def reflect(self, prev_position: Point, circle: Circle) -> None:
"""
Reflects the photon on the given circle.
- calculates distance covered and subtracts it from self.distance
- calculates new direction vector
- jumps to the new position and prints it
:rtype: None
"""
if prev_position.distance(self.position) > self.distance:
self.position = prev_position.translate(
self.ray.direction.x * self.distance,
self.ray.direction.y * self.distance)
self.distance = 0
return
self.distance -= prev_position.distance(self.position).evalf(PRECISION)
self.checked_circles = [circle]
tangent = circle.tangent_lines(self.position)[0]
self.position = Point(self.position.x.evalf(PRECISION),
self.position.y.evalf(PRECISION))
self.imprecise_position = self.position
direction = self.position + self.ray.reflect(tangent).direction
direction = Point(direction.x.evalf(PRECISION),
direction.y.evalf(PRECISION))
self.ray = Ray(self.position, direction)
self.jump_to_position()
dot()
self.print_position()
def test_point():
p1 = Point(x1, x2)
p2 = Point(y1, y2)
p3 = Point(0, 0)
p4 = Point(1, 1)
assert len(p1) == 1
assert p1 in p1
assert p1 not in p2
assert p2[1] == y2
assert (p3 + p4) == p4
assert (p2 - p1) == Point(y1 - x1, y2 - x2)
assert p4 * 5 == Point(5, 5)
assert -p2 == Point(-y1, -y2)
assert Point.midpoint(p3, p4) == Point(half, half)
assert Point.midpoint(p1, p4) == Point(half + half * x1, half + half * x2)
assert Point.midpoint(p2, p2) == p2
assert p2.midpoint(p2) == p2
assert Point.distance(p3, p4) == sqrt(2)
assert Point.distance(p1, p1) == 0
assert Point.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2)
p1_1 = Point(x1, x1)
p1_2 = Point(y2, y2)
p1_3 = Point(x1 + 1, x1)
assert Point.is_collinear(p3)
assert Point.is_collinear(p3, p4)
assert Point.is_collinear(p3, p4, p1_1, p1_2)
assert Point.is_collinear(p3, p4, p1_1, p1_3) == False
assert p3.intersection(Point(0, 0)) == [p3]
assert p3.intersection(p4) == []
x_pos = Symbol('x', real=True, positive=True)
p2_1 = Point(x_pos, 0)
p2_2 = Point(0, x_pos)
p2_3 = Point(-x_pos, 0)
p2_4 = Point(0, -x_pos)
p2_5 = Point(x_pos, 5)
assert Point.is_concyclic(p2_1)
assert Point.is_concyclic(p2_1, p2_2)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_5) == False
assert Point.is_concyclic(p4, p4 * 2, p4 * 3) == False
assert p4.scale(2, 3) == Point(2, 3)
assert p3.scale(2, 3) == p3
assert p4.rotate(pi, Point(0.5, 0.5)) == p3
assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2)
assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2)
assert p4 * 5 == Point(5, 5)
assert p4 / 5 == Point(0.2, 0.2)
raises(ValueError, 'Point(0,0) + 10')
def test_point():
p1 = Point(x1, x2)
p2 = Point(y1, y2)
p3 = Point(0, 0)
p4 = Point(1, 1)
assert len(p1) == 1
assert p1 in p1
assert p1 not in p2
assert p2[1] == y2
assert (p3+p4) == p4
assert (p2-p1) == Point(y1-x1, y2-x2)
assert p4*5 == Point(5, 5)
assert -p2 == Point(-y1, -y2)
assert Point.midpoint(p3, p4) == Point(half, half)
assert Point.midpoint(p1, p4) == Point(half + half*x1, half + half*x2)
assert Point.midpoint(p2, p2) == p2
assert p2.midpoint(p2) == p2
assert Point.distance(p3, p4) == sqrt(2)
assert Point.distance(p1, p1) == 0
assert Point.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2)
p1_1 = Point(x1, x1)
p1_2 = Point(y2, y2)
p1_3 = Point(x1 + 1, x1)
assert Point.is_collinear(p3)
assert Point.is_collinear(p3, p4)
assert Point.is_collinear(p3, p4, p1_1, p1_2)
assert Point.is_collinear(p3, p4, p1_1, p1_3) == False
assert p3.intersection(Point(0, 0)) == [p3]
assert p3.intersection(p4) == []
x_pos = Symbol('x', real=True, positive=True)
p2_1 = Point(x_pos, 0)
p2_2 = Point(0, x_pos)
p2_3 = Point(-x_pos, 0)
p2_4 = Point(0, -x_pos)
p2_5 = Point(x_pos, 5)
assert Point.is_concyclic(p2_1)
assert Point.is_concyclic(p2_1, p2_2)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_5) == False
assert Point.is_concyclic(p4, p4 * 2, p4 * 3) == False
assert p4.scale(2, 3) == Point(2, 3)
assert p3.scale(2, 3) == p3
assert p4.rotate(pi, Point(0.5, 0.5)) == p3
assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2)
assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2)
assert p4 * 5 == Point(5, 5)
assert p4 / 5 == Point(0.2, 0.2)
raises(ValueError, 'Point(0,0) + 10')
def closest_station_of(pos, stations):
station_coords = [station.coords for station in stations]
p = Point(pos)
best_dist = p.distance(stations[0].coords)
best_station = stations[0]
for station in stations[1:]:
new_dist = p.distance(station.coords)
if new_dist < best_dist:
best_dist = new_dist
best_station = station
return best_station
def test_point():
p1 = Point(x1, x2)
p2 = Point(y1, y2)
p3 = Point(0, 0)
p4 = Point(1, 1)
assert p3.x == 0
assert p3.y == 0
assert p4.x == 1
assert p4.y == 1
assert len(p1) == 2
assert p2[1] == y2
assert (p3+p4) == p4
assert (p2-p1) == Point(y1-x1, y2-x2)
assert p4*5 == Point(5, 5)
assert -p2 == Point(-y1, -y2)
assert Point.midpoint(p3, p4) == Point(half, half)
assert Point.midpoint(p1, p4) == Point(half + half*x1, half + half*x2)
assert Point.midpoint(p2, p2) == p2
assert Point.distance(p3, p4) == sqrt(2)
assert Point.distance(p1, p1) == 0
#assert Point.distance(p3, p2) == abs(p2)
p1_1 = Point(x1, x1)
p1_2 = Point(y2, y2)
