def _contains_point(self, point):
"""Tests whether or not the current room cointains a specific point
Return true if this room object contains the supplied object
Uses the ray casting algorithm:
http://en.wikipedia.org/wiki/Point_in_polygon#Ray_casting_algorithm
For simplicity we assume the ray is casted horizontally to the left
"""
# We first compare against the bounding box. For most points this will be
# enough
min_point, max_point = self.bounding_box
if ((point.x > max_point.x) or (point.x < min_point.x)
or (point.y > max_point.y) or (point.y < min_point.y)):
return False
# Amount of intersections counted
match_count = 0
# Handle some special cases
counted_vertices = []
for (a, b) in circular_pairwise(self.points):
# Is the y coordinate of the point valid? I.e.: is it between
# the y coordinates of a and b?
if (a.y <= point.y <= b.y or a.y >= point.y >= b.y):
# The following function returns -1 if the point is to the left
# of the segment, 0 if it is on the same line as the segment,
# +1 if it is to the right
comparison = Polygon._compare_line_and_point(a, b, point)
# If the point is on the same line, we can conclude it belongs
# to the shape if its x coordinates are between a's and b's
if (comparison == 0
and max(a.x, b.x) >= point.x >= min(a.x, b.x)
and max(a.y, b.y) >= point.y >= min(a.y, b.y)):
return True # the point is over a border
# If the point is not over the line, is it to the right?
# Being to the right means that the ray being cast to the left
# might actually intersect the segment.
elif (comparison > 0):
# Simple case, the ray does not match any vertice, so it
# intersects inside the segment.
if ((point.y != a.y) and (point.y != b.y)):
match_count = match_count + 1
else:
# Special cases, the ray intersects precisely one of the vertices
if a.y == point.y and a.x <= point.x and a not in counted_vertices:
counted_vertices.append(a)
match_count = match_count + 1
if b.y == point.y and b.x <= point.x and (
b not in counted_vertices):
counted_vertices.append(b)
match_count = match_count + 1
# After analyzing all segments, if we found an even amount of intersections
# it means the point is outside of the polygon
return match_count % 2 != 0
def as_segment_list(self):
return [
Segment(a.clone(), b.clone())
for a, b in circular_pairwise(self.points)
]
def test_polygon_contains_point(self):
def polygon_contains(polygon, x, y):
self.assertTrue(polygon._contains_point(Point(x, y)),
"{} should contain {}, {}".format(polygon, x, y))
def polygon_not_contains(polygon, x, y):
self.assertFalse(
polygon._contains_point(Point(x, y)),
"{} should not contain {}, {}".format(polygon, x, y))
# Generic points inside the square polygon
for x, y in circular_pairwise(range(1, 10)):
polygon_contains(self.polygon1, x, y)
test_data = [
{
"polygon":
self.polygon1,
"truths": [
# Inside, but near borders
(0.1, 0.001),
(9.99, 9.7),
(5, 9.99),
(0.1, 8),
# Close to the border
(0.001, 0.001),
(9.999, 9.999),
# Points precisely on the border
(5, 0),
(10, 5),
(5, 10),
(0, 5),
(0, 0),
(10, 0),
(10, 10),
(0, 10)
],
"falses": [(5, -4), (5, 11), (10.001, 10.001), (-2, 5)]
},
{
"polygon":
self.polygon2,
"truths": [
# Close to the vertices
(9.9, 0),
(0, 9.9),
(-9.9, 0),
(0, -9.9),
# Close to the center
(0.001, 0.001),
(3, 3),
(-4.8, -4.8),
(4.1, 3.8),
# Points precisely over the border
(10, 0),
(0, 10),
(-10, 0),
(0, -10)
],
"falses": [
# Points definetely outside
(9.9, 9.9),
(10.2, 0),
(0, -10.1),
(10.001, 10.001),
(33, 12)
]
},
{
"polygon":
self.polygon3,
"truths": [
# Close to the vertices
(1, 2),
(0.1, 0.1),
(9.9, 0.1),
(0.1, 9.9),
# Close to the center
(2, 3),
(4, 5),
(8, 2),
(1, 7),
# Points precisely over the vertices
(0, 0),
(10, 0),
(10, 5),
(5, 5),
(5, 10),
(0, 10)
],
"falses": [
# Points definetely outside
(10.1, 0.3),
(-0.1, 1),
(2, 10.1),
(-0.1, -0.1),
(1, -0.1),
(6, 6),
(5.1, 5.1)
]
},
{
"polygon": self.polygon4,
"truths": [(5, 5)],
"falses": [
# Points definetely outside
(11, 5)
]
}
]
for test_polygon in test_data:
for (x, y) in test_polygon["truths"]:
polygon_contains(test_polygon["polygon"], x, y)
for (x, y) in test_polygon["falses"]:
polygon_not_contains(test_polygon["polygon"], x, y)
