a
    Ø¶îaª  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clipÚhypot)	Úp1Úp2Zp0Zx21Zy21Zx01Zy01ÚuÚd© r
   úk/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/mpl_toolkits/mplot3d/proj3d.pyÚ_line2d_seg_dist	   s     r   c              	   C   sŽ   ||  }|| }|| }	|durB|\}
}}||
 }|| }|	| }	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dzÚ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  |¡r‚|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yD   Y n0 |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    
r5   c                 C   s   t  | ||t  | ¡g¡S ©N)r   r   Z	ones_like)r2   r3   r4   r
   r
   r   r0   ‡   s    r0   c                 C   s   t | ||ƒ}t||ƒS )z7
    Transform the points by the projection matrix
    )r0   r,   ©r2   r3   r4   r&   r%   r
   r
   r   Úproj_transform‹   s    r8   c                 C   s   t | ||ƒ}t||ƒS )zy
    Transform the points by the projection matrix
    and return the clipping result
    returns txs, tys, tzs, tis
    )r0   r.   r7   r
   r
   r   Úproj_transform_clip–   s    r9   c                 C   s   t  t| |ƒ¡S r6   )r   Zcolumn_stackÚproj_trans_points)Úpointsr&   r
   r
   r   Úproj_points    s    r<   c                 C   s   t | Ž \}}}t||||ƒS r6   )Úzipr8   )r;   r&   r2   r3   r4   r
   r
   r   r:   ¤   s    r:   c                 C   sN   t  |¡t  |¡ }}t  g d¢d|| dgd||dgg d¢g¡}t  || ¡S )Nr   r   r   )r   ÚcosÚsinr   r   )r   ÚalphaZcosaZsinaZM1r
   r
   r   Úrot_x©   s    

ýrA   )N)Ú__doc__Znumpyr   Znumpy.linalgr   r   r   r   r!   r"   r,   r.   r5   r0   r8   Z	transformr9   r<   r:   rA   r
   r
   r
   r   Ú<module>   s$    þ
 	