p1_3 = Point(x1 + 1, x1)
assert Point.is_collinear(p3)
assert Point.is_collinear(p3, p4)
assert Point.is_collinear(p3, p4, p1_1, p1_2)
assert Point.is_collinear(p3, p4, p1_1, p1_3) == False
x_pos = Symbol('x', real=True, positive=True)
p2_1 = Point(x_pos, 0)
p2_2 = Point(0, x_pos)
p2_3 = Point(-x_pos, 0)
p2_4 = Point(0, -x_pos)
p2_5 = Point(x_pos, 5)
assert Point.is_concyclic(p2_1)
assert Point.is_concyclic(p2_1, p2_2)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_5) == False
def test_point():
p1 = Point(x1, x2)
p2 = Point(y1, y2)
p3 = Point(0, 0)
p4 = Point(1, 1)
assert p3.x == 0
assert p3.y == 0
assert p4.x == 1
assert p4.y == 1
assert len(p1) == 2
assert p2[1] == y2
assert (p3 + p4) == p4
assert (p2 - p1) == Point(y1 - x1, y2 - x2)
assert p4 * 5 == Point(5, 5)
assert -p2 == Point(-y1, -y2)
assert Point.midpoint(p3, p4) == Point(half, half)
assert Point.midpoint(p1, p4) == Point(half + half * x1, half + half * x2)
assert Point.midpoint(p2, p2) == p2
assert Point.distance(p3, p4) == sqrt(2)
assert Point.distance(p1, p1) == 0
#assert Point.distance(p3, p2) == abs(p2)
p1_1 = Point(x1, x1)
p1_2 = Point(y2, y2)
p1_3 = Point(x1 + 1, x1)
assert Point.is_collinear(p3)
assert Point.is_collinear(p3, p4)
assert Point.is_collinear(p3, p4, p1_1, p1_2)
assert Point.is_collinear(p3, p4, p1_1, p1_3) == False
x_pos = Symbol('x', real=True, positive=True)
p2_1 = Point(x_pos, 0)
p2_2 = Point(0, x_pos)
p2_3 = Point(-x_pos, 0)
p2_4 = Point(0, -x_pos)
p2_5 = Point(x_pos, 5)
assert Point.is_concyclic(p2_1)
assert Point.is_concyclic(p2_1, p2_2)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_5) == False
def store_midpoints_for_line(column_lines):
column_lines['cluster_group'] = 0
column_lines['linelength'] = 0
for index in range(len(column_lines)):
p1, p2 = Point(column_lines.iloc[index]['x1'], column_lines.iloc[index]['y1']), Point(column_lines.iloc[index]['x2'], column_lines.iloc[index]['y2'])
column_lines.iloc[index, column_lines.columns.get_loc('linelength')] = p1.distance(p2)
column_lines['x_midpoint'] = (column_lines['x1'] + column_lines['x2']) / 2.0
column_lines['y_midpoint'] = (column_lines['y1'] + column_lines['y2']) / 2.0
return column_lines
def compute_station_list(self, stations, shortest_path_stations):
start = Point(self.start)
end = Point(self.end)
start_station = closest_station_of(start, stations)
end_station = closest_station_of(end, stations)
shortest_path_transport, shortest_length_transport = shortest_path_stations[
start_station][end_station]
shortest_by_foot = start.distance(end) / (5 * 60)
if shortest_by_foot > shortest_length_transport:
self.stations_list = shortest_path_transport
def navigator():
pub = rospy.Publisher('/nav_target', Pose2D, queue_size=10)
rospy.Subscriber('/trajectory', Pose2D_Array, callbackTrajectory)
rospy.Subscriber('/y_r0', Pose2D, callbackSelf)
rospy.init_node('navigation')
rate = rospy.Rate(1) # Hz
while not rospy.is_shutdown():
pSelf = Point(poseSelf.x, poseSelf.y)
pNav = Point(poseNav.x, poseNav.y)
dist = pSelf.distance(pNav)
print "Dist: ", dist
yDiff = (poseNav.y - poseSelf.y)
xDiff = (poseNav.x - poseSelf.x)
print "Y difference: ", yDiff
print "X difference: ", xDiff
s = math.atan2(yDiff, xDiff)
print "Angle: ", s
print "Robot angle: ", poseSelf.theta
angleErr1 = s - poseSelf.theta
angleErr2 = poseSelf.theta - s
if (abs(angleErr1) > abs(angleErr2)):
angleErr = angleErr2
else:
angleErr = angleErr1
print "Angle error: ", angleErr
velVector.theta = -0.3 * (angleErr)
if (dist > 500):
v = 350
elif (dist > 100):
v = 0.3 * dist + 230
else:
v = 200
velVector.x = v
pub.publish(velVector)
rate.sleep()
def test_point():
x = Symbol('x', real=True)
y = Symbol('y', real=True)
x1 = Symbol('x1', real=True)
x2 = Symbol('x2', real=True)
y1 = Symbol('y1', real=True)
y2 = Symbol('y2', real=True)
half = S.Half
p1 = Point(x1, x2)
p2 = Point(y1, y2)
p3 = Point(0, 0)
p4 = Point(1, 1)
p5 = Point(0, 1)
line = Line(Point(1, 0), slope=1)
assert p1 in p1
assert p1 not in p2
assert p2.y == y2
assert (p3 + p4) == p4
assert (p2 - p1) == Point(y1 - x1, y2 - x2)
assert -p2 == Point(-y1, -y2)
raises(ValueError, lambda: Point(3, I))
raises(ValueError, lambda: Point(2 * I, I))
raises(ValueError, lambda: Point(3 + I, I))
assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3))
assert Point.midpoint(p3, p4) == Point(half, half)
assert Point.midpoint(p1, p4) == Point(half + half * x1, half + half * x2)
assert Point.midpoint(p2, p2) == p2
assert p2.midpoint(p2) == p2
assert Point.distance(p3, p4) == sqrt(2)
assert Point.distance(p1, p1) == 0
assert Point.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2)
# distance should be symmetric
assert p1.distance(line) == line.distance(p1)
assert p4.distance(line) == line.distance(p4)
assert Point.taxicab_distance(p4, p3) == 2
assert Point.canberra_distance(p4, p5) == 1
p1_1 = Point(x1, x1)
p1_2 = Point(y2, y2)
p1_3 = Point(x1 + 1, x1)
assert Point.is_collinear(p3)
with warns(UserWarning):
assert Point.is_collinear(p3, Point(p3, dim=4))
assert p3.is_collinear()
assert Point.is_collinear(p3, p4)
assert Point.is_collinear(p3, p4, p1_1, p1_2)
assert Point.is_collinear(p3, p4, p1_1, p1_3) is False
assert Point.is_collinear(p3, p3, p4, p5) is False
