U Ev f@sdZddlZddlmZddZd%ddZddZd d Zd d Z d dZ ddZ ddZ ddZ ddZddZddZddZeZddZdd Zd!d"Zd#d$ZdS)&z, Various transforms used for by the 3D code NcCslt|}||}||}||}t||d}|tjt|||dd|}||djdddS)a7 Return the distance(s) from point(s) *p* to segment(s) (*s0*, *s1*). Parameters ---------- p : (ndim,) or (N, ndim) array-like The points from which the distances are computed. s0, s1 : (ndim,) or (N, ndim) array-like The xy(z...) coordinates of the segment endpoints. r)Zaxisg?)npZasarraywheremultiplyouterZclipsum)ps0s1Zs01Zs0pl2p1r?/tmp/pip-unpacked-wheel-7vhvci0g/mpl_toolkits/mplot3d/proj3d.py_line2d_seg_dist s $rc Cs||}||}||} |dk rB|\} } } || }|| }| | } td|dd| |gdd|d| |gddd| | | gddddggS)z Produce a matrix that scales homogeneous coords in the specified ranges to [0, 1], or [0, pb_aspect[i]] if the plotbox aspect ratio is specified. Nrrrarray) ZxminZxmaxZyminZymaxZzminZzmaxZ pb_aspectZdxZdyZdzZaxZayazrrrworld_transformation s  rc Cs|tj|\}}}t|}t|}dt|dd}t||||||||||||||g||||||||||||||g||||||||||||||gg}|S)zK Produce a rotation matrix for an angle in radians about a vector. r)rlinalgnormsincosr) vZangleZvxZvyZvzsctRrrrrotation_about_vector6s  444rcCsv||}|tj|}t||}|tj|}t||}|dkrlt|| }t||}t||}|||fS)a Get the unit viewing axes in data coordinates. Parameters ---------- E : 3-element numpy array The coordinates of the eye/camera. R : 3-element numpy array The coordinates of the center of the view box. V : 3-element numpy array Unit vector in the direction of the vertical axis. roll : float The roll angle in radians. Returns ------- u : 3-element numpy array Unit vector pointing towards the right of the screen. v : 3-element numpy array Unit vector pointing towards the top of the screen. w : 3-element numpy array Unit vector pointing out of the screen. r)rrrZcrossrdot)ErVrollwurZRrollrrr _view_axesGs     r&cCsPtd}td}|||g|ddddf<| |dddf<t||}|S)a Return the view transformation matrix. Parameters ---------- u : 3-element numpy array Unit vector pointing towards the right of the screen. v : 3-element numpy array Unit vector pointing towards the top of the screen. w : 3-element numpy array Unit vector pointing out of the screen. E : 3-element numpy array The coordinates of the eye/camera. Nr)rZeyer )r%rr$r!ZMrZMtMrrr_view_transformation_uvwns    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*)r!rr"r#r%rr$r)rrrview_transformationsr+c Csf|}d}||||}d||||}t|dddgd||ddgdd||gddddgg}|S)Nrrrr)zfrontzbackZ focal_lengtheabr proj_matrixrrrpersp_transformations  r3c CsJ|| }|| }tddddgddddgddddgdd||gg}|S)Nrrr,r)r-r.r0r1r2rrrortho_transformations     r4cCsFt||}|d}|d||d||d|}}}|||fSNr(rrr)rr )vecr)vecwr$txstystzsrrr_proj_transform_vecs (r;cCst||}|d}|d||d||d|}}}d|dk|ddk@d|dk@|ddk@}t|r|ddk}||||fSr5)rr any)r6r)r7r$r8r9r:Ztisrrr_proj_transform_vec_clips (0  r=cCs^t|}t|||}t||}z||d}Wntk rFYnX|d|d|dfS)zK Transform the points by the inverse of the projection matrix *M*. r(rrr)rinv _vec_pad_onesrr OverflowError)xsyszsr)ZiMr6Zvecrrrr inv_transforms   rDcCst|||t|gSN)rrZ ones_like)rArBrCrrrr?sr?cCst|||}t||S)z< Transform the points by the projection matrix *M*. )r?r;rArBrCr)r6rrrproj_transforms rGcCst|||}t||S)zy Transform the points by the projection matrix and return the clipping result returns txs, tys, tzs, tis )r?r=rFrrrproj_transform_clips rHcCstt||SrE)rZ column_stackproj_trans_points)pointsr)rrr proj_pointssrKcCst|\}}}t||||SrE)ziprG)rJr)rArBrCrrrrIsrIc CsVt|t|}}tddddgd|| dgd||dgddddgg}t||S)Nrr)rrrrr )r"alphaZcosaZsinaZM1rrrrot_xs   rN)N)__doc__ZnumpyrZ numpy.linalgrrrrr&r*r+r3r4r;r=rDr?rGZ transformrHrKrIrNrrrrs*  '