o i@s$dZddlZddlmZ d2ddZedddZd d Zd d Z d dZ edddZ edddZ ddZ edddZddZddZddZddZdd Zd!d"Zejdd#d$d"d%eZd&d'Zedd(d)Zd*d+Zedd,d-Zd.d/Zedd0d1ZdS)3z, Various transforms used for by the 3D code N)_apic Cs||}||}||} |dur!|\} } } || }|| }| | } td|dd| |gdd|d| |gddd| | | 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. Nrrrrrnparray) ZxminZxmaxZyminZymaxZzminZzmaxZ pb_aspectZdxZdyZdzaxZayazr j/var/www/html/eduruby.in/lip-sync/lip-sync-env/lib/python3.10/site-packages/mpl_toolkits/mplot3d/proj3d.pyworld_transformation s r z3.8cC t||S)K Produce a rotation matrix for an angle in radians about a vector. )_rotation_about_vector)vangler r r rotation_about_vector s rc Cs|tj|\}}}t|}t|}dt|dd}t||||||||||||||g||||||||||||||g||||||||||||||gg}|S)r)rlinalgnormsincosr) rrZvxZvyZvzsctRr r r r(s  444rcCsv||}|tj|}t||}|tj|}t||}|dkr6t|| }t||}t||}|||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)rrrcrossrdot)ErVrollwurZRrollr r r _view_axes9s      r#cCsPtd}td}|||g|ddddf<| |dddf<t||}|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)r"rr!rZMrZMtMr r r _view_transformation_uvw`s   r)cCs&t||||\}}}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. )r#r))rrrr r"rr!r(r r r view_transformationwsr*cCs t|||SN)_persp_transformation)zfrontzback focal_lengthr r r persp_transformations r0cCsb|}d}||||}d||||}t|dddgd||ddgdd||ggdg}|S)Nrr)rrr&rr)r-r.r/eabr proj_matrixr r r r,s r,cCr r+)_ortho_transformation)r-r.r r r ortho_transformation r7c Cs>|| }|| }tgdgdgddd||gg}|S)N)rrrr)rrrr)rrr1rrr)r-r.r3r4r5r r r r6s    r6cCsFt||}|d}|d||d||d|}}}|||fSNr%rrr)rr)vecr(vecwr!txstystzsr r r _proj_transform_vecs ( r?cCst||}|d}|d||d||d|}}}d|dk|ddk@d|dk@|ddk@}t|rA|ddk}||||fSr9)rrany)r:r(r;r!r<r=r>Ztisr r r _proj_transform_vec_clips (0   rAcCst|||}t||}|jdkr|d}t|jdD]}|d|dkr;|dd|f|d||dd|f<q|d|d|dfS)zO Transform the points by the inverse of the projection matrix, *invM*. )r$)r$rrr%rNr) _vec_pad_onesrrshapeZreshaperange)xsyszsZinvMr:Zvecrir r r inv_transforms    (rIcCst|||t|gSr+)rrZ ones_like)rErFrGr r r rBsrBcCt|||}t||S)z< Transform the points by the projection matrix *M*. )rBr?rErFrGr(r:r r r proj_transforms  rLfunction transform)obj_typename alternativecCrJ)zy Transform the points by the projection matrix and return the clipping result returns txs, tys, tzs, tis )rBrArKr r r proj_transform_clips  rRcCr r+) _proj_pointspointsr(r r r proj_pointsr8rVcCstt||Sr+)rZ column_stack_proj_trans_pointsrTr r r rSsrScCr r+)rWrTr r r proj_trans_pointsr8rXcCst|\}}}t||||Sr+)ziprL)rUr(rErFrGr r r rWsrWcCsNt|t|}}tgdd|| dgd||dggdg}t||S)N)rrrrrr)rrrrr)ralphaZcosaZsinaZM1r r r rot_xs    r[r+)__doc__numpyrZ matplotlibrr deprecatedrrr#r)r*r0r,r7r6r?rArIrBrLrNrRrVrSrXrWr[r r r r sL   '