def compute_venn2_regions(centers, radii):
'''
Returns a triple of VennRegion objects, describing the three regions of the diagram, corresponding to sets
(Ab, aB, AB)
>>> centers, radii = solve_venn2_circles((1, 1, 0.5))
>>> regions = compute_venn2_regions(centers, radii)
'''
A = VennCircleRegion(centers[0], radii[0])
B = VennCircleRegion(centers[1], radii[1])
Ab, AB = A.subtract_and_intersect_circle(B.center, B.radius)
aB, _ = B.subtract_and_intersect_circle(A.center, A.radius)
return (Ab, aB, AB)
def compute_venn3_regions(centers, radii):
'''
Given the 3x2 matrix with circle center coordinates, and a 3-element list (or array) with circle radii [as returned from solve_venn3_circles],
returns the 7 regions, comprising the venn diagram, as VennRegion objects.
Regions are returned in order (Abc, aBc, ABc, abC, AbC, aBC, ABC)
>>> centers, radii = solve_venn3_circles((1, 1, 1, 1, 1, 1, 1))
>>> regions = compute_venn3_regions(centers, radii)
'''
A = VennCircleRegion(centers[0], radii[0])
B = VennCircleRegion(centers[1], radii[1])
C = 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)
return [Abc, aBc, ABc, abC, AbC, aBC, ABC]
def compute_venn2_regions(centers, radii):
"""
Returns a triple of VennRegion objects, describing the three regions of the diagram, corresponding to sets
(Ab, aB, AB)
>>> centers, radii = solve_venn2_circles((1, 1, 0.5))
>>> regions = compute_venn2_regions(centers, radii)
"""
A = VennCircleRegion(centers[0], radii[0])
B = VennCircleRegion(centers[1], radii[1])
Ab, AB = A.subtract_and_intersect_circle(B.center, B.radius)
aB, _ = B.subtract_and_intersect_circle(A.center, A.radius)
return Ab, aB, AB
def compute_venn3_regions(centers, radii):
'''
Given the 3x2 matrix with circle center coordinates, and a 3-element list (or array) with circle radii [as returned from solve_venn3_circles],
returns the 7 regions, comprising the venn diagram, as VennRegion objects.
Regions are returned in order (Abc, aBc, ABc, abC, AbC, aBC, ABC)
>>> centers, radii = solve_venn3_circles((1, 1, 1, 1, 1, 1, 1))
>>> regions = compute_venn3_regions(centers, radii)
'''
A = VennCircleRegion(centers[0], radii[0])
B = VennCircleRegion(centers[1], radii[1])
C = 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)
return [Abc, aBc, ABc, abC, AbC, aBC, ABC]
def test_circle_region():
with pytest.raises(VennRegionException):
vcr = VennCircleRegion((0, 0), -1)
vcr = VennCircleRegion((0, 0), 10)
assert abs(vcr.size() - np.pi*100) <= tol
# Interact with non-intersecting circle
sr, ir = vcr.subtract_and_intersect_circle((11, 1), 1)
assert sr == vcr
assert ir.is_empty()
# Interact with self
sr, ir = vcr.subtract_and_intersect_circle((0, 0), 10)
assert sr.is_empty()
assert ir == vcr
# Interact with a circle that makes a hole
with pytest.raises(VennRegionException):
sr, ir = vcr.subtract_and_intersect_circle((0, 8.9), 1)
# Interact with a circle that touches the side from the inside
for (a, r) in [(0, 1), (90, 2), (180, 3), (290, 0.01), (42, 9.99), (-0.1, 9.999), (180.1, 0.001)]:
cx = np.cos(a * np.pi / 180.0) * (10 - r)
cy = np.sin(a * np.pi / 180.0) * (10 - r)
#print "Next test case", a, r, cx, cy, r
TEST_TOLERANCE = tol if r > 0.001 and r < 9.999 else 1e-4 # For tricky circles the numeric errors for arc lengths are just too big here
sr, ir = vcr.subtract_and_intersect_circle((cx, cy), r)
sr.verify()
ir.verify()
assert len(sr.arcs) == 2 and len(ir.arcs) == 2
for a in sr.arcs:
assert abs(a.length_degrees() - 360) < TEST_TOLERANCE
assert abs(ir.arcs[0].length_degrees() - 0) < TEST_TOLERANCE
assert abs(ir.arcs[1].length_degrees() - 360) < TEST_TOLERANCE
assert abs(sr.size() + np.pi*r**2 - vcr.size()) < tol
assert abs(ir.size() - np.pi*r**2) < tol
# Interact with a circle that touches the side from the outside
for (a, r) in [(0, 1), (90, 2), (180, 3), (290, 0.01), (42, 9.99), (-0.1, 9.999), (180.1, 0.001)]:
cx = np.cos(a * np.pi / 180.0) * (10 + r)
cy = np.sin(a * np.pi / 180.0) * (10 + r)
sr, ir = vcr.subtract_and_intersect_circle((cx, cy), r)
# Depending on numeric roundoff we may get either an self and VennEmptyRegion or two arc regions. In any case the sizes should match
assert abs(sr.size() + ir.size() - vcr.size()) < tol
