Venn region subtraction & intersection geometry :: Visual examination



In [1]:

    
from pylab import *
from matplotlib_venn import _region, _math
import warnings
warnings.simplefilter("error") # Have warnings raise exceptions in this test

def show_region(r, c='r', xlim=(-2,2), ylim=(-2,2)):
    gca().set_aspect('equal')
    gca().set_xlim(*xlim)
    gca().set_ylim(*ylim)
    p = r.make_patch()
    if p is not None:
        p.set_color(c)
        p.set_ec('none')
        p.set_alpha(0.5)
        gca().add_patch(p)
        
def test_region_subtraction_intersection(region, center, radius, xlim=(-2, 2), ylim=(-2, 2)):
    vcr = _region.VennCircleRegion(center, radius)
    subplot(121)
    show_region(region, 'r')
    show_region(vcr, 'b', xlim, ylim)
    subplot(122)
    s, i = region.subtract_and_intersect_circle(center, radius)
    s.verify()
    i.verify()
    assert abs(s.size() + i.size() - region.size()) < _math.tol
    show_region(s, 'r')
    show_region(i, 'm', xlim, ylim)

def test_two_circles(c1, r1, c2, r2, xlim, ylim=(-2, 2)):
    test_region_subtraction_intersection(_region.VennCircleRegion(c1, r1), c2, r2, xlim)
    
r1, r2 = _region.VennCircleRegion((0, 0), 1).subtract_and_intersect_circle((1, 0), 1)
r3, r4 = _region.VennCircleRegion((0, 0), 1).subtract_and_intersect_circle((0.6,0), 0.45)

Circular regions



In [4]:

    
test_two_circles((0, 0), 1, (1, 0), 1, (-1.5, 2.5))
suptitle("The usual case");



In [5]:

    
test_two_circles((0, 0), 1, (0.5, 0), 0.5, (-1.5, 1.5))
suptitle("One smaller inside the other");



In [6]:

    
test_two_circles((0, 0), 1, (0, 0), 1, (-1.5, 1.5))
suptitle("Two equal circles");



In [7]:

    
test_two_circles((0.6, 0), 0.5, (0, 0), 1, (-1.5, 1.5))
suptitle("Subtracting larger from smaller");



In [8]:

    
test_two_circles((0.5, 0), 0.5, (0, 0), 1, (-1.5, 1.5))
suptitle("Subtracting larger from smaller, corner case");



In [9]:

    
test_two_circles((0, 0), 1, (1.5, 0), 0.5, (-1.5, 2.5))
suptitle("Subtracting external circle");



In [10]:

    
test_two_circles((0, 0), 1, (1.4, 0), 0.5, (-1.5, 2.5))
suptitle("Small intersection");

2-arc-gon regions

The following examples illustrates all the special cases covered in the 2-arc-gon/circle subtraction-intersection routine.

I. No intersection points



In [11]:

    
test_region_subtraction_intersection(r2, (2, 0), 0.9, (-2, 4))









    



[[], []]



In [12]:

    
test_region_subtraction_intersection(r2, (0.5, 0), 1.0)









    



[[], []]



In [13]:

    
test_region_subtraction_intersection(r1, (0.51, 0), 0.5)









    



[[], []]



In [14]:

    
test_region_subtraction_intersection(r1, (1.1, 1.1), 0.5)









    



[[], []]



In [15]:

    
test_region_subtraction_intersection(r1, (0, 0), 1.1)









    



[[], []]



In [16]:

    
test_region_subtraction_intersection(r3, (0.6, 0), 0.4)









    



[[], []]

II. Four intersection points



In [17]:

    
test_region_subtraction_intersection(r2, (0.5, 0), 0.6)









    



[[array([ 0.89      , -0.45596052]), array([ 0.89      ,  0.45596052])], [array([ 0.11      ,  0.45596052]), array([ 0.11      , -0.45596052])]]
True



In [18]:

    
test_region_subtraction_intersection(r2, (0.5, 0), sin(pi/3))









    



[[], []]



In [19]:

    
test_region_subtraction_intersection(r2, (0.5, np.sin(np.pi/3)/2), np.sin(np.pi/3)/2)









    



[[array([ 0.92857143,  0.37115374])], [array([ 0.07142857,  0.37115374])]]



In [20]:

    
test_region_subtraction_intersection(r2, (0.5, 0), 0.5, (-2, 2))









    



[[array([ 1.,  0.]), array([ 1.,  0.])], [array([ 0.,  0.]), array([ 0.,  0.])]]
True



In [21]:

    
test_region_subtraction_intersection(r1, (-0.5, 0), 0.5, (-2, 2))









    



[[array([ 0.,  0.]), array([ 0.,  0.])], [array([-1.,  0.]), array([-1.,  0.])]]
True



In [22]:

    
test_region_subtraction_intersection(r1, (-0.5, 0), 0.6, (-2, 2))









    



