OgVddlmZddlmZmZmZmZmZddlZddl Z ddl mZ ddlm Z mZmZddlmZddlmZmZmZmZmZmZerddlmZd gZd d ZGd d Zy) ) annotations)SequenceIterableIterator TYPE_CHECKINGOptionalN)sincostan)chain)Vec3X_AXISY_AXISZ_AXISNULLVECVec2)UVecMatrix44c>|Dcgc] }t|c}Scc}wNfloat)itemsvs Y/var/www/html/public_html/myphp/venv/lib/python3.12/site-packages/ezdxf/math/_matrix44.pyfloatsrs# $E!H $$ $sc*eZdZUdZdZded<ejgdejZ dZ d7dZ d8d Z e d9d Zd:d Zd;d ZddZeZed?dZej.d@dZed?dZed?dZed?dZedAdZedAdZe dB dCdZedDdZedEdZ edEdZ!edEdZ"edFdZ#edGdZ$edHdIdZ%e dJd Z&e dKd!Z'e dLd"Z(e e)e*e+e,f dMd#Z-dNd$Z.dOd%Z/dPd&Z0dQd'Z1dQd(Z2dQd)Z3dRd*Z4dRd+Z5dSd,Z6dTdSd-Z7e7Z8dUd.Z9dVd/Z:dWd0Z; dT dUd1Ze>Z?dYd4Z@dZd5ZAdYd6ZBy)[raAn 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!dtypect|}|dk(r$tjj|_n}|dk(r.t j |dt j|_nJ|dk(r:t j tt|t j|_n td|jjdk7r tdy) 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__zMatrix44.__init__BsD  A:#--224DL aZ88DG2::>DL aZ88D$6bjjIDL(  <<   &34 4 'c`dddjfd|jDzS)zReturns the representation string of the matrix in row-major order: ``Matrix44((col0, col1, col2, col3), (...), (...), (...))`` c8ddjd|DzS)Nz(%s), c32K|]}t|ywr)str).0values r z8Matrix44.__repr__..format_row..`s%BUc%j%Bs)join)rows r format_rowz%Matrix44.__repr__..format_row_sDII%Bc%BBB Br5z Matrix44(%s)r8c3.K|] }|ywr)r;r?r@s rr=z$Matrix44.__repr__..bs)Qc*S/)Qs)r>rows)r1r@s @r__repr__zMatrix44.__repr__Zs+  C )QTYY[)Q QQQr5c T|j}|d|dd|d|dd|d|ddf S) 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!rr1ms rget_2d_transformationzMatrix44.get_2d_transformationds> LLtQqT3!adC2"sBBr5ct|dk7r tdt}|j}|d|d<|d|d<|d|d<|d|d<|d|d <|d|d <|S) 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&rFrGrH)r(r/rr ) componentsm44rJs rfrom_2d_transformationzMatrix44.from_2d_transformationns z?a X j KK!}!!}!!}!!}!1 "1 " r5czd|cxkrdkr#nn |dz}t|j||dzStd|)zbGet row as list of four float values. Args: row: row index [0 .. 3] rr&invalid row index: )tupler IndexError)r1r?indexs rget_rowzMatrix44.get_rowsE vDLLV!4 523%89 9r5cd|cxkrdkr*nn'|j}||||dz||dz||dzfStd|)zjReturns a column as a tuple of four floats. Args: col: column index [0 .. 3] rr&rGrTr rV)r1colrJs rget_colzMatrix44.get_colsV  >23%89 9r5cd|cxkrdkrXnnU|j}|\}}}}t|||<t|||dz<t|||dz<t|||dz<ytd|)zSets the values in a column. Args: col: column index [0 .. 3] values: iterable of four column values rr&r]rGrTN)r rrV)r1r_rZrJabcds rset_colzMatrix44.set_colsx )rrr|rvryabsdot)r1rrrvrys r is_orthogonalzMatrix44.is_orthogonalsWW    WW    WW    r Ot # (BFF2J4' (BFF2J4' r5Nc|||}||}|t|ddddt|ddddt|dddddg}|S)zReturns a scaling transformation matrix. If `sy` is ``None``, `sy` = `sx`, and if `sz` is ``None`` `sz` = `sx`. r"r!r)clssxsyszrJs rscalezMatrix44.scales^ :B :B  "Ir2r b 2r E"Ir B   r5ch|ddddddddddddt|t|t|dgS)zAReturns a translation matrix for translation vector (dx, dy, dz).r!r"r)rdxdydzs