raises(TypeError, lambda: Point.is_collinear(line))
raises(TypeError, lambda: p1_1.is_collinear(line))
assert p3.intersection(Point(0, 0)) == [p3]
assert p3.intersection(p4) == []
x_pos = Symbol('x', real=True, positive=True)
p2_1 = Point(x_pos, 0)
p2_2 = Point(0, x_pos)
p2_3 = Point(-x_pos, 0)
p2_4 = Point(0, -x_pos)
p2_5 = Point(x_pos, 5)
assert Point.is_concyclic(p2_1)
assert Point.is_concyclic(p2_1, p2_2)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
for pts in permutations((p2_1, p2_2, p2_3, p2_5)):
assert Point.is_concyclic(*pts) is False
assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False
assert Point(0, 0).is_concyclic((1, 1), (2, 2), (2, 1)) is False
assert p4.scale(2, 3) == Point(2, 3)
assert p3.scale(2, 3) == p3
assert p4.rotate(pi, Point(0.5, 0.5)) == p3
assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2)
assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2)
assert p4 * 5 == Point(5, 5)
assert p4 / 5 == Point(0.2, 0.2)
assert 5 * p4 == Point(5, 5)
raises(ValueError, lambda: Point(0, 0) + 10)
# Point differences should be simplified
assert Point(x * (x - 1), y) - Point(x**2 - x, y + 1) == Point(0, -1)
a, b = S.Half, Rational(1, 3)
assert Point(a, b).evalf(2) == \
Point(a.n(2), b.n(2), evaluate=False)
raises(ValueError, lambda: Point(1, 2) + 1)
# test transformations
p = Point(1, 0)
assert p.rotate(pi / 2) == Point(0, 1)
assert p.rotate(pi / 2, p) == p
p = Point(1, 1)
assert p.scale(2, 3) == Point(2, 3)
assert p.translate(1, 2) == Point(2, 3)
assert p.translate(1) == Point(2, 1)
assert p.translate(y=1) == Point(1, 2)
assert p.translate(*p.args) == Point(2, 2)
# Check invalid input for transform
raises(ValueError, lambda: p3.transform(p3))
raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
def test_point():
p1 = Point(x1, x2)
p2 = Point(y1, y2)
p3 = Point(0, 0)
p4 = Point(1, 1)
p5 = Point(0, 1)
assert p1 in p1
assert p1 not in p2
assert p2.y == y2
assert (p3 + p4) == p4
assert (p2 - p1) == Point(y1 - x1, y2 - x2)
assert p4 * 5 == Point(5, 5)
assert -p2 == Point(-y1, -y2)
assert Point.midpoint(p3, p4) == Point(half, half)
assert Point.midpoint(p1, p4) == Point(half + half * x1, half + half * x2)
assert Point.midpoint(p2, p2) == p2
assert p2.midpoint(p2) == p2
assert Point.distance(p3, p4) == sqrt(2)
assert Point.distance(p1, p1) == 0
assert Point.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2)
p1_1 = Point(x1, x1)
p1_2 = Point(y2, y2)
p1_3 = Point(x1 + 1, x1)
assert Point.is_collinear(p3)
assert Point.is_collinear(p3, p4)
assert Point.is_collinear(p3, p4, p1_1, p1_2)
assert Point.is_collinear(p3, p4, p1_1, p1_3) is False
assert Point.is_collinear(p3, p3, p4, p5) is False
assert p3.intersection(Point(0, 0)) == [p3]
assert p3.intersection(p4) == []
x_pos = Symbol('x', real=True, positive=True)
p2_1 = Point(x_pos, 0)
p2_2 = Point(0, x_pos)
p2_3 = Point(-x_pos, 0)
p2_4 = Point(0, -x_pos)
p2_5 = Point(x_pos, 5)
assert Point.is_concyclic(p2_1)
assert Point.is_concyclic(p2_1, p2_2)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_5) is False
assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False
assert p4.scale(2, 3) == Point(2, 3)
assert p3.scale(2, 3) == p3
assert p4.rotate(pi, Point(0.5, 0.5)) == p3
assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2)
assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2)
assert p4 * 5 == Point(5, 5)
assert p4 / 5 == Point(0.2, 0.2)
raises(ValueError, lambda: Point(0, 0) + 10)
# Point differences should be simplified
assert Point(x * (x - 1), y) - Point(x**2 - x, y + 1) == Point(0, -1)
a, b = Rational(1, 2), Rational(1, 3)
assert Point(a, b).evalf(2) == \
Point(a.n(2), b.n(2))
raises(ValueError, lambda: Point(1, 2) + 1)
# test transformations
p = Point(1, 0)
assert p.rotate(pi / 2) == Point(0, 1)
assert p.rotate(pi / 2, p) == p
p = Point(1, 1)
assert p.scale(2, 3) == Point(2, 3)
assert p.translate(1, 2) == Point(2, 3)
assert p.translate(1) == Point(2, 1)
assert p.translate(y=1) == Point(1, 2)
assert p.translate(*p.args) == Point(2, 2)
def generate_map():
screen.fill((0, 0, 0))
points = generate_random_points(num_points, width, height, buf)
#for x, y in points:
# pygame.draw.circle(screen, WHITE, (x,y), 2, 1)
voronoi_context = voronoi(points)
voronoi_point_dict = {}
point_to_segment_dict = {}
segments = []
vertices = []
top_l = Point(0,0)
top_r = Point(width,0)
bottom_l = Point(0, height)
bottom_r = Point(width, height)
top = Line(top_l, top_r)
left = Line(top_l, bottom_l)
right = Line(top_r, bottom_r)
bottom = Line(bottom_l, bottom_r)
boundaries = [top, right, bottom, left]
for edge in voronoi_context.edges:
il, i1, i2 = edge # index of line, index of vertex 1, index of vertex 2
line_color = RED
vert1 = None
vert2 = None
print_line = True
if i1 is not -1 and i2 is not -1:
vert1 = voronoi_context.vertices[i1]
vert2 = voronoi_context.vertices[i2]
else:
line_point = None
if i1 is -1:
line_p = voronoi_context.vertices[i2]
if i2 is -1:
line_p = voronoi_context.vertices[i1]
line_point = Point(line_p[0], line_p[1])
line = voronoi_context.lines[il]
p1 = None
p2 = None
if line[1] == 0:
p1 = line_point
p2 = Point(line[0]/line[2], 1)
else:
p1 = Point(0, line[2]/line[1])
p2 = line_point
