def __sub__(self, other):
"""
Creates a `Vector` going from `other` to `self`.
:param other: `Point`
:return: `Vector`: `other` -> `self`
"""
return Vector(self.x - other.x, self.y - other.y)
def make_versor(u: float, v: float):
"""
Creates a `Vector` with `u` and `v` projections, then
normalizes it.
:param u: `float` horizontal projection
:param v: `float` vertical projection
:return: `Vector` with unitary norm
"""
return Vector(u, v).normalized()
def displaced(self, vector: Vector, times=1):
"""
Creates a new `Point` result of displacing this one the
given `vector` and number of times `times`.
:param vector: displacement `Vector`
:param times: times the displacement vector is applied
:return: `Point`
"""
scaled_vec = vector.scaled_by(times)
return Point(self.x + scaled_vec.u, self.y + scaled_vec.v)
class Circle(Shape):
def __init__(self, center=(0, 0), radius=1.0):
self.center = Vector(*center)
self.radius = radius
def __info__(self):
return "c=%s, r=%s" % (self.center, self.radius)
# --------------------------------------------------------------------------
# Geometry interface
def move(self, dx=0.0, dy=0.0):
if dx == 0.0 and dy == 0.0:
return
self.center.move(dx, dy)
def scale(self, factor, pivot=None):
if factor == 1.0:
return
if pivot is not None:
self.center.scale(factor, pivot)
self.radius *= factor
def rotate(self, alpha, pivot=None):
if alpha == 0.0:
return
if pivot is not None:
self.center.rotate(alpha, pivot)
# --------------------------------------------------------------------------
# Shape interface
def contains_point(self, point):
radius = self.radius
delta = point - self.center
return delta.squared_length <= radius * radius
def segment_intersections(self, segment):
points = []
cx, cy = self.center
r = self.radius
m = segment.slope
if m is None: # vertical segment
if cx - r <= segment.a.x <= cx + r:
pass
else:
b = segment.y_at(0.0)
A = 1 + m*m
B = -2*cx + 2*m*b -2*m*cy
C = cx*cx + cy*cy + b*b - r*r - 2*b*cy
x0, x1 = solve_quadratic(A, B, C)
xinterval = segment.xrange
if x0 in xinterval:
points.append(Vector(x0, segment.y_at(x0)))
if x1 in xinterval:
points.append(Vector(x1, segment.y_at(x1)))
return points
def __init__(self, center=(0, 0), radius=1.0):
self.center = Vector(*center)
self.radius = radius
def test_vector():
for _ in xrange(1000):
v = random_vector()
x, y = v
assert v + (2, 0) == Vector(x+2, y)
assert v - (2, 0) == Vector(x-2, y)
assert +v == Vector(x, y)
assert -v == Vector(-x, -y)
assert v * 2 == Vector(2*x, 2*y)
assert v / 2 == Vector(x/2, y/2)
v = Vector(1, 0)
assert v.angle == 0
v.angle = pi/2
v.x, v.y = map(Approx, v)
assert v == Vector(0, 1)
v.length = 2
v.x, v.y = map(Approx, v)
assert v == Vector(0, 2)
v.move(2, 2)
assert v == Vector(2, 4)
v.scale(2, 2, pivot=(1, 1))
assert v == Vector(3, 7)
v.rotate(pi/2, pivot=(3, 3))
v.x, v.y = [Approx(n) for n in v]
assert v == Vector(-1, 3)
def test_parallel_lines_no_intersection(self):
l1 = Line(Point(0, 0), Vector(1, 1))
l2 = Line(Point(10, 10), Vector(1, 1))
self.assertIsNone(l1.intersection_with(l2))
def test_lines_intersection(self):
l1 = Line(Point(50, 0), Vector(0, 1))
l2 = Line(Point(0, 30), Vector(1, 0))
actual = l1.intersection_with(l2)
expected = Point(50, 30)
self.assertEqual(expected, actual)
def test_penetration(self):
other = Circle(Point(30, 30), 20)
actual = self.circle.penetration_vector(other)
pen_proj = -(math.sqrt(2) * 15 - 20)
expected = Vector(pen_proj, pen_proj)
self.assertEqual(expected, actual)
def test_rotate_right_angle(self):
actual = self.east.rotated_radians(math.pi / 2)
