U Pe@s(dZdZddlmZddZddZdS) zo Geometry utilities ================== This module contains some helper functions for geometric calculations. ) circumcircleminimum_bounding_circleVectorc CsJt|d|d}t|d|d}t|d|d}||d}||d}|j |j|j|j|j|j|j|j|j|j|j|j|j|j|j|j }|j |j|j|j|j|j|j|j|j|j|j|j} || } | |j|j|j} | |j|j|j} | | f|| | ffS)a Computes the circumcircle of a triangle defined by a, b, c. See: http://en.wikipedia.org/wiki/Circumscribed_circle :Parameters: `a`: iterable containing at least 2 values (for x and y) The 1st point of the triangle. `b`: iterable containing at least 2 values (for x and y) The 2nd point of the triangle. `c`: iterable containing at least 2 values (for x and y) The 3rd point of the triangle. :Return: A tuple that defines the circle : * The first element in the returned tuple is the center as (x, y) * The second is the radius (float) r?)ryxlength) abcPQRZmPQZmQRZnumerZdenomtZcxcyr1/tmp/pip-unpacked-wheel-xzebddm3/kivy/geometry.pyr s2  0    $   rcs.dd|D}t|dkr2|dj|djfdfSt|dkrb|\}}||d||dfSt|dd d fd d }t||d |D]}fd d}t||d }||dkr؈ddfSt|dkr|qt|dkr|qq"qt|S)a Returns the minimum bounding circle for a set of points. For a description of the problem being solved, see the `Smallest Circle Problem `_. The function uses Applet's Algorithm, the runtime is ``O(h^3, *n)``, where h is the number of points in the convex hull of the set of points. **But** it runs in linear time in almost all real world cases. See: http://tinyurl.com/6e4n5yb :Parameters: `points`: iterable A list of points (2 tuple with x,y coordinates) :Return: A tuple that defines the circle: * The first element in the returned tuple is the center (x, y) * The second the radius (float) cSsg|]}t|d|dqS)rrr).0prrr Isz+minimum_bounding_circle..rrgrcSs|jS)N)r)rrrrSz)minimum_bounding_circle..)keycs|kr dSt|dS)N _B)rrabsangle)q)rrr x_axis_angleWsz-minimum_bounding_circle..x_axis_anglecs&|fkrdSt||S)Nrr)rrrrrangle_pq_s z)minimum_bounding_circle..angle_pqgV@Z)lenr rr minrrr)Zpointsp1p2r!rr$rrr#rr3s,       rN)__doc____all__Z kivy.vectorrrrrrrrs &