r translatezMatrix44.translatesF B B B "IuRy%)R    r5c`t|}t|}|ddddd||dd| |dddddgS)zqReturns a rotation matrix about the x-axis. Args: angle: rotation angle in radians r!r"r r ranglecos_asin_as rx_rotatezMatrix44.x_rotatesNE E  B ub r B    r5c`t|}t|}||d| ddddd|d|dddddgS)zqReturns a rotation matrix about the y-axis. Args: angle: rotation angle in radians r"r!rrs ry_rotatezMatrix44.y_rotate$sNE E  2vr B 2ub B    r5c`t|}t|}|||dd| |ddddddddddgS)zqReturns a rotation matrix about the z-axis. Args: angle: rotation angle in radians r"r!rrs rz_rotatezMatrix44.z_rotate7sNE E  5"b FE2r B B    r5cht|}t|}d|z }t|j\}}}|||z|z|z||z|z||zz||z|z||zz d||z|z||zz ||z|z|z||z|z||zzd||z|z||zz||z|z||zz ||z|z|zdddddgS)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|) raxisrrdsomcxyzs r axis_rotatezMatrix44.axis_rotateJs J JAgt*&&(1a ECK!OQUS[1q50!a%#+A2Er ECK!a% Qq!a%#+A2Er ECK!a% Qq1u!4a!eckAor B    r5c2t|}t|}t|}t|}t|}t|} ||z} ||z} |||z| |z|| zz| |z|| zzd| | z| | z||zz| | z||zzd|| |z||zdddddgS)aReturns 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_rotatezMatrix44.xyz_rotate`s\ \ \ \ \ \BwBw GTBYb(4%"*rBw*> C"Htebj27*D2IR,? b"r'2 B    r5ctj|}tj|}|d|dd|dddddddddddgS)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_xyzMatrix44.shear_xy|sVXXg  XXg  B B B B    r5c|d|z||z z ddddd|z||z z dd||z||z z ||z||z z ||z||z z dddd|z|z||z z dgS)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"grB)rleftrighttopbottomnearfars rperspective_projectionzMatrix44.perspective_projections, $Y54< ("b" dsV|,b" T\edl +cFlsV|-LTzcDj) *C rCx$3:67    r5cp|t|dz z}| |z}||z}| }|} |j|||| ||S)a Returns 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_fovz#Matrix44.perspective_projection_fovsRC#I&w))$vsD#NNr5c2t}|D]}||z} |S)z.> U#>rr rNrOrBris`rrCz Matrix44.rows>>>r5cfddDS)z!Iterate over columns as 4-tuples.c3@K|]}j|ywr)r`rs rr=z#Matrix44.columns.. rrrrBris`rcolumnszMatrix44.columnsrr5c|j}t|\}}}t||dz||dzz||dzz|dz||dz||dzz||dzz|dz||d z||d zz||d zz|d zS) zReturns a transformed vertex.rr&r]rGr rF rHrNrM rlrm)r1vectorrJrrrs r transformzMatrix44.transform"s LLv,1a !Hq1Q4x !ad( *QrU 2 !Hq1Q4x !ad( *QrU 2 !Hq1Q4x !ae) +ae 3  r5c |j}t|\}}}t||dz||dzz||dzz||dz||dzz||dzz||dz||dzz||d zz}|r|jS|S) z;Returns a transformed direction vector without translation.rr&r]r rFrrNrMrr rr|)r1rr|rJrrrrs rtransform_directionzMatrix44.transform_direction.s LLv,1a  !Hq1Q4x !ad( * !Hq1Q4x !ad( * !Hq1Q4x !ae) +  !