l = Line(p1, p2)
top_intersect = l.intersection(top)
bottom_intersect = l.intersection(bottom)
right_intersect = l.intersection(right)
left_intersect = l.intersection(left)
distances = []
top_dist = None
bottom_dist = None
right_dist = None
left_dist = None
if len(top_intersect) != 0:
top_dist = abs(line_point.distance(top_intersect[0]))
distances.append(top_dist)
if len(bottom_intersect) != 0 :
bottom_dist = abs(line_point.distance(bottom_intersect[0]))
distances.append(bottom_dist)
if len(right_intersect) != 0:
right_dist = abs(line_point.distance(right_intersect[0]))
distances.append(right_dist)
if len(left_intersect) != 0:
left_dist = abs(line_point.distance(left_intersect[0]))
distances.append(left_dist)
vert1 = line_p
v2 = None
if top_dist == min(distances):
v2 = top_intersect[0]
elif bottom_dist == min(distances):
v2 = bottom_intersect[0]
elif right_dist == min(distances):
v2 = right_intersect[0]
elif left_dist == min(distances):
v2 = left_intersect[0]
else:
v2 = Point(0, 0)
vert2 = (v2.x, v2.y)
if vert1[0] < 0 or vert1[1] < 0 or vert2[0] < 0 or vert2[1] < 0 or vert1[0] > width or vert1[1] > height or vert2[0] > width or vert2[1] > height:
print_line = False
if print_line:
vert1, vert2 = adjust_out_of_bounds_points(vert1, vert2, boundaries)
seg = None
if vert1 == None or vert2 == None:
print_line = False
if print_line:
vert1_p = Point(vert1)
vert2_p = Point(vert2)
seg = Segment(vert1_p, vert2_p)
segments.append(seg)
if not vert1_p in voronoi_point_dict:
voronoi_point_dict[vert1_p] = []
if not vert2_p in voronoi_point_dict:
voronoi_point_dict[vert2_p] = []
voronoi_point_dict[vert1_p].append(vert2_p)
voronoi_point_dict[vert2_p].append(vert1_p)
if not vert1_p in point_to_segment_dict:
point_to_segment_dict[vert1_p] = []
if not vert2_p in point_to_segment_dict:
point_to_segment_dict[vert2_p] = []
point_to_segment_dict[vert1_p].append(seg)
point_to_segment_dict[vert2_p].append(seg)
pygame.draw.line(screen, line_color, vert1, vert2, 1)
pygame.display.flip()
top_intersects = []
bottom_intersects = []
right_intersects = []
left_intersects = []
for seg in segments:
if seg.p1.y <= 1:
top_intersects.append(seg.p1)
if seg.p2.y <= 1:
top_intersects.append(seg.p2)
if seg.p1.x >= width -1:
right_intersects.append(seg.p1)
if seg.p2.x >= width-1:
right_intersects.append(seg.p2)
if seg.p1.x <= 1:
left_intersects.append(seg.p1)
if seg.p2.x <= 1:
left_intersects.append(seg.p2)
if seg.p1.y >= height-1:
bottom_intersects.append(seg.p1)
if seg.p2.y >= height-1:
bottom_intersects.append(seg.p2)
top_intersects = sorted(top_intersects, key=lambda point: point.x)
bottom_intersects = sorted(bottom_intersects, key=lambda point: point.x)
left_intersects = sorted(left_intersects, key=lambda point: point.y)
right_intersects = sorted(right_intersects, key=lambda point: point.y)
for i in range(0, 4):
intersect = None
prev_vertex = None
final_vertex = None
if i == 0:
prev_vertex = top_l
intersect = top_intersects
intersect.append(top_r)
if i == 1:
prev_vertex = bottom_l
intersect = bottom_intersects
intersect.append(bottom_r)
if i == 2:
prev_vertex = top_l
intersect = left_intersects
intersect.append(bottom_l)
if i == 3:
prev_vertex = top_r
intersect = right_intersects
intersect.append(bottom_r)
if not prev_vertex in voronoi_point_dict:
voronoi_point_dict[prev_vertex] = []
if not final_vertex in voronoi_point_dict:
voronoi_point_dict[final_vertex] = []
if not prev_vertex in point_to_segment_dict:
point_to_segment_dict[prev_vertex] = []
if not final_vertex in point_to_segment_dict:
point_to_segment_dict[final_vertex] = []
for vertex in intersect:
if not vertex in voronoi_point_dict:
voronoi_point_dict[vertex] = []
if not prev_vertex in voronoi_point_dict:
voronoi_point_dict[prev_vertex] = []
s = Segment(prev_vertex, vertex)
voronoi_point_dict[vertex].append(prev_vertex)
voronoi_point_dict[prev_vertex].append(vertex)
if not vertex in point_to_segment_dict:
point_to_segment_dict[vertex] = []
if not prev_vertex in point_to_segment_dict:
point_to_segment_dict[prev_vertex] = []
point_to_segment_dict[vertex].append(s)
point_to_segment_dict[prev_vertex].append(s)
prev_vertex = vertex
try:
polygons, segments_to_polygons = generate_polygons(voronoi_point_dict, segments, points, point_to_segment_dict)
except Exception as e:
print e
print "crashed"
while 1:
""" helllo"""
for seg, gons in segments_to_polygons.iteritems():
for gon in gons:
gon.connect_adjacent_nodes(gons)
for polygon in polygons:
for node in polygon.adjacent_nodes:
s = Segment(node.center, polygon.center)
draw_segment(s, WHITE)
highest_points_of_elevation = []
frontiers = []
for i in range(0, number_of_peaks):
p = random.choice(polygons)
p.elevation = max_elevation
highest_points_of_elevation.append(p)
frontiers.append(set(p.adjacent_nodes))
marked_polygons = set([])
elevation = max_elevation
while len(marked_polygons) < num_points:
elevation -= 1
for i in range(0, number_of_peaks):
new_frontier = set([])
while len(frontiers[i]) > 0:
node = frontiers[i].pop()
node.elevation = elevation
draw_point(node.center, ORANGE)
for n in node.adjacent_nodes:
if n not in marked_polygons:
new_frontier.add(n)
marked_polygons.add(node)
frontiers[i] = new_frontier
