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Edit File: bezier.cpython-38.pyc
U ��]�; � @ s$ d Z ddlZddlmZ ddlmZ G dd� de�Zdd� Z dd � Z d d � Z d d � Z e� ddd�d1dd��ZG dd� de�Ze� ddd�d2dd��Ze�d�e� ddd�d3dd���Ze� ddd�d4d d ��Zd d � Zd!d"� Ze� ddd�d5d$d%��Zd&d'� Zd(d)� Zd6d+d,�Zd-d.� Zd/d0� Z dS )7zO A module providing some utility functions regarding bezier path manipulation. � N)�Pathc @ s e Zd ZdS )� NonIntersectingPathExceptionN)�__name__� __module__� __qualname__� r r �3/usr/lib/python3/dist-packages/matplotlib/bezier.pyr s r c s� || || }|| || } || } } || } } | | | | � t �� �dk r^td��| | }}| | }}� fdd�||||fD �\}}}}|| || }|| || }||fS )z� Return the intersection between the line through (*cx1*, *cy1*) at angle *t1* and the line through (*cx2, cy2) at angle *t2*. g�-���q=zcGiven lines do not intersect. Please verify that the angles are not equal or differ by 180 degrees.c s g | ] }|� �qS r r )�.0�k�Zad_bcr r � <listcomp>* s z$get_intersection.<locals>.<listcomp>)�np�abs� ValueError)Zcx1Zcy1�cos_t1�sin_t1Zcx2Zcy2�cos_t2�sin_t2Z line1_rhsZ line2_rhs�a�b�c�dZa_Zb_Zc_Zd_�x�yr r r �get_intersection s "r c C sl |dkr| || |fS || }}| | }}|| | || | } } || | || | } } | | | | fS )z� For a line passing through (*cx*, *cy*) and having a angle *t*, return locations of the two points located along its perpendicular line at the distance of *length*. � r ) �cx�cy�cos_t�sin_tZlengthr r r r �x1�y1Zx2Zy2r r r �get_normal_points2 s r" c C s( | d d� d| | dd � | }|S )N���� r )�beta�tZ next_betar r r �_de_casteljau1K s $r' c C s\ t �| �} | g}t| |�} |�| � t| �dkrq4qdd� |D �}dd� t|�D �}||fS )z� Split a bezier segment defined by its control points *beta* into two separate segments divided at *t* and return their control points. r$ c S s g | ] }|d �qS )r r �r r% r r r r \ s z&split_de_casteljau.<locals>.<listcomp>c S s g | ] }|d �qS )r# r r( r r r r ] s )r �asarrayr' �append�len�reversed)r% r& Z beta_listZ left_betaZ right_betar r r �split_de_casteljauP s r- z3.1Z tolerence� tolerancer � �?�{�G�z�?c C s� | |�}| |�}||�}||�}||kr8||kr8t d��t�|d |d |d |d �|k rh||fS d|| } | | �} || �} || A r�| }| }| }q8| }| }| }q8dS )a$ Find a parameter t0 and t1 of the given bezier path which bounds the intersecting points with a provided closed path(*inside_closedpath*). Search starts from *t0* and *t1* and it uses a simple bisecting algorithm therefore one of the end point must be inside the path while the other doesn't. The search stop when |t0-t1| gets smaller than the given tolerance. value for - bezier_point_at_t : a function which returns x, y coordinates at *t* - inside_closedpath : return True if the point is inside the path z3Both points are on the same side of the closed pathr r$ � �?N)r r Zhypot) �bezier_point_at_t�inside_closedpath�t0�t1r. �start�endZ start_insideZ end_insideZmiddle_tZmiddleZ middle_insider r r �*find_bezier_t_intersecting_with_closedpathb s( �( r8 c @ sP e Zd ZdZe�ddg�e�dddg�e�ddddg�d�Zdd� Zdd � Zd S ) � BezierSegmentz: A simple class of a 2-dimensional bezier segment r/ � @g @)r$ � � c C sJ t |�}t�|�| _tj|d }t�|�j\}}|| | _|| | _ dS )z� *control_points* : location of contol points. It needs have a shape of n * 2, where n is the order of the bezier line. 1<= n <= 3 is supported. r$ N) r+ r Zarange�_ordersr9 � _binom_coeffr) �T�_px�_py)�selfZcontrol_pointsZ_oZ_coeffZxxZyyr r r �__init__� s zBezierSegment.__init__c C sF d| | j ddd� || j }t�|| j�}t�|| j�}||fS )zevaluate a point at tr$ Nr# )r= r �dotr@ rA )rB r& ZttZ_xZ_yr r r � point_at_t� s "zBezierSegment.point_at_tN) r r r �__doc__r Zarrayr> rC rE r r r r r9 � s �r9 c C s> t | �}|j}t|||d�\}}t| || d �\}}||fS )z� bezier : control points of the bezier segment inside_closedpath : a function which returns true if the point is inside the path )r. r: )r9 rE r8 r- ) Zbezierr3 r. Zbzr2 r4 r5 Z_leftZ_rightr r r �)split_bezier_intersecting_with_closedpath� s � rG c s0 |\��� ���fdd�}t || |||d� dS )z� Find a radius r (centered at *xy*) between *rmin* and *rmax* at which it intersect with the path. inside_closedpath : function cx, cy : center cos_t, sin_t : cosine and sine for the angle rmin, rmax : c s � | � �| � fS )Nr )�r�r r r r r r �_f� s z,find_r_to_boundary_of_closedpath.