def test_polygon_contains_point(self):
def polygon_contains(polygon, x, y):
self.assertTrue( polygon._contains_point(Point(x, y)), "{} should contain {}, {}".format(polygon, x, y) )
def polygon_not_contains(polygon, x, y):
self.assertFalse( polygon._contains_point(Point(x, y)), "{} should not contain {}, {}".format(polygon, x, y) )
# Generic points inside the square polygon
for x, y in circular_pairwise(range(1,10)):
polygon_contains(self.polygon1, x, y)
test_data = [
{
"polygon" : self.polygon1,
"truths" : [
# Inside, but near borders
(0.1, 0.001),
(9.99, 9.7),
(5, 9.99),
(0.1, 8),
# Close to the border
(0.001, 0.001),
(9.999, 9.999),
# Points precisely on the border
(5, 0),
(10, 5),
(5, 10),
(0, 5),
(0, 0),
(10, 0),
(10, 10),
(0, 10)
],
"falses" : [
(5, -4),
(5, 11),
(10.001, 10.001),
(-2, 5)
]
},
{
"polygon" : self.polygon2,
"truths" : [
# Close to the vertices
(9.9, 0), (0, 9.9), (-9.9, 0), (0, -9.9),
# Close to the center
(0.001, 0.001), (3, 3), (-4.8, -4.8), (4.1, 3.8),
# Points precisely over the border
(10, 0), (0, 10), (-10, 0), (0, -10)
],
"falses" : [
# Points definetely outside
(9.9, 9.9), (10.2, 0), (0, -10.1), (10.001, 10.001), (33, 12)
]
},
{
"polygon" : self.polygon3,
"truths" : [
# Close to the vertices
(1, 2), (0.1, 0.1), (9.9, 0.1), (0.1, 9.9),
# Close to the center
(2, 3), (4, 5), (8, 2), (1, 7),
# Points precisely over the vertices
(0,0),(10,0),(10,5),(5,5),(5,10),(0,10)
],
"falses" : [
# Points definetely outside
(10.1, 0.3), (-0.1, 1), (2, 10.1), (-0.1, -0.1), (1, -0.1),
(6,6), (5.1, 5.1)
]
},
{
"polygon" : self.polygon4,
"truths" : [
(5, 5)
],
"falses" : [
# Points definetely outside
(11, 5)
]
}
]
for test_polygon in test_data:
for (x, y) in test_polygon["truths"]:
polygon_contains(test_polygon["polygon"], x, y)
for (x, y) in test_polygon["falses"]:
polygon_not_contains(test_polygon["polygon"], x, y)
def _contains_point(self, point):
"""Tests whether or not the current room cointains a specific point
Return true if this room object contains the supplied object
Uses the ray casting algorithm:
http://en.wikipedia.org/wiki/Point_in_polygon#Ray_casting_algorithm
For simplicity we assume the ray is casted horizontally to the left
"""
# We first compare against the bounding box. For most points this will be
# enough
min_point, max_point = self.bounding_box
if (
(point.x > max_point.x) or
(point.x < min_point.x) or
(point.y > max_point.y) or
(point.y < min_point.y)
):
return False
# Amount of intersections counted
match_count = 0
# Handle some special cases
counted_vertices = []
for (a, b) in circular_pairwise(self.points):
# Is the y coordinate of the point valid? I.e.: is it between
# the y coordinates of a and b?
if( a.y <= point.y <= b.y or a.y >= point.y >= b.y ):
# The following function returns -1 if the point is to the left
# of the segment, 0 if it is on the same line as the segment,
# +1 if it is to the right
comparison = Polygon._compare_line_and_point(a, b, point)
# If the point is on the same line, we can conclude it belongs
# to the shape if its x coordinates are between a's and b's
if(comparison == 0 and
max(a.x, b.x) >= point.x >= min(a.x, b.x) and
max(a.y, b.y) >= point.y >= min(a.y, b.y)):
return True # the point is over a border
# If the point is not over the line, is it to the right?
# Being to the right means that the ray being cast to the left
# might actually intersect the segment.
elif(comparison > 0):
# Simple case, the ray does not match any vertice, so it
# intersects inside the segment.
if ((point.y != a.y) and (point.y != b.y)):
match_count = match_count + 1
else:
# Special cases, the ray intersects precisely one of the vertices
if a.y == point.y and a.x <= point.x and a not in counted_vertices:
counted_vertices.append(a)
match_count = match_count + 1
if b.y == point.y and b.x <= point.x and (b not in counted_vertices):
counted_vertices.append(b)
match_count = match_count + 1
# After analyzing all segments, if we found an even amount of intersections
# it means the point is outside of the polygon
return match_count % 2 != 0
def as_segment_list(self):
return [ Segment(a.clone(), b.clone()) for a, b in circular_pairwise(self.points) ]