expected = Vector(0, 1)
self.assertEqual(expected, actual)
def test_rotate_positive_angle(self):
sqrt2 = math.sqrt(2)
actual = self.east.rotated_radians(math.pi / 4)
expected = Vector(1 / sqrt2, 1 / sqrt2)
self.assertEqual(expected, actual)
class TestVector(unittest.TestCase):
u = Vector(1, 2)
v = Vector(4, 6)
east = Vector(1, 0)
west = Vector(-1, 0)
north_east = Vector(1, 1)
south_east = Vector(1, -1)
# <----- Operations -----> #
def test_plus(self):
expected = Vector(5, 8)
actual = self.u + self.v
self.assertEqual(expected, actual)
def test_minus(self):
expected = Vector(-3, -4)
actual = self.u - self.v
self.assertEqual(expected, actual)
# <----- Products -----> #
def test_dot_product(self):
expected = 16
actual = self.u.dot(self.v)
self.assertAlmostEqual(expected, actual)
def test_cross_product(self):
expected = -2
actual = self.u.cross(self.v)
self.assertAlmostEqual(expected, actual)
# <----- Parallel & Perpendicular -----> #
def test_are_parallel(self):
self.assertTrue(self.u.is_parallel_to(self.u))
def test_are_not_parallel(self):
self.assertFalse(self.u.is_parallel_to(self.v))
def test_are_perpendicular(self):
perp = Vector(-2, 1)
self.assertTrue(self.u.is_perpendicular_to(perp))
def test_are_not_perpendicular(self):
self.assertFalse(self.u.is_perpendicular_to(self.v))
# <----- Angle Value -----> #
def test_angle_value_of_zero(self):
actual = self.east.angle_value_to(self.east)
expected = 0
self.assertAlmostEqual(expected, actual)
def test_angle_value_of_pi(self):
actual = self.east.angle_value_to(self.west)
expected = math.pi
self.assertAlmostEqual(expected, actual)
def test_angle_value_when_angle_positive(self):
actual = self.east.angle_value_to(self.north_east)
expected = math.pi / 4
self.assertAlmostEqual(expected, actual)
def test_angle_value_when_angle_negative(self):
actual = self.east.angle_value_to(self.north_east)
expected = math.pi / 4
self.assertAlmostEqual(expected, actual)
# <----- Angle Value -----> #
def test_angle_when_angle_positive(self):
actual = self.east.angle_to(self.north_east)
expected = math.pi / 4
self.assertAlmostEqual(expected, actual)
def test_angle_when_angle_negative(self):
actual = self.east.angle_to(self.south_east)
expected = -math.pi / 4
self.assertAlmostEqual(expected, actual)
# <----- Rotate Angle -----> #
def test_rotate_zero_radians(self):
actual = self.east.rotated_radians(0)
expected = self.east
self.assertEqual(expected, actual)
def test_rotate_positive_angle(self):
sqrt2 = math.sqrt(2)
actual = self.east.rotated_radians(math.pi / 4)
expected = Vector(1 / sqrt2, 1 / sqrt2)
self.assertEqual(expected, actual)
def test_rotate_right_angle(self):
actual = self.east.rotated_radians(math.pi / 2)
expected = Vector(0, 1)
self.assertEqual(expected, actual)
def test_rotate_straight_angle(self):
actual = self.north_east.rotated_radians(math.pi)
expected = Vector(-1, -1)
self.assertEqual(expected, actual)
def test_rotate_negative_angle(self):
sqrt2 = math.sqrt(2)
actual = self.east.rotated_radians(-math.pi / 4)
expected = Vector(1 / sqrt2, -1 / sqrt2)
self.assertEqual(expected, actual)
def test_are_perpendicular(self):
perp = Vector(-2, 1)
self.assertTrue(self.u.is_perpendicular_to(perp))
def test_minus(self):
expected = Vector(-3, -4)
actual = self.u - self.v
self.assertEqual(expected, actual)
def test_plus(self):
expected = Vector(5, 8)
actual = self.u + self.v
self.assertEqual(expected, actual)
def test_rotate_straight_angle(self):
actual = self.north_east.rotated_radians(math.pi)
expected = Vector(-1, -1)
self.assertEqual(expected, actual)
