def size(self):
'''Return the area of the patch.
The area can be computed using the standard polygon area formula + signed segment areas of each arc.
'''
polygon_area = 0
for a in self.arcs:
polygon_area += box_product(a.start_point(), a.end_point())
polygon_area /= 2.0
return polygon_area + sum([a.sign * a.segment_area() for a in self.arcs])
def size(self):
"""Return the area of the patch.
The area can be computed using the standard polygon area formula + signed segment areas of each arc.
"""
polygon_area = 0
for a in self.arcs:
polygon_area += box_product(a.start_point(), a.end_point())
polygon_area /= 2.0
return polygon_area + sum([a.sign * a.segment_area() for a in self.arcs])
def verify(self):
'''
Verify the correctness of the region arcs. Throws an VennRegionException if verification fails
(or any other exception if it happens during verification).
'''
# Verify size of arcs list
if (len(self.arcs) < 2):
raise VennRegionException(
"At least two arcs needed in a poly-arc region")
if (len(self.arcs) > 4):
raise VennRegionException(
"At most 4 arcs are supported currently for poly-arc regions")
TRIG_TOL = 100 * tol # We need to use looser tolerance level here because conversion to angles and back is prone to large errors.
# Verify connectedness of arcs
for i in range(len(self.arcs)):
if not np.all(self.arcs[i - 1].end_point() -
self.arcs[i].start_point() < TRIG_TOL):
raise VennRegionException(
"Arcs of an poly-arc-gon must be connected via endpoints")
# Verify that arcs do not cross-intersect except at endpoints
for i in range(len(self.arcs) - 1):
for j in range(i + 1, len(self.arcs)):
ips = self.arcs[i].intersect_arc(self.arcs[j])
for ip in ips:
if not (np.all(
abs(ip - self.arcs[i].start_point()) < TRIG_TOL)
or np.all(
abs(ip - self.arcs[i].end_point()) < TRIG_TOL)
):
raise VennRegionException(
"Arcs of a poly-arc-gon may only intersect at endpoints"
)
if len(ips) != 0 and (i - j) % len(
self.arcs) > 1 and (j - i) % len(self.arcs) > 1:
# Two non-consecutive arcs intersect. This is in general not good, but
# may occasionally happen when all arcs inbetween have length 0.
pass # raise VennRegionException("Non-consecutive arcs of a poly-arc-gon may not intersect")
# Verify that vertices are ordered so that at each point the direction along the polyarc changes towards the left.
# Note that this test only makes sense for polyarcs obtained using circle intersections & subtractions.
# A "flower-like" polyarc may have its vertices ordered counter-clockwise yet the direction would turn to the right at each of them.
for i in range(len(self.arcs)):
prev_arc = self.arcs[i - 1]
cur_arc = self.arcs[i]
if box_product(prev_arc.direction_vector(prev_arc.to_angle),
cur_arc.direction_vector(
cur_arc.from_angle)) < -tol:
raise VennRegionException(
"Arcs must be ordered so that the direction at each vertex changes counter-clockwise"
)
def verify(self):
"""
Verify the correctness of the region arcs. Throws an VennRegionException if verification fails
(or any other exception if it happens during verification).
"""
# Verify size of arcs list
if len(self.arcs) < 2:
raise VennRegionException("At least two arcs needed in a poly-arc region")
if len(self.arcs) > 4:
raise VennRegionException("At most 4 arcs are supported currently for poly-arc regions")
TRIG_TOL = (
100 * tol
) # We need to use looser tolerance level here because conversion to angles and back is prone to large errors.
# Verify connectedness of arcs
for i in range(len(self.arcs)):
if not np.all(self.arcs[i - 1].end_point() - self.arcs[i].start_point() < TRIG_TOL):
raise VennRegionException("Arcs of an poly-arc-gon must be connected via endpoints")
# Verify that arcs do not cross-intersect except at endpoints
for i in range(len(self.arcs) - 1):
for j in range(i + 1, len(self.arcs)):
ips = self.arcs[i].intersect_arc(self.arcs[j])
for ip in ips:
if not (
np.all(abs(ip - self.arcs[i].start_point()) < TRIG_TOL)
or np.all(abs(ip - self.arcs[i].end_point()) < TRIG_TOL)
):
raise VennRegionException("Arcs of a poly-arc-gon may only intersect at endpoints")
if len(ips) != 0 and (i - j) % len(self.arcs) > 1 and (j - i) % len(self.arcs) > 1:
# Two non-consecutive arcs intersect. This is in general not good, but
# may occasionally happen when all arcs inbetween have length 0.
pass # raise VennRegionException("Non-consecutive arcs of a poly-arc-gon may not intersect")
# Verify that vertices are ordered so that at each point the direction along the polyarc changes towards the left.
# Note that this test only makes sense for polyarcs obtained using circle intersections & subtractions.
# A "flower-like" polyarc may have its vertices ordered counter-clockwise yet the direction would turn to the right at each of them.
for i in range(len(self.arcs)):
prev_arc = self.arcs[i - 1]
cur_arc = self.arcs[i]
if (
box_product(prev_arc.direction_vector(prev_arc.to_angle), cur_arc.direction_vector(cur_arc.from_angle))
< -tol
):
raise VennRegionException(
"Arcs must be ordered so that the direction at each vertex changes counter-clockwise"
)