o :ήc @sddlZddlmZddZddgddgfddgddgfgdgdfgd gd fgd gd fgd gdfgdgdfdZdddZdS)N)signalcCsl|dkr|St|jdd}t|jd}d|d<d|d<d|jddfg}d}|s.|\}}||ddf\}} ||ddf\} } | |} | | } t| |  }| t||t|}||d|ddf}||d|}|dddf|}|dddf| }|dddf| }|dddf| }|| || }| | || }t|dk|dk}t|}t ||dft|||dft||||<t t ||d||dt ||d||d||<t ||kr#|t |d}|||f|||fd||<t|dkr,d}|r.||ddfS) aApproximate a polygonal chain with the specified tolerance. It is based on the Douglas-Peucker algorithm. Note that the approximated polygon is always within the convex hull of the original polygon. Parameters ---------- coords : (N, 2) array Coordinate array. tolerance : float Maximum distance from original points of polygon to approximated polygonal chain. If tolerance is 0, the original coordinate array is returned. Returns ------- coords : (M, 2) array Approximated polygonal chain where M <= N. References ---------- .. [1] https://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm rboolTFN)npzerosshapepoparctan2sincos logical_and logical_notabsminimumsqrtanyargmaxappendlen)coords tolerancechaindists pos_stack end_of_chainstartendr0c0r1c1drdc segment_angle segment_distsegment_coords segment_distsdr0dc0dr1dc1projected_lengths0projected_lengths1perpeuclnew_endr2?/tmp/pip-target-vg8gfxp4/lib/python/skimage/measure/_polygon.pyapproximate_polygons`   2r4r)rr)rr7) r)rr9r8)rr:r)rr6r6)#r)rr>r=r<)rFr?r)r8rBrA)rrr5r7r8r6r<rFc CsN|tvrtdt|dddf|dddfk}d}|r+|ddddf}d}t|\}}t|td|}t|td|}tj|jt ||dd }tj|jt ||dd }t |j d |j d df} |j| d dd<|j| ddd<|rt | | dddfg} |r|st |dddf| |dddfg} | S) aSubdivision of polygonal curves using B-Splines. Note that the resulting curve is always within the convex hull of the original polygon. Circular polygons stay closed after subdivision. Parameters ---------- coords : (N, 2) array Coordinate array. degree : {1, 2, 3, 4, 5, 6, 7}, optional Degree of B-Spline. Default is 2. preserve_ends : bool, optional Preserve first and last coordinate of non-circular polygon. Default is False. Returns ------- coords : (M, 2) array Subdivided coordinate array. References ---------- .. [1] http://mrl.nyu.edu/publications/subdiv-course2000/coursenotes00.pdf z8Invalid B-Spline degree. Only degree 1 - 7 is supported.rNrvalidsamerwrap)modeboundaryr) _SUBDIVISION_MASKS ValueErrorrallarrayfloatr convolve2dT atleast_2drr vstack) rdegree preserve_endscircularmethod mask_evenmask_oddevenoddoutr2r2r3subdivide_polygonms0& (rZ)rF)numpyrscipyrr4rHrZr2r2r2r3s ^