction vectors without translation. Nr$)r2r(rr)rrr*r+r,r-r.r/r0r1_r rrrrs rtransform_directionsMatrix44.transform_directionss;?,,7F6lGAq!BR!b&(BR!b&(BR!c')A $-!++-! 3sBBc<URXR- 5$)zxReturns an UCS vector from WCS vertex. Works only if matrix is used as cartesian UCS without scaling. (internal API) )ucs_direction_from_wcsr{)r2wcss rucs_vertex_from_wcsMatrix44.ucs_vertex_from_wcss**3+<==r7c URt p#pEpgpppUupn[X-X--UU--X-X--UU--X-X--UU --5$)zReturns UCS direction vector from WCS direction. Works only if matrix is used as cartesian UCS without scaling. (internal API) rz)r2rJr)rrr*r+r,r-r.r/r0r1rErrrs rrIMatrix44.ucs_direction_from_wcssl;?,,7a FQVOa"f $ FQVOa"f $ FQVOa#g %  r7cURRSS5n[R"UR5Ulg)z#Swaps the rows for columns inplace.r'N)r!rr,rTrOs r transposeMatrix44.transposes+ LL A &xx} r7ct[RRURR SS55$)zReturns determinant.r')r,linalgdetr!rrus r determinantMatrix44.determinants&yy}}T\\11!Q788r7c[RRURR SS55n[R"U5Ulg![RR a [ ef=f)zbCalculates the inverse of the matrix. Raises: ZeroDivisionError: if matrix has no inverse. r'N)r,rTinvr!r LinAlgErrorZeroDivisionErrorr)r2inverses rr\Matrix44.inverses] $iimmDLL$8$8A$>?Gxx( yy$$ $# # $s 9A%A<)returnr<)r^tuple[float, ...])rWSequence[float]r^r)rBintr^r_)rBrarcr`r^None)rirar^r_)rirarcr`)r^r)r^r)rrr^rb)r^bool)NN)rrrOptional[float]rrdr^r)rrrrrrr^r)rrr^r)rrrrr^r)rrrrrrr^r)rr)rrrrr^r)rrrrrrrrrrrrr^r) rrrrrrrrr^r)rrr^r) rrrrrrr{rr^r)r_tuple[int, int]r>r)r_re)r^zIterator[float])rrr^r)r^zIterator[tuple[float, ...]])r rr^r)F)r(Iterable[UVec]r^zIterator[Vec3])r:rfr^zIterator[Vec2])r-z np.ndarrayrArar^rb)rJrr^r)r^rb)r^r)E__name__ __module__ __qualname____firstlineno____doc__ __slots____annotations__r,r-r.r*r5rIrQ staticmethodrYr`rdrjrqr+__copy__propertyr{setterrrrrr classmethodrrrrrrrrrrr rrrrrrrrrr r rHrr!r% ocs_to_wcsr7r<rBrFrKrI ocs_from_wcsrQrVr\__static_attributes__rFr7rrr!sJ&I $$  I50RC& : : ::$,H )) ]]&&''''((OO   JN+8G *    $  $  $  *  6  (             <OO!&O.3O:?O OO&           :=="00??   1%J(E<-6274%4 4&> $*L% 9 )r7)rrr^z list[float]) __future__rtypingrrrrrrnumpyr, numpy.typingnptr r r itertoolsr _vectorrrrrrr ezdxf.mathr__all__rrrFr7rrsI#HH A@ ,%m )m )r7