o
    ¡:´aª  ã                   @   s”   d Z ddlZddlmZ dd„ Z	ddd„Zdd„ Zd	d
„ Zdd„ Z	dd„ Z
dd„ Zdd„ Zdd„ Zdd„ ZeZdd„ Zdd„ Zdd„ Zdd„ ZdS ) z,
Various transforms used for by the 3D code
é    Nc           	      C   sš   |d | d  }|d | d  }t  |d ¡| d  }t  |d ¡| d  }|| ||  |d |d   }t  |dd¡}t  |||  |||  ¡}|S )zâ
    Return the distance(s) from line defined by p1 - p2 to point(s) p0.

    p0[0] = x(s)
    p0[1] = y(s)

    intersection point p = p1 + u*(p2-p1)
    and intersection point lies within segment if u is between 0 and 1
    r   é   é   )ÚnpZasarrayZclipZhypot)	Zp1Zp2Zp0Zx21Zy21Zx01Zy01ÚuÚd© r   ú=/usr/lib/python3/dist-packages/mpl_toolkits/mplot3d/proj3d.pyÚ_line2d_seg_dist	   s    r	   c              	   C   sŽ   ||  }|| }|| }	|dur!|\}
}}||
 }|| }|	| }	t  d| dd|  | gdd| d| | gddd|	 | |	 gg d¢g¡S )zŸ
    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.
    Nr   r   ©r   r   r   r   ©r   Úarray)ZxminZxmaxZyminZymaxZzminZzmaxZ	pb_aspectZdxZdyZdzZaxZayÚazr   r   r   Úworld_transformation    s   
ýr   c                 C   sÒ   | | }|t j |¡ }t  ||¡}|t j |¡ }t  ||¡}|d |d |d dg|d |d |d dg|d |d |d dgg d¢g}ddd| d  gddd| d  gddd| d  gg d¢g}t  ||¡S )Nr   r   r   r
   )r   ÚlinalgZnormZcrossÚdot)ÚEÚRÚVÚnr   ÚvZMrZMtr   r   r   Úview_transformation6   s    ýýr   c                 C   sJ   | | | |  }d| |  | |  }t  g d¢g d¢dd||gg d¢g¡S )Néþÿÿÿ©r   r   r   r   )r   r   r   r   r   )r   r   éÿÿÿÿr   r   ©ZzfrontZzbackÚaÚbr   r   r   Úpersp_transformationV   s   

ýr   c              	   C   s:   | |  }| |  }t  g d¢g d¢g d¢dd||gg¡S )N)r   r   r   r   )r   r   r   r   )r   r   r   r   r   r   r   r   r   r   Úortho_transformation_   s   



ýr   c                 C   sF   t  || ¡}|d }|d | |d | |d | }}}|||fS ©Né   r   r   r   )r   r   )ÚvecÚMÚvecwÚwÚtxsÚtysÚtzsr   r   r   Ú_proj_transform_veci   s   (
r(   c                 C   sŽ   t  || ¡}|d }|d | |d | |d | }}}d|d k|d dk@ d|d k@ |d dk@ }t  |¡rA|d dk }||||fS r   )r   r   Úany)r!   r"   r#   r$   r%   r&   r'   Ztisr   r   r   Ú_proj_transform_vec_clipq   s   (0
r*   c                 C   s\   t  |¡}t| ||ƒ}t ||¡}z||d  }W n	 ty"   Y nw |d |d |d fS r   )r   ÚinvÚ_vec_pad_onesr   r   ÚOverflowError)ÚxsÚysÚzsr"   ZiMr!   Zvecrr   r   r   Úinv_transform|   s   
ÿr1   c                 C   s   t  | ||t  | ¡g¡S ©N)r   r   Z	ones_like)r.   r/   r0   r   r   r   r,   ‡   s   r,   c                 C   ó   t | ||ƒ}t||ƒS )z7
    Transform the points by the projection matrix
    )r,   r(   ©r.   r/   r0   r"   r!   r   r   r   Úproj_transform‹   s   
r5   c                 C   r3   )zy
    Transform the points by the projection matrix
    and return the clipping result
    returns txs, tys, tzs, tis
    )r,   r*   r4   r   r   r   Úproj_transform_clip–   s   
r6   c                 C   s   t  t| |ƒ¡S r2   )r   Zcolumn_stackÚproj_trans_points)Úpointsr"   r   r   r   Úproj_points    s   r9   c                 C   s   t | Ž \}}}t||||ƒS r2   )Úzipr5   )r8   r"   r.   r/   r0   r   r   r   r7   ¤   s   r7   c                 C   sN   t  |¡t  |¡}}t  g d¢d|| dgd||dgg d¢g¡}t  || ¡S )Nr   r   r
   )r   ZcosZsinr   r   )r   ZalphaZcosaZsinaZM1r   r   r   Úrot_x©   s   

ýr;   r2   )Ú__doc__Znumpyr   Znumpy.linalgr   r	   r   r   r   r   r(   r*   r1   r,   r5   Z	transformr6   r9   r7   r;   r   r   r   r   Ú<module>   s&    
þ 	

