U md@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)ps0s1Zs01Zs0pl2p1rT/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/mpl_toolkits/mplot3d/proj3d.py_line2d_seg_dist s $rc Cs||}||}||} |dk rB|\} } } || }|| }| | } td|dd| |gdd|d| |gddd| | | gddddggS)z Produce a matrix that scales homogeneous coords in the specified ranges to [0, 1], or [0, pb_aspect[i]] if the plotbox aspect ratio is specified. Nrrrarray) ZxminZxmaxZyminZymaxZzminZzmaxZ pb_aspectZdxZdyZdzZaxZayazrrrworld_transformation s  rc Cs|tj|\}}}t|}t|}dt|dd}t||||||||||||||g||||||||||||||g||||||||||||||gg}|S)zK Produce a rotation matrix for an angle in radians about a vector. r)rlinalgnormsincosr) vZangleZvxZvyZvzsctRrrrrotation_about_vector6s  444rcCsv||}|tj|}t||}|tj|}t||}|dkrlt|| }t||}t||}|||fS)a Get the unit viewing axes in data coordinates. Parameters ---------- E : 3-element numpy array The coordinates of the eye/camera. R : 3-element numpy array The coordinates of the center of the view box. V : 3-element numpy array Unit vector in the direction of the vertical axis. roll : float The roll angle in radians. Returns ------- u : 3-element numpy array Unit vector pointing towards the right of the screen. v : 3-element numpy array Unit vector pointing towards the top of the screen. w : 3-element numpy array Unit vector pointing out of the screen. r)rrrcrossrdot)ErVrollwurZRrollrrr _view_axesGs     r'cCsPtd}td}|||g|ddddf<| |dddf<t||}|S)a Return the view transformation matrix. Parameters ---------- u : 3-element numpy array Unit vector pointing towards the right of the screen. v : 3-element numpy array Unit vector pointing towards the top of the screen. w : 3-element numpy array Unit vector pointing out of the screen. E : 3-element numpy array The coordinates of the eye/camera. Nr)reyer!)r&rr%r"ZMrZMtMrrr_view_transformation_uvwns    r,cCs&t||||\}}}t||||}|S)az Return the view transformation matrix. Parameters ---------- E : 3-element numpy array The coordinates of the eye/camera. R : 3-element numpy array The coordinates of the center of the view box. V : 3-element numpy array Unit vector in the direction of the vertical axis. roll : float The roll angle in radians. )r'r,)r"rr#r$r&rr%r+rrrview_transformationsr-c Csf|}d}||||}d||||}t|dddgd||ddgdd||gddddgg}|S)Nrrrr)zfrontzbackZ focal_lengtheabr proj_matrixrrrpersp_transformations  r5c CsJ|| }|| }tddddgddddgddddgdd||gg}|S)Nrrr.r)r/r0r2r3r4rrrortho_transformations     r6cCsFt||}|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}||||fSr7)rr!any)r8r+r9r%r:r;r<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+ZiMr8Zvecrrrr inv_transforms   rFcCst|||t|gSN)rrZ ones_like)rCrDrErrrrAsrAcCst|||}t||S)z< Transform the points by the projection matrix *M*. )rAr=rCrDrEr+r8rrrproj_transforms rIcCst|||}t||S)zy Transform the points by the projection matrix and return the clipping result returns txs, tys, tzs, tis )rAr?rHrrrproj_transform_clips rJcCstt||SrG)rZ column_stackproj_trans_points)pointsr+rrr proj_pointssrMcCst|\}}}t||||SrG)ziprI)rLr+rCrDrErrrrKsrKc CsVt|t|}}tddddgd|| dgd||dgddddgg}t||S)Nrr)rrrrr!)r#alphaZcosaZsinaZM1rrrrot_xs   rP)N)__doc__numpyrZ numpy.linalgrrrrr'r,r-r5r6r=r?rFrArIZ transformrJrMrKrPrrrrs*  '