for polygon in polygons:
if polygon.elevation <= 0:
vertices = []
for edge in polygon.edge_list:
p = (edge.x, edge.y)
vertices.append(p)
pygame.draw.polygon(screen, BLUE, vertices, 0)
pygame.display.flip()
pygame.display.flip()
def intersectionsInsideSquareBASE(lineSegmentT, xCoordinates, yCoordinates):
p1 = Point(xCoordinates[0], yCoordinates[0])
p2 = Point(xCoordinates[1], yCoordinates[1])
p3 = Point(xCoordinates[2], yCoordinates[2])
p4 = Point(xCoordinates[3], yCoordinates[3])
lp1 = Point(lineSegmentT.X1, lineSegmentT.Y1)
lp2 = Point(lineSegmentT.X2, lineSegmentT.Y2)
gcodeSegment = Segment(lp1, lp2)
square = Polygon(p1, p2, p3, p4)
insideSquare = False
startTime = parser.parse(lineSegmentT.timeStart)
stopTime = parser.parse(lineSegmentT.timeStop)
startTime1 = startTime
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot([lineSegmentT.X1, lineSegmentT.X2],
[lineSegmentT.Y1, lineSegmentT.Y2],
color='r',
linewidth=5.0)
for i in range(4):
ax.plot([xCoordinates[i], xCoordinates[i + 1]],
[yCoordinates[i], yCoordinates[i + 1]],
color='k',
linewidth=1.0)
interSections = gcodeSegment.intersection(square)
print('intersection size: ', np.size(interSections))
print('Intersection results', interSections)
insideSquare = False
print('Square Encloses: ', lp1, square.encloses(lp1))
print('Square Encloses: ', lp2, square.encloses(lp2))
d = lp1.distance(lp2)
timewidth = stopTime - startTime
if np.size(interSections) == 4:
insideSquare = True
d1 = lp1.distance(interSections[0])
d2 = lp1.distance(interSections[1])
xt1, yt1 = interSections[0]
xt2, yt2 = interSections[1]
ax.plot([xt1, xt2], [yt1, yt2], color='g', linewidth=5.0)
if d1 < d2:
startTime = startTime1 + timewidth * float(d1 / d)
stopTime = startTime1 + timewidth * float(d2 / d)
else:
startTime = startTime1 + timewidth * float(d2 / d)
stopTime = startTime1 + timewidth * float(d1 / d)
elif np.size(interSections) == 2:
if square.encloses(lp1):
insideSquare = True
d1 = lp1.distance(interSections[0])
xt1, yt1 = lp1
xt2, yt2 = interSections[0]
ax.plot([xt1, xt2], [yt1, yt2], color='g', linewidth=5.0)
stopTime = startTime1 + timewidth * float(d1 / d)
elif square.encloses(lp2):
insideSquare = True
d1 = lp1.distance(interSections[0])
xt1, yt1 = lp2
xt2, yt2 = interSections[0]
ax.plot([xt1, xt2], [yt1, yt2], color='g', linewidth=5.0)
startTime = startTime1 + timewidth * float(d1 / d)
elif ('Segment' in str(type(interSections[0]))):
insideSquare = True
xt1, yt1 = interSections[0].p1
xt2, yt2 = interSections[0].p2
ax.plot([xt1, xt2], [yt1, yt2], color='g', linewidth=5.0)
d1 = lp1.distance(interSections[0].p1)
d2 = lp1.distance(interSections[0].p2)
lengthtointersection = lp1.distance(interSections[1])
if interSections[0].contains(lp2):
startTime = startTime1 + timewidth * float(
lengthtointersection / d)
else:
stopTime = startTime1 + timewidth * float(
lengthtointersection / d)
else:
insideSquare = False
elif np.size(interSections) == 1:
if ('Segment' in str(type(interSections[0]))):
insideSquare = True
xt1, yt1 = interSections[0].p1
xt2, yt2 = interSections[0].p2
ax.plot([xt1, xt2], [yt1, yt2], color='g', linewidth=5.0)
elif np.size(interSections) == 3:
insideSquare = True
for val in interSections:
if ('Segment' in str(type(val))):
xt1, yt1 = val.p1
xt2, yt2 = val.p2
ax.plot([xt1, xt2], [yt1, yt2], color='g', linewidth=5.0)
d1 = lp1.distance(val.p1)
d2 = lp1.distance(val.p2)
if d1 < d2:
startTime = startTime1 + timewidth * float(d1 / d)
stopTime = startTime1 + timewidth * float(d2 / d)
else:
startTime = startTime1 + timewidth * float(d2 / d)
stopTime = startTime1 + timewidth * float(d1 / d)
elif np.size(interSections) == 0:
if square.encloses(lp1) and square.encloses(lp2):
insideSquare = True
xt1, yt1 = lp1
xt2, yt2 = lp2
ax.plot([xt1, xt2], [yt1, yt2], color='g', linewidth=5.0)
else:
insideSquare = False
plt.show()
return insideSquare, startTime, stopTime
def test_point():
x = Symbol('x', real=True)
y = Symbol('y', real=True)
x1 = Symbol('x1', real=True)
x2 = Symbol('x2', real=True)
y1 = Symbol('y1', real=True)
y2 = Symbol('y2', real=True)
half = Rational(1, 2)
p1 = Point(x1, x2)
p2 = Point(y1, y2)
p3 = Point(0, 0)
p4 = Point(1, 1)
p5 = Point(0, 1)
assert p1 in p1
assert p1 not in p2
assert p2.y == y2
assert (p3 + p4) == p4
assert (p2 - p1) == Point(y1 - x1, y2 - x2)
assert p4*5 == Point(5, 5)
assert -p2 == Point(-y1, -y2)
raises(ValueError, lambda: Point(3, I))
raises(ValueError, lambda: Point(2*I, I))
raises(ValueError, lambda: Point(3 + I, I))
assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3))
assert Point.midpoint(p3, p4) == Point(half, half)
assert Point.midpoint(p1, p4) == Point(half + half*x1, half + half*x2)
assert Point.midpoint(p2, p2) == p2
assert p2.midpoint(p2) == p2
assert Point.distance(p3, p4) == sqrt(2)
assert Point.distance(p1, p1) == 0
assert Point.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2)
assert Point.taxicab_distance(p4, p3) == 2
p1_1 = Point(x1, x1)
p1_2 = Point(y2, y2)
p1_3 = Point(x1 + 1, x1)
assert Point.is_collinear(p3)
assert Point.is_collinear(p3, p4)
assert Point.is_collinear(p3, p4, p1_1, p1_2)
assert Point.is_collinear(p3, p4, p1_1, p1_3) is False
assert Point.is_collinear(p3, p3, p4, p5) is False