[[array([ 0.03666667, -0.26830745]), array([ 0.03666667,  0.26830745])], [array([-0.89      ,  0.45596052]), array([-0.89      , -0.45596052])]]
True



In [23]:

    
test_region_subtraction_intersection(r3, (0.9, 0), 0.6, (-2, 2))









    



[[array([ 0.4875    , -0.43571063]), array([ 0.4875    ,  0.43571063])], [array([ 0.80555556,  0.59252025]), array([ 0.80555556, -0.59252025])]]
False



In [24]:

    
test_region_subtraction_intersection(r1, (-1, 0), 1, (-2, 2))









    



[[array([ 0.,  0.]), array([ 0.,  0.])], [array([-0.5      ,  0.8660254]), array([-0.5      , -0.8660254])]]
True

III. Two intersection points

IIIa: 2+0



In [25]:

    
test_region_subtraction_intersection(r1, (-1.1, 0), 1)









    



[[], [array([-0.55      ,  0.83516465]), array([-0.55      , -0.83516465])]]



In [26]:

    
test_region_subtraction_intersection(r1, (0.5, 0), 0.6)









    



[[array([ 0.11      , -0.45596052]), array([ 0.11      ,  0.45596052])], []]



In [27]:

    
test_region_subtraction_intersection(r1, (0.5, 0), 0.5)









    



[[array([ 0.,  0.]), array([ 0.,  0.])], []]



In [28]:

    
test_region_subtraction_intersection(r1, (0.5, 0), 1)









    



[[], [array([ 0.25      ,  0.96824584]), array([ 0.25      , -0.96824584])]]



In [29]:

    
test_region_subtraction_intersection(r2, (0, 0), 0.5)









    



[[], [array([ 0.125     ,  0.48412292]), array([ 0.125     , -0.48412292])]]



In [30]:

    
test_region_subtraction_intersection(r2, (-2, 0), 3)









    



[[array([ 1.,  0.]), array([ 1.,  0.])], []]



In [31]:

    
test_region_subtraction_intersection(r3, (0.6, 0), 0.5)









    



[[], [array([ 0.925    ,  0.3799671]), array([ 0.925    , -0.3799671])]]



In [32]:

    
test_region_subtraction_intersection(r3, (0.6, 0), 0.45)



In [33]:

    
test_region_subtraction_intersection(r2, (-2, 0), 2.8)









    



[[array([ 0.71      , -0.70420168]), array([ 0.71      ,  0.70420168])], []]

IIIb: 1+1



In [34]:

    
test_region_subtraction_intersection(r1, (1, 1), 0.5)









    



[[], []]



In [35]:

    
test_region_subtraction_intersection(r1, (0.9, 0.9), 0.5)









    



[[array([ 0.40881342,  0.80653482])], [array([ 0.40026896,  0.91639771])]]



In [36]:

    
test_region_subtraction_intersection(r1, (0.5, np.sin(pi/3)), 0.5)









    



[[array([ 0.14323725,  0.51571077])], [array([ 0.01823725,  0.99983369])]]



In [37]:

    
test_region_subtraction_intersection(r2, (0.5, 0.5), 0.5)









    



[[array([ 0.95571891,  0.29428109])], [array([ 0.04428109,  0.29428109])]]



In [38]:

    
test_region_subtraction_intersection(r2, (0, 0), 1.0)



In [39]:

    
r = np.linalg.norm(np.array([-1, 0]) - np.array([0.5, sin(np.pi/3)]))
test_region_subtraction_intersection(r2, (-1, 0), r)









    



[[array([ 0.5      , -0.8660254]), array([ 0.5      ,  0.8660254])], []]

Various corner cases



In [4]:

    
centers = np.array([[-0.0823120, 0.02842443], [ 0.02131832, 0.02842443], [ 0.05033492, -0.07106106]])
radii = np.array([ 0.46065887, 0.56418958, 0.46065887])
A = _region.VennCircleRegion(centers[0], radii[0])
B = _region.VennCircleRegion(centers[1], radii[1])
C = _region.VennCircleRegion(centers[2], radii[2])
Ab, AB = A.subtract_and_intersect_circle(B.center, B.radius)
ABc, ABC = AB.subtract_and_intersect_circle(C.center, C.radius)
Abc, AbC = Ab.subtract_and_intersect_circle(C.center, C.radius)
aB, _ = B.subtract_and_intersect_circle(A.center, A.radius)
aBc, aBC = aB.subtract_and_intersect_circle(C.center, C.radius)
aC, _ = C.subtract_and_intersect_circle(A.center, A.radius)
abC, _ = aC.subtract_and_intersect_circle(B.center, B.radius) 
rs = (Abc, aBc, ABc, abC, AbC, aBC, ABC)



In [7]:

    
for r in rs:
    show_region(r)
    lpos = r.label_position()
    if lpos is not None:
        scatter(lpos[0], lpos[1])