DVfdZddlZddlmZ ddZej ddZdZdZ d Z ej dd Z ej dd Z d Z ej dd ZdZdZdZdZdZdZej ddddeZdZej ddZdZej ddZdZej ddZy)z, Various transforms used for by the 3D code N)_apic ||z }||z }||z } ||\} } } || z}|| z}| | z} tjd|z dd| |z gdd|z d| |z gddd| z | | z ggdgS)z Produce a matrix that scales homogeneous coords in the specified ranges to [0, 1], or [0, pb_aspect[i]] if the plotbox aspect ratio is specified. rrrrrnparray) xminxmaxyminymaxzminzmax pb_aspectdxdydzaxayazs d/var/www/html/software/conda/envs/catlas/lib/python3.12/site-packages/mpl_toolkits/mplot3d/proj3d.pyworld_transformationr s B B B B b b b 88adA!b1AbD!b1A!B$b1*, --z3.8ct||S)K Produce a rotation matrix for an angle in radians about a vector. )_rotation_about_vector)vangles rrotation_about_vectorr s "!U ++rc|tjj|z \}}}tj|}tj|}dtj|dz dzz}tj ||z|z|z||z|z||zz ||z|z||zzg||z|z||zz||z|z|z||z|z||zz g||z|z||zz ||z|z||zz||z|z|zgg}|S)r)rlinalgnormsincosr ) rrvxvyvzsctRs rrr(sRYY^^A&&JBB u A u A "&&q/1 A  2b12b2a42b2a48 2b2a42b12b2a48 2b2a42b2a42b157 8A Hrcr||z }|tjj|z }tj||}|tjj|z }tj||}|dk7r9t || }tj ||}tj ||}|||fS)a Get the unit viewing axes in data coordinates. Parameters ---------- E : 3-element numpy array The coordinates of the eye/camera. R : 3-element numpy array The coordinates of the center of the view box. V : 3-element numpy array Unit vector in the direction of the vertical axis. roll : float The roll angle in radians. Returns ------- u : 3-element numpy array Unit vector pointing towards the right of the screen. v : 3-element numpy array Unit vector pointing towards the top of the screen. w : 3-element numpy array Unit vector pointing out of the screen. r)rr"r#crossrdot)Er,VrollwurRrolls r _view_axesr69s0 QA ")).. A AA ")).. A AA qy&q4%0 FF5!  FF5!  a7Nrctjd}tjd}|||g|ddddf<| |dddf<tj||}|S)a Return the view transformation matrix. Parameters ---------- u : 3-element numpy array Unit vector pointing towards the right of the screen. v : 3-element numpy array Unit vector pointing towards the top of the screen. w : 3-element numpy array Unit vector pointing out of the screen. E : 3-element numpy array The coordinates of the eye/camera. N)reyer/)r4rr3r0MrMtMs r_view_transformation_uvwr?`s` B BQBrr2A2vJBrr2vJ r2A HrcFt||||\}}}t||||}|S)az Return the view transformation matrix. Parameters ---------- E : 3-element numpy array The coordinates of the eye/camera. R : 3-element numpy array The coordinates of the center of the view box. V : 3-element numpy array Unit vector in the direction of the vertical axis. roll : float The roll angle in radians. )r6r?)r0r,r1r2r4rr3r>s rview_transformationrAws/ Aq$'GAq! Aq!,A Hrct|||SN)_persp_transformation)zfrontzback focal_lengths rpersp_transformationrHs  ==rc|}d}||z||z z }d||zz||z z }tj|dddgd||z ddgdd||ggdg}|S)Nrr)rrr:rr)rErFrGeabr* proj_matrixs rrDrDswA A u %A F5L6%<(A((Q!aO!aO!aO+-.K rct||SrC)_ortho_transformation)rErFs rortho_transformationrQs  //rc d||z }||z }tjgdgdgddd||gg}|S)N)r!rrr)rr!rr)rrrJrrr)rErFrLrMrNs rrPrPsH 5.A 5.A((M))AqM+,K rcrtj||}|d}|d|z |d|z |d|z }}}|||fSNr9rrr!)rr/)vecr>vecwr3txstystzss r_proj_transform_vecrZsK 66!S>D QAGAItAwqy$q'!)cC S=rctj||}|d}|d|z |d|z |d|z }}}d|dk|ddkzd|dkz|ddkz}tj|r|ddk}||||fSrT)rr/any)rUr>rVr3rWrXrYtiss r_proj_transform_vec_clipr^s 66!S>D QAGaKa1d1gkcC QrUs rproj_transformros B #C sA &&rfunction transformro)obj_typename alternativec4t|||}t||S)zy Transform the points by the projection matrix and return the clipping result returns txs, tys, tzs, tis )r`r^rns rproj_transform_cliprvs B #C #C ++rct||SrC) _proj_pointspointsr>s r proj_pointsr{s  ""rc@tjt||SrC)r column_stack_proj_trans_pointsrys rrxrxs ??-fa8 99rct||SrC)r~rys rproj_trans_pointsrs fa ((rc6t|\}}}t||||SrC)zipro)rzr>rdrerfs rr~r~s"fJBB "b"a ((rctj|tj|}}tjgdd|| dgd||dggdg}tj||S)N)rrrrrr)rr%r$r r/)r1alphacosasinaM1s rrot_xrs_u $D <tdUA&tT1%! "B 66"a=rrC)__doc__numpyr matplotlibrr deprecatedrrr6r?rArHrDrQrPrZr^rjr`rorqrvr{rxrr~rrrrs] 04-,,, "$N .  (>> 00 %4' "ODOO J[  ""0 2 ,##:))) r