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Various transforms used for by the 3D code
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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 � � )�np�asarray�clip�hypot) �p1�p2�p0�x21�y21�x01�y01�u�d� r �=/usr/lib/python3/dist-packages/mpl_toolkits/mplot3d/proj3d.py�_line2d_seg_dist s r c
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}|| }| | } t �d| dd| | gdd| d| | gddd| | | gg d�g�S )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.
Nr r �r r r r �r �array)
�xmin�xmax�ymin�ymax�zmin�zmax� pb_aspect�dx�dy�dz�ax�ay�azr r r �world_transformation s
�r$ c C s� | | }|t j�|� }t �||�}|t j�|� }t �||�}|d |d |d dg|d |d |d dg|d |d |d dgg d�g}ddd| d gddd| d gddd| d gg d�g}t �||�S )Nr r r r )r �linalg�norm�cross�dot)�E�R�V�nr �v�Mr�Mtr r r �view_transformation6 s
�� r0 c C sJ | | | | }d| | | | }t �g d�g d�dd||gg d�g�S )N����r r r r )r r r r r )r r ���r r ��zfront�zback�a�br r r �persp_transformationV s
�r9 c C s: | | }| | }t �g d�g d�g d�dd||gg�S )N)r r r r )r r r r )r r r1 r r r r4 r r r �ortho_transformation_ s
�r: c C sF t �|| �}|d }|d | |d | |d | }}}|||fS �N� r r r )r r( )�vec�M�vecw�w�txs�tys�tzsr r r �_proj_transform_veci s (
rD c C s� t �|| �}|d }|d | |d | |d | }}}d|d k|d dk@ d|d k@ |d dk@ }t �|�rA|d dk }||||fS r; )r r( �any)r= r> r? r@ rA rB rC �tisr r r �_proj_transform_vec_clipq s (0
rG c C s\ t �|�}t| ||�}t�||�}z||d }W n ty" Y nw |d |d |d fS r; )r% �inv�
_vec_pad_onesr r( �
OverflowError)�xs�ys�zsr> �iMr= �vecrr r r �
inv_transform| s
�rP c C s t �| ||t �| �g�S �N)r r � ones_like)rK rL rM r r r rI � s rI c C � t | ||�}t||�S )z7
Transform the points by the projection matrix
)rI rD �rK rL rM r> r= r r r �proj_transform� s
rU c C rS )zy
Transform the points by the projection matrix
and return the clipping result
returns txs, tys, tzs, tis
)rI rG rT r r r �proj_transform_clip� s
rV c C s t �t| |��S rQ )r � column_stack�proj_trans_points)�pointsr> r r r � proj_points� s rZ c C s t | � \}}}t||||�S rQ )�ziprU )rY r> rK rL rM r r r rX � s rX c C sN t �|�t �|�}}t �g d�d|| dgd||dgg d�g�}t �|| �S )Nr2 r r )r �cos�sinr r( )r+ �alpha�cosa�sina�M1r r r �rot_x� s
� rb rQ )�__doc__�numpyr � numpy.linalgr% r r$ r0 r9 r: rD rG rP rI rU � transformrV rZ rX rb r r r r �<module> s&
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