if (sr == vcr):
assert ir.is_empty()
else:
sr.verify()
ir.verify()
assert len(sr.arcs) == 2 and len(ir.arcs) == 2
assert abs(sr.arcs[0].length_degrees() - 0) < tol
assert abs(sr.arcs[1].length_degrees() - 360) < tol
assert abs(ir.arcs[0].length_degrees() - 0) < tol
assert abs(ir.arcs[1].length_degrees() - 0) < tol
# Interact with some cases of intersecting circles
for (a, r) in [(0, 1), (90, 2), (180, 3), (290, 0.01), (42, 9.99), (-0.1, 9.999), (180.1, 0.001)]:
cx = np.cos(a * np.pi / 180.0) * 10
cy = np.sin(a * np.pi / 180.0) * 10
sr, ir = vcr.subtract_and_intersect_circle((cx, cy), r)
sr.verify()
ir.verify()
assert len(sr.arcs) == 2 and len(ir.arcs) == 2
assert abs(sr.size() + ir.size() - vcr.size()) < tol
assert sr.size() > 0
assert ir.size() > 0
# Do intersection the other way
vcr2 = VennCircleRegion([cx, cy], r)
sr2, ir2 = vcr2.subtract_and_intersect_circle(vcr.center, vcr.radius)
sr2.verify()
ir2.verify()
assert len(sr2.arcs) == 2 and len(ir2.arcs) == 2
assert abs(sr2.size() + ir2.size() - vcr2.size()) < tol
assert sr2.size() > 0
assert ir2.size() > 0
for i in range(2):
assert ir.arcs[i].approximately_equal(ir.arcs[i])
def test_circle_region():
with pytest.raises(VennRegionException):
vcr = VennCircleRegion((0, 0), -1)
vcr = VennCircleRegion((0, 0), 10)
assert abs(vcr.size() - np.pi * 100) <= tol
# Interact with non-intersecting circle
sr, ir = vcr.subtract_and_intersect_circle((11, 1), 1)
assert sr == vcr
assert ir.is_empty()
# Interact with self
sr, ir = vcr.subtract_and_intersect_circle((0, 0), 10)
assert sr.is_empty()
assert ir == vcr
# Interact with a circle that makes a hole
with pytest.raises(VennRegionException):
sr, ir = vcr.subtract_and_intersect_circle((0, 8.9), 1)
# Interact with a circle that touches the side from the inside
for (a, r) in [(0, 1), (90, 2), (180, 3), (290, 0.01), (42, 9.99),
(-0.1, 9.999), (180.1, 0.001)]:
cx = np.cos(a * np.pi / 180.0) * (10 - r)
cy = np.sin(a * np.pi / 180.0) * (10 - r)
#print "Next test case", a, r, cx, cy, r
TEST_TOLERANCE = tol if r > 0.001 and r < 9.999 else 1e-4 # For tricky circles the numeric errors for arc lengths are just too big here
sr, ir = vcr.subtract_and_intersect_circle((cx, cy), r)
sr.verify()
ir.verify()
assert len(sr.arcs) == 2 and len(ir.arcs) == 2
for a in sr.arcs:
assert abs(a.length_degrees() - 360) < TEST_TOLERANCE
assert abs(ir.arcs[0].length_degrees() - 0) < TEST_TOLERANCE
assert abs(ir.arcs[1].length_degrees() - 360) < TEST_TOLERANCE
assert abs(sr.size() + np.pi * r**2 - vcr.size()) < tol
assert abs(ir.size() - np.pi * r**2) < tol
# Interact with a circle that touches the side from the outside
for (a, r) in [(0, 1), (90, 2), (180, 3), (290, 0.01), (42, 9.99),
(-0.1, 9.999), (180.1, 0.001)]:
cx = np.cos(a * np.pi / 180.0) * (10 + r)
cy = np.sin(a * np.pi / 180.0) * (10 + r)
sr, ir = vcr.subtract_and_intersect_circle((cx, cy), r)
# Depending on numeric roundoff we may get either an self and VennEmptyRegion or two arc regions. In any case the sizes should match
assert abs(sr.size() + ir.size() - vcr.size()) < tol
if (sr == vcr):
assert ir.is_empty()
else:
sr.verify()
ir.verify()
assert len(sr.arcs) == 2 and len(ir.arcs) == 2
assert abs(sr.arcs[0].length_degrees() - 0) < tol
assert abs(sr.arcs[1].length_degrees() - 360) < tol
assert abs(ir.arcs[0].length_degrees() - 0) < tol
assert abs(ir.arcs[1].length_degrees() - 0) < tol
# Interact with some cases of intersecting circles
for (a, r) in [(0, 1), (90, 2), (180, 3), (290, 0.01), (42, 9.99),
(-0.1, 9.999), (180.1, 0.001)]:
cx = np.cos(a * np.pi / 180.0) * 10
cy = np.sin(a * np.pi / 180.0) * 10
sr, ir = vcr.subtract_and_intersect_circle((cx, cy), r)
sr.verify()
ir.verify()
assert len(sr.arcs) == 2 and len(ir.arcs) == 2
assert abs(sr.size() + ir.size() - vcr.size()) < tol
assert sr.size() > 0
assert ir.size() > 0
# Do intersection the other way
vcr2 = VennCircleRegion([cx, cy], r)
sr2, ir2 = vcr2.subtract_and_intersect_circle(vcr.center, vcr.radius)
sr2.verify()
ir2.verify()
assert len(sr2.arcs) == 2 and len(ir2.arcs) == 2
assert abs(sr2.size() + ir2.size() - vcr2.size()) < tol
assert sr2.size() > 0
assert ir2.size() > 0
for i in range(2):
assert ir.arcs[i].approximately_equal(ir.arcs[i])