*q{{}0q0r5c#K|j\}}}}}}}} } } } } }}}}|D]V}t|\}}}t||z||zz|| zz|z||z||zz|| zz|z||z||zz|| zz|zXyw)z,Returns an iterable of transformed vertices.Nrm)r1vectorsm0rrm3m4m5m6m7m8m9m10m11m12m13m14m15rrrrs rtransform_verticeszMatrix44.transform_vertices=s LL  B B C c3 F6lGAq!BR!b&(3.BR!b&(3.BR!c')C/  sA:A<c#K|j}|d}|d}|d}|d}|d}|d}|D]K} t| } | j} | j} t| |z| |zz|z| |z| |zz|zMyw)a-Fast 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&rFrGrHN)r rrr) r1pointsrJrrrrrr pntrrrs rfast_2d_transformzMatrix44.fast_2d_transformQs" LL qT qT qT qTee ECS AAAq2vB,a"fq2vo.CD D  EsAc |dk(r;tj|jtj}d|_nG|dk(r7tj|j tj}d|_n t dtjtj|ddd|ftj|jdd ffd |}|ddd|fj|ddd|f<y) a3Transforms 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 rNr#)rOrOrO)r&r&zndim has to be 2 or 3Nrr )r) r+r,rKr-r0r r/r concatenateonesr*)r1r,ndimrJrs rtransform_array_inplacez Matrix44.transform_array_inplaceos 19335RZZHAAG QYRZZ8AAG45 5 II NNE!UdU(ORWWekk!na5H-IJQR SUV AuuH+**,a$hr5c #K|j^ }}}}}}} } } } } }|D]a}t|\}}}t||z||zz|| zz||z||zz|| zz||z|| zz|| zz}|r|jn|cyw)z[Returns an iterable of transformed direction vectors without translation. Nr)r1rr|rrrrrrrrrrr_rrrrrs rtransform_directionszMatrix44.transform_directionss;?,,7BBBBBa 4F6lGAq!BR!b&(BR!b&(BR!c')A $-!++-! 3 4sBBc>|j||jz S)zReturns an UCS vector from WCS vertex. Works only if matrix is used as cartesian UCS without scaling. (internal API) )ucs_direction_from_wcsrn)r1wcss rucs_vertex_from_wcszMatrix44.ucs_vertex_from_wcss**3+<==r5c |j^ }}}}}}}} } } } } |\}}}t||z||zz||zz||z||zz||zz|| z|| zz|| zzS)zReturns UCS direction vector from WCS direction. Works only if matrix is used as cartesian UCS without scaling. (internal API) rm)r1rrrrrrrrrrrrrrrrs rrzMatrix44.ucs_direction_from_wcss;?,,7BBBBBa1a FQVOa"f $ FQVOa"f $ FQVOa#g %  r5c|jjdd}tj|j|_y)z#Swaps the rows for columns inplace.r&N)r rr+rTrIs r transposezMatrix44.transposes+ LL A &xx} r5cttjj|jj ddS)zReturns determinant.r&)r+linalgdetr rris r determinantzMatrix44.determinants&yy}}T\\11!Q788r5c tjj|jj dd}tj||_y#tjj $rt wxYw)zzCalculates the inverse of the matrix. Raises: ZeroDivisionError: if matrix has no inverse. r&N)r+r"invr r LinAlgErrorZeroDivisionErrorr)r1inverses rr)zMatrix44.inverses] $iimmDLL$8$8A$>?Gxx( yy$$ $# # $s 9A$A:)returnr:)r*tuple[float, ...])rPSequence[float]r*r)r?intr*r+)r?r-rZr,r*None)r_r-r*r+)r_r-rZr,)r*r)r*r)rrr*r.)r*bool)NN)rrrOptional[float]rr0r*r)rrrrrrr*r)rrr*r)rrrrr*r)rrrrrrr*r)rr)rrrrr*r)rrrrrrrrrrrrr*r) rrrrrrrrr*r)rrr*r) rrrrvrryrrnrr*r)rWtuple[int, int]r<r)rWr1)r*zIterator[float])rrr*r)r*zIterator[tuple[float, ...]])rrr*r)F)rIterable[UVec]r*zIterator[Vec3])rr2r*zIterator[Vec2])r,z np.ndarrayrr-r*r.)rrr*r)r*r.)r*r)C__name__ __module__ __qualname____doc__ __slots____annotations__r+r,r-r)r4rDrK staticmethodrRrXr[r`rfr*__copy__propertyrnsetterrrrvryr~r classmethodrrrrrrrrrrr rrrrrrrrrrrrCrrr ocs_to_wcsr rrrrr ocs_from_wcsr r$r)rBr5rrr!sL&I $$  I50RC& : : ::$,H )) ]]&&''''((OO   JN+8G *    $  $  $  *  6  (             <OO!&O.3O:?O OO&           :=="00??   1%J(E<-6274%4 4&> $*L% 9 )r5)rrr*z list[float]) __future__rtypingrrrrrrnumpyr+ numpy.typingnptr r r itertoolsr _vectorrrrrrr ezdxf.mathr__all__rrrBr5rrIsI#HH A@ ,%m )m )r5