line = Line(Point(1,0), slope = 1)
raises(TypeError, lambda: Point.is_collinear(line))
raises(TypeError, lambda: p1_1.is_collinear(line))
assert p3.intersection(Point(0, 0)) == [p3]
assert p3.intersection(p4) == []
assert p1.dot(p4) == x1 + x2
assert p3.dot(p4) == 0
assert p4.dot(p5) == 1
x_pos = Symbol('x', real=True, positive=True)
p2_1 = Point(x_pos, 0)
p2_2 = Point(0, x_pos)
p2_3 = Point(-x_pos, 0)
p2_4 = Point(0, -x_pos)
p2_5 = Point(x_pos, 5)
assert Point.is_concyclic(p2_1)
assert Point.is_concyclic(p2_1, p2_2)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_5) is False
assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False
assert p4.scale(2, 3) == Point(2, 3)
assert p3.scale(2, 3) == p3
assert p4.rotate(pi, Point(0.5, 0.5)) == p3
assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2)
assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2)
assert p4 * 5 == Point(5, 5)
assert p4 / 5 == Point(0.2, 0.2)
raises(ValueError, lambda: Point(0, 0) + 10)
# Point differences should be simplified
assert Point(x*(x - 1), y) - Point(x**2 - x, y + 1) == Point(0, -1)
a, b = Rational(1, 2), Rational(1, 3)
assert Point(a, b).evalf(2) == \
Point(a.n(2), b.n(2))
raises(ValueError, lambda: Point(1, 2) + 1)
# test transformations
p = Point(1, 0)
assert p.rotate(pi/2) == Point(0, 1)
assert p.rotate(pi/2, p) == p
p = Point(1, 1)
assert p.scale(2, 3) == Point(2, 3)
assert p.translate(1, 2) == Point(2, 3)
assert p.translate(1) == Point(2, 1)
assert p.translate(y=1) == Point(1, 2)
assert p.translate(*p.args) == Point(2, 2)
# Check invalid input for transform
raises(ValueError, lambda: p3.transform(p3))
raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
def generate_map():
screen.fill((0, 0, 0))
points = generate_random_points(num_points, width, height, buf)
#for x, y in points:
# pygame.draw.circle(screen, WHITE, (x,y), 2, 1)
voronoi_context = voronoi(points)
voronoi_point_dict = {}
point_to_segment_dict = {}
segments = []
vertices = []
top_l = Point(0, 0)
top_r = Point(width, 0)
bottom_l = Point(0, height)
bottom_r = Point(width, height)
top = Line(top_l, top_r)
left = Line(top_l, bottom_l)
right = Line(top_r, bottom_r)
bottom = Line(bottom_l, bottom_r)
boundaries = [top, right, bottom, left]
for edge in voronoi_context.edges:
il, i1, i2 = edge # index of line, index of vertex 1, index of vertex 2
line_color = RED
vert1 = None
vert2 = None
print_line = True
if i1 is not -1 and i2 is not -1:
vert1 = voronoi_context.vertices[i1]
vert2 = voronoi_context.vertices[i2]
else:
line_point = None
if i1 is -1:
line_p = voronoi_context.vertices[i2]
if i2 is -1:
line_p = voronoi_context.vertices[i1]
line_point = Point(line_p[0], line_p[1])
line = voronoi_context.lines[il]
p1 = None
p2 = None
if line[1] == 0:
p1 = line_point
p2 = Point(line[0] / line[2], 1)
else:
p1 = Point(0, line[2] / line[1])
p2 = line_point
l = Line(p1, p2)
top_intersect = l.intersection(top)
bottom_intersect = l.intersection(bottom)
right_intersect = l.intersection(right)
left_intersect = l.intersection(left)
distances = []
top_dist = None
bottom_dist = None
right_dist = None
left_dist = None
if len(top_intersect) != 0:
top_dist = abs(line_point.distance(top_intersect[0]))
distances.append(top_dist)
if len(bottom_intersect) != 0:
bottom_dist = abs(line_point.distance(bottom_intersect[0]))
distances.append(bottom_dist)
if len(right_intersect) != 0:
right_dist = abs(line_point.distance(right_intersect[0]))
distances.append(right_dist)
if len(left_intersect) != 0:
left_dist = abs(line_point.distance(left_intersect[0]))
distances.append(left_dist)
vert1 = line_p
v2 = None
if top_dist == min(distances):
v2 = top_intersect[0]
elif bottom_dist == min(distances):
v2 = bottom_intersect[0]
elif right_dist == min(distances):
v2 = right_intersect[0]
elif left_dist == min(distances):
v2 = left_intersect[0]
else:
v2 = Point(0, 0)
vert2 = (v2.x, v2.y)
if vert1[0] < 0 or vert1[1] < 0 or vert2[0] < 0 or vert2[
1] < 0 or vert1[0] > width or vert1[1] > height or vert2[
0] > width or vert2[1] > height:
print_line = False
if print_line:
vert1, vert2 = adjust_out_of_bounds_points(vert1, vert2,
boundaries)
seg = None
if vert1 == None or vert2 == None:
print_line = False
if print_line:
vert1_p = Point(vert1)
vert2_p = Point(vert2)
seg = Segment(vert1_p, vert2_p)
segments.append(seg)
if not vert1_p in voronoi_point_dict:
voronoi_point_dict[vert1_p] = []
if not vert2_p in voronoi_point_dict:
voronoi_point_dict[vert2_p] = []
voronoi_point_dict[vert1_p].append(vert2_p)
voronoi_point_dict[vert2_p].append(vert1_p)
if not vert1_p in point_to_segment_dict:
point_to_segment_dict[vert1_p] = []
if not vert2_p in point_to_segment_dict:
point_to_segment_dict[vert2_p] = []
point_to_segment_dict[vert1_p].append(seg)
point_to_segment_dict[vert2_p].append(seg)
pygame.draw.line(screen, line_color, vert1, vert2, 1)
pygame.display.flip()
top_intersects = []
bottom_intersects = []
right_intersects = []
left_intersects = []
for seg in segments:
if seg.p1.y <= 1:
top_intersects.append(seg.p1)
if seg.p2.y <= 1:
top_intersects.append(seg.p2)
if seg.p1.x >= width - 1:
right_intersects.append(seg.p1)
if seg.p2.x >= width - 1:
right_intersects.append(seg.p2)
if seg.p1.x <= 1:
left_intersects.append(seg.p1)
if seg.p2.x <= 1:
left_intersects.append(seg.p2)
if seg.p1.y >= height - 1:
bottom_intersects.append(seg.p1)
if seg.p2.y >= height - 1:
bottom_intersects.append(seg.p2)
top_intersects = sorted(top_intersects, key=lambda point: point.x)
bottom_intersects = sorted(bottom_intersects, key=lambda point: point.x)
left_intersects = sorted(left_intersects, key=lambda point: point.y)
right_intersects = sorted(right_intersects, key=lambda point: point.y)
for i in range(0, 4):
intersect = None
prev_vertex = None
final_vertex = None
if i == 0:
prev_vertex = top_l
intersect = top_intersects
intersect.append(top_r)
if i == 1:
prev_vertex = bottom_l
intersect = bottom_intersects
intersect.append(bottom_r)
if i == 2:
prev_vertex = top_l
intersect = left_intersects
intersect.append(bottom_l)
if i == 3:
prev_vertex = top_r
intersect = right_intersects
intersect.append(bottom_r)
if not prev_vertex in voronoi_point_dict:
voronoi_point_dict[prev_vertex] = []
if not final_vertex in voronoi_point_dict:
voronoi_point_dict[final_vertex] = []
if not prev_vertex in point_to_segment_dict:
point_to_segment_dict[prev_vertex] = []
if not final_vertex in point_to_segment_dict:
point_to_segment_dict[final_vertex] = []
for vertex in intersect:
if not vertex in voronoi_point_dict:
voronoi_point_dict[vertex] = []
if not prev_vertex in voronoi_point_dict:
voronoi_point_dict[prev_vertex] = []
s = Segment(prev_vertex, vertex)
voronoi_point_dict[vertex].append(prev_vertex)
voronoi_point_dict[prev_vertex].append(vertex)
if not vertex in point_to_segment_dict:
point_to_segment_dict[vertex] = []
if not prev_vertex in point_to_segment_dict:
point_to_segment_dict[prev_vertex] = []
point_to_segment_dict[vertex].append(s)
point_to_segment_dict[prev_vertex].append(s)
prev_vertex = vertex
try:
polygons, segments_to_polygons = generate_polygons(
voronoi_point_dict, segments, points, point_to_segment_dict)
except Exception as e:
print e
print "crashed"
while 1:
""" helllo"""
for seg, gons in segments_to_polygons.iteritems():
for gon in gons:
gon.connect_adjacent_nodes(gons)
for polygon in polygons:
for node in polygon.adjacent_nodes:
s = Segment(node.center, polygon.center)
draw_segment(s, WHITE)
highest_points_of_elevation = []
frontiers = []
for i in range(0, number_of_peaks):
p = random.choice(polygons)
p.elevation = max_elevation
highest_points_of_elevation.append(p)
frontiers.append(set(p.adjacent_nodes))
marked_polygons = set([])
elevation = max_elevation
while len(marked_polygons) < num_points:
elevation -= 1
for i in range(0, number_of_peaks):
new_frontier = set([])
while len(frontiers[i]) > 0:
node = frontiers[i].pop()
node.elevation = elevation
draw_point(node.center, ORANGE)
for n in node.adjacent_nodes:
if n not in marked_polygons:
new_frontier.add(n)
marked_polygons.add(node)
frontiers[i] = new_frontier
for polygon in polygons:
if polygon.elevation <= 0:
vertices = []
for edge in polygon.edge_list:
p = (edge.x, edge.y)
vertices.append(p)
pygame.draw.polygon(screen, BLUE, vertices, 0)
pygame.display.flip()
pygame.display.flip()
def test_point():
x = Symbol('x', real=True)
y = Symbol('y', real=True)
x1 = Symbol('x1', real=True)
x2 = Symbol('x2', real=True)
y1 = Symbol('y1', real=True)
y2 = Symbol('y2', real=True)
half = S.Half
p1 = Point(x1, x2)
p2 = Point(y1, y2)
p3 = Point(0, 0)
p4 = Point(1, 1)
p5 = Point(0, 1)
line = Line(Point(1, 0), slope=1)
assert p1 in p1
assert p1 not in p2
assert p2.y == y2
assert (p3 + p4) == p4
assert (p2 - p1) == Point(y1 - x1, y2 - x2)
assert -p2 == Point(-y1, -y2)
raises(TypeError, lambda: Point(1))
raises(ValueError, lambda: Point([1]))
raises(ValueError, lambda: Point(3, I))
raises(ValueError, lambda: Point(2*I, I))
raises(ValueError, lambda: Point(3 + I, I))
assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3))
assert Point.midpoint(p3, p4) == Point(half, half)
assert Point.midpoint(p1, p4) == Point(half + half*x1, half + half*x2)
assert Point.midpoint(p2, p2) == p2
assert p2.midpoint(p2) == p2
assert p1.origin == Point(0, 0)
assert Point.distance(p3, p4) == sqrt(2)
assert Point.distance(p1, p1) == 0
assert Point.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2)
raises(TypeError, lambda: Point.distance(p1, 0))
raises(TypeError, lambda: Point.distance(p1, GeometryEntity()))
# distance should be symmetric
assert p1.distance(line) == line.distance(p1)
assert p4.distance(line) == line.distance(p4)
assert Point.taxicab_distance(p4, p3) == 2
assert Point.canberra_distance(p4, p5) == 1
raises(ValueError, lambda: Point.canberra_distance(p3, p3))
p1_1 = Point(x1, x1)
p1_2 = Point(y2, y2)
p1_3 = Point(x1 + 1, x1)
assert Point.is_collinear(p3)
with warns(UserWarning, test_stacklevel=False):
assert Point.is_collinear(p3, Point(p3, dim=4))
assert p3.is_collinear()
assert Point.is_collinear(p3, p4)
assert Point.is_collinear(p3, p4, p1_1, p1_2)
assert Point.is_collinear(p3, p4, p1_1, p1_3) is False
assert Point.is_collinear(p3, p3, p4, p5) is False
raises(TypeError, lambda: Point.is_collinear(line))
raises(TypeError, lambda: p1_1.is_collinear(line))
assert p3.intersection(Point(0, 0)) == [p3]
assert p3.intersection(p4) == []
assert p3.intersection(line) == []