<locals>._f)r4 r5 r. N)r8 )r3 �xyr r ZrminZrmaxr. rJ r rI r � find_r_to_boundary_of_closedpath� s �rL Fc C s | � � }t|�\}}||dd� �}|}tj} d} d} |D ]L\}}| } | t|�d 7 } ||dd� �|kr�| |dd� |g�} q�|}q:td��| �d�} t| ||�\}}t|�dkr�tj g}tj tj g}nft|�dkr�tj tj g}tj tj tj g}n<t|�d k�r*tj tj tj g}tj tj tj tj g}nt d ��|dd� }|dd� }| jdk�r�t| | jd| � |g��}t| || j| d� g��}n\t| | jd| � |g�| | jd| � |g��}t| || j| d� g�| || j| d� g��}|�r�|�s�|| }}||fS ) zW divide a path into two segment at the point where inside(x, y) becomes False. ���Nr r$ r; z*The path does not intersect with the patch)r# r; r< � z This should never be reached)Z iter_segments�nextr � concatenater+ r ZreshaperG r �LINETO�MOVETOZCURVE3ZCURVE4�AssertionError�codes�vertices)�pathZinsider. Z reorder_inoutZ path_iterZ ctl_pointsZcommandZ begin_insideZctl_points_old�concatZiold�iZ bezier_pathZbp�left�rightZ codes_leftZ codes_rightZ verts_leftZ verts_rightZpath_inZpath_outr r r �split_path_inout� sZ � �� r[ c s |d �� ��fdd�}|S )Nr; c s$ | \}}|� d |� d �k S )Nr; r )rK r r �r r Zr2r r rJ # s zinside_circle.<locals>._fr )r r rH rJ r r\ r � inside_circle s r] c C sB || || }}|| || d }|dkr2dS || || fS )Nr1 r )r r r )Zx0Zy0r r! ZdxZdyr r r r � get_cos_sin+ s r^ ��h㈵��>c C sR t �| |�}t �||�}t �|| �}||k r2dS t �|t j �|k rJdS dS dS )z� returns * 1 if two lines are parallel in same direction * -1 if two lines are parallel in opposite direction * 0 otherwise r$ r# FN)r Zarctan2r Zpi)Zdx1Zdy1Zdx2Zdy2r. Ztheta1Ztheta2Zdthetar r r �check_if_parallel4 s r` c C sn | d \}}| d \}}| d \}}t || || || || �}|dkrrt�d� t||||�\} } | | } } n$t||||�\} } t||||�\} } t||| | |�\} }}}t||| | |�\}}}}|dk�rd| | d|| }}d|| d|| }}n4t| || | ||| | �\}}t||| | ||| | �\}}| |f||f||fg}||f||f||fg}||fS )z� Given the quadratic bezier control points *bezier2*, returns control points of quadratic bezier lines roughly parallel to given one separated by *width*. r r$ r; r# z8Lines do not intersect. A straight line is used instead.r1 )r` �cbookZ_warn_externalr^ r" r )�bezier2�width�c1x�c1y�cmx�cmy�c2x�c2yZ parallel_testr r r r �c1x_left�c1y_left� c1x_right� c1y_rightZc2x_leftZc2y_leftZ c2x_rightZ c2y_rightZcmx_leftZcmy_leftZ cmx_rightZ cmy_right� path_left� path_rightr r r � get_parallelsF sb �� � � � � � ���rp c C s> dd| | | }dd| || }| |f||f||fgS )z� Find control points of the Bezier curve passing through (*c1x*, *c1y*), (*mmx*, *mmy*), and (*c2x*, *c2y*), at parametric values 0, 0.5, and 1. r1 rN r )rd re ZmmxZmmyrh ri rf rg r r r �find_control_points� s rq r1 c % C s( | d \}}| d \}}| d \} } t ||||�\} } t ||| | �\} }t||| | || �\}}}}t| | | ||| �\}}}}|| d || d }}|| d || d }}|| d || d }} t ||||�\} } t|| | | || �\} } }!}"t||| | ||�}#t|||!|"||�}$|#|$fS )z� Being similar to get_parallels, returns control points of two quadratic bezier lines having a width roughly parallel to given one separated by *width*. r r$ r; r1 )r^ r" rq )%rb rc Zw1ZwmZw2rd re rf rg Zc3xZc3yr r r r rj rk rl rm Zc3x_leftZc3y_leftZ c3x_rightZ c3y_rightZc12xZc12yZc23xZc23yZc123xZc123yZcos_t123Zsin_t123Z c123x_leftZ c123y_leftZ c123x_rightZ c123y_rightrn ro r r r �make_wedged_bezier2� s8 � � � � �rr c C sF | j }|dkr>tjt| j�tjtjd�}tj|d< t| j|�S | S dS )z� If the :attr:`codes` attribute of `Path` *p* is None, return a copy of *p* with the :attr:`codes` set to (MOVETO, LINETO, LINETO, ..., LINETO); otherwise return *p* itself. N)Zdtyper ) rT r Zfullr+ rU r rQ Z code_typerR )�pr r r r �make_path_regular� s rt c C s2 t �dd� | D ��}t �dd� | D ��}t||�S )z/Concatenate a list of paths into a single path.c S s g | ] }|j �qS r )rU �r rs r r r r � s z%concatenate_paths.<locals>.<listcomp>c S s g | ]}t |�j�qS r )rt rT ru r r r r � s )r rP r )�pathsrU rT r r r �concatenate_paths� s rw )r r/ r0 )r0 )r r/ r0 )r0 F)r_ )r/ r1 r ) rF Znumpyr Zmatplotlib.cbookra Zmatplotlib.pathr r r r r" r' r- Z_rename_parameterr8 �objectr9 rG Z deprecatedrL r[ r] r^ r` rp rq rr rt rw r r r r �<module> sD ! � 0! � � > J 3