def rotate(self, rotation_angle, origin=None):
""" Rotates the position value by the specified angle using a standard
2D rotation matrix formulation. If an origin Position2D instance is
not specified the rotation will occur around the origin. Also, if
an origin is specified, the uncertainty in that origin value will
be propagated through to the uncertainty of the rotated result.
:param rotation_angle:
:param origin: (optional)
:return:
"""
if origin is None:
origin = self.__class__(value.ValueUncertainty(0, 0), value.ValueUncertainty(0, 0))
a = rotation_angle.radians
x = self.x.raw - origin.x.raw
y = self.y.raw - origin.y.raw
self.x.update(
x * math.cos(a) - y * math.sin(a) + origin.x.raw,
ops.sqrt_sum_of_squares(self.x.uncertainty, origin.x.uncertainty),
)
self.y.update(
y * math.cos(a) + x * math.sin(a) + origin.y.raw,
ops.sqrt_sum_of_squares(self.y.uncertainty, origin.y.uncertainty),
)
return self
def rotate(self, rotation_angle, origin=None):
""" Rotates the position value by the specified angle using a standard
2D rotation matrix formulation. If an origin Position2D instance is
not specified the rotation will occur around the origin. Also, if
an origin is specified, the uncertainty in that origin value will
be propagated through to the uncertainty of the rotated result.
:param rotation_angle:
:param origin: (optional)
:return:
"""
if origin is None:
origin = self.__class__(
value.ValueUncertainty(0, 0),
value.ValueUncertainty(0, 0)
)
a = rotation_angle.radians
x = self.x.raw - origin.x.raw
y = self.y.raw - origin.y.raw
self.x.update(
x * math.cos(a) - y*math.sin(a) + origin.x.raw,
ops.sqrt_sum_of_squares(self.x.uncertainty, origin.x.uncertainty)
)
self.y.update(
y * math.cos(a) + x*math.sin(a) + origin.y.raw,
ops.sqrt_sum_of_squares(self.y.uncertainty, origin.y.uncertainty)
)
return self
def closest_point_on_line(point, line_start, line_end, contained=True):
"""
Finds the closest point on a line to the specified point using the formulae
discussed in the "another formula" section of:
wikipedia.org/wiki/Distance_from_a_point_to_a_line#Another_formula
"""
length = line_start.distance_from(line_end)
if not length:
raise ValueError("Cannot calculate point. Invalid line segment.")
s = line_start
e = line_end
delta_x = e.x.raw - s.x.raw
delta_y = e.y.raw - s.y.raw
rotate = False
slope = 0.0
slope_unc = 0.0
try:
slope = delta_y / delta_x
slope_unc = abs(1.0 / delta_x) * (s.y.raw_uncertainty + e.y.raw_uncertainty) + abs(slope / delta_x) * (
s.x.raw_uncertainty + e.x.raw_uncertainty
)
except Exception:
rotate = True
raise
if rotate or (abs(slope) > 1.0 and abs(slope_unc / slope) > 0.5):
a = angle.Angle(degrees=20.0)
e2 = e.clone().rotate(a, s)
p2 = point.clone().rotate(a, s)
print(point, p2)
print(e, e2)
result = closest_point_on_line(p2, s, e2, contained)
if result is None:
return result
a.degrees = -20.0
result.rotate(a, s)
return result
intercept = s.y.raw - slope * s.x.raw
denom = slope * slope + 1.0
numer = point.x.raw + slope * (point.y.raw - intercept)
x = numer / denom
y = (slope * numer) / denom + intercept
if contained:
# Check to see if point is between start and end values
x_range = sorted([s.x.raw, e.x.raw])
y_range = sorted([s.y.raw, e.y.raw])
eps = 1e-8
x_min = x - eps
x_max = x + eps
y_min = y - eps
y_max = y + eps
out_of_bounds = x_range[1] < x_min or x_max < x_range[0] or y_range[1] < y_min or y_max < y_range[0]
if out_of_bounds:
return None
start_dist = ops.sqrt_sum_of_squares(s.x.raw - x, s.y.raw - y)
end_dist = ops.sqrt_sum_of_squares(e.x.raw - x, e.y.raw - y)
x_unc = start_dist / length.raw * s.x.raw_uncertainty + end_dist / length.raw * e.x.raw_uncertainty
x_unc = math.sqrt(x_unc ** 2 + point.x.raw_uncertainty ** 2)
y_unc = start_dist / length.raw * s.y.raw_uncertainty + end_dist / length.raw * e.y.raw_uncertainty
y_unc = math.sqrt(y_unc ** 2 + point.y.raw_uncertainty ** 2)
return create_point(x=x, y=y, x_unc=x_unc, y_unc=y_unc)
def closest_point_on_line(point, line_start, line_end, contained=True):
"""
Finds the closest point on a line to the specified point using the formulae
discussed in the "another formula" section of:
wikipedia.org/wiki/Distance_from_a_point_to_a_line#Another_formula
"""
length = line_start.distance_from(line_end)
if not length:
raise ValueError('Cannot calculate point. Invalid line segment.')
s = line_start
e = line_end
delta_x = e.x.raw - s.x.raw
delta_y = e.y.raw - s.y.raw
rotate = False
slope = 0.0
slope_unc = 0.0
try:
slope = delta_y / delta_x
slope_unc = (
abs(1.0 / delta_x) * (
s.y.raw_uncertainty + e.y.raw_uncertainty
) + abs(
slope / delta_x
) * (
s.x.raw_uncertainty + e.x.raw_uncertainty
)
)
except Exception:
rotate = True
raise
if rotate or (abs(slope) > 1.0 and abs(slope_unc / slope) > 0.5):
a = angle.Angle(degrees=20.0)
e2 = e.clone().rotate(a, s)
p2 = point.clone().rotate(a, s)
print(point, p2)
print(e, e2)
result = closest_point_on_line(