with warns(UserWarning, test_stacklevel=False):
assert Point.intersection(Point(0, 0, 0), Point(0, 0)) == [Point(0, 0, 0)]
x_pos = Symbol('x', positive=True)
p2_1 = Point(x_pos, 0)
p2_2 = Point(0, x_pos)
p2_3 = Point(-x_pos, 0)
p2_4 = Point(0, -x_pos)
p2_5 = Point(x_pos, 5)
assert Point.is_concyclic(p2_1)
assert Point.is_concyclic(p2_1, p2_2)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
for pts in permutations((p2_1, p2_2, p2_3, p2_5)):
assert Point.is_concyclic(*pts) is False
assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False
assert Point(0, 0).is_concyclic((1, 1), (2, 2), (2, 1)) is False
assert Point.is_concyclic(Point(0, 0, 0, 0), Point(1, 0, 0, 0), Point(1, 1, 0, 0), Point(1, 1, 1, 0)) is False
assert p1.is_scalar_multiple(p1)
assert p1.is_scalar_multiple(2*p1)
assert not p1.is_scalar_multiple(p2)
assert Point.is_scalar_multiple(Point(1, 1), (-1, -1))
assert Point.is_scalar_multiple(Point(0, 0), (0, -1))
# test when is_scalar_multiple can't be determined
raises(Undecidable, lambda: Point.is_scalar_multiple(Point(sympify("x1%y1"), sympify("x2%y2")), Point(0, 1)))
assert Point(0, 1).orthogonal_direction == Point(1, 0)
assert Point(1, 0).orthogonal_direction == Point(0, 1)
assert p1.is_zero is None
assert p3.is_zero
assert p4.is_zero is False
assert p1.is_nonzero is None
assert p3.is_nonzero is False
assert p4.is_nonzero
assert p4.scale(2, 3) == Point(2, 3)
assert p3.scale(2, 3) == p3
assert p4.rotate(pi, Point(0.5, 0.5)) == p3
assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2)
assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2)
assert p4 * 5 == Point(5, 5)
assert p4 / 5 == Point(0.2, 0.2)
assert 5 * p4 == Point(5, 5)
raises(ValueError, lambda: Point(0, 0) + 10)
# Point differences should be simplified
assert Point(x*(x - 1), y) - Point(x**2 - x, y + 1) == Point(0, -1)
a, b = S.Half, Rational(1, 3)
assert Point(a, b).evalf(2) == \
Point(a.n(2), b.n(2), evaluate=False)
raises(ValueError, lambda: Point(1, 2) + 1)
# test project
assert Point.project((0, 1), (1, 0)) == Point(0, 0)
assert Point.project((1, 1), (1, 0)) == Point(1, 0)
raises(ValueError, lambda: Point.project(p1, Point(0, 0)))
# test transformations
p = Point(1, 0)
assert p.rotate(pi/2) == Point(0, 1)
assert p.rotate(pi/2, p) == p
p = Point(1, 1)
assert p.scale(2, 3) == Point(2, 3)
assert p.translate(1, 2) == Point(2, 3)
assert p.translate(1) == Point(2, 1)
assert p.translate(y=1) == Point(1, 2)
assert p.translate(*p.args) == Point(2, 2)
# Check invalid input for transform
raises(ValueError, lambda: p3.transform(p3))
raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
# test __contains__
assert 0 in Point(0, 0, 0, 0)
assert 1 not in Point(0, 0, 0, 0)
# test affine_rank
assert Point.affine_rank() == -1
def test_point():
p1 = Point(x1, x2)
p2 = Point(y1, y2)
p3 = Point(0, 0)
p4 = Point(1, 1)
assert p1 in p1
assert p1 not in p2
assert p2.y == y2
assert (p3 + p4) == p4
assert (p2 - p1) == Point(y1 - x1, y2 - x2)
assert p4 * 5 == Point(5, 5)
assert -p2 == Point(-y1, -y2)
assert Point.midpoint(p3, p4) == Point(half, half)
assert Point.midpoint(p1, p4) == Point(half + half * x1, half + half * x2)
assert Point.midpoint(p2, p2) == p2
assert p2.midpoint(p2) == p2
assert Point.distance(p3, p4) == sqrt(2)
assert Point.distance(p1, p1) == 0
assert Point.distance(p3, p2) == sqrt(p2.x ** 2 + p2.y ** 2)
p1_1 = Point(x1, x1)
p1_2 = Point(y2, y2)
p1_3 = Point(x1 + 1, x1)
assert Point.is_collinear(p3)
assert Point.is_collinear(p3, p4)
assert Point.is_collinear(p3, p4, p1_1, p1_2)
assert Point.is_collinear(p3, p4, p1_1, p1_3) == False
assert p3.intersection(Point(0, 0)) == [p3]
assert p3.intersection(p4) == []
x_pos = Symbol("x", real=True, positive=True)
p2_1 = Point(x_pos, 0)
p2_2 = Point(0, x_pos)
p2_3 = Point(-x_pos, 0)
p2_4 = Point(0, -x_pos)
p2_5 = Point(x_pos, 5)
assert Point.is_concyclic(p2_1)
assert Point.is_concyclic(p2_1, p2_2)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4)
assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_5) == False
assert Point.is_concyclic(p4, p4 * 2, p4 * 3) == False
assert p4.scale(2, 3) == Point(2, 3)
assert p3.scale(2, 3) == p3
assert p4.rotate(pi, Point(0.5, 0.5)) == p3
assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2)
assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2)
assert p4 * 5 == Point(5, 5)
assert p4 / 5 == Point(0.2, 0.2)
raises(ValueError, lambda: Point(0, 0) + 10)
# Point differences should be simplified
assert Point(x * (x - 1), y) - Point(x ** 2 - x, y + 1) == Point(0, -1)
a, b = Rational(1, 2), Rational(1, 3)
assert Point(a, b).evalf(2) == Point(a.n(2), b.n(2))
raises(ValueError, lambda: Point(1, 2) + 1)
# test transformations
p = Point(1, 0)
assert p.rotate(pi / 2) == Point(0, 1)
assert p.rotate(pi / 2, p) == p
p = Point(1, 1)
assert p.scale(2, 3) == Point(2, 3)
assert p.translate(1, 2) == Point(2, 3)
assert p.translate(1) == Point(2, 1)
assert p.translate(y=1) == Point(1, 2)
assert p.translate(*p.args) == Point(2, 2)
def point_within_tolerance(self, point1, point2, tolerance=None):
if tolerance is None:
tolerance = self.tolerance['point_distance'] / self.xscale
p1 = Point(*point1)
return p1.distance(Point(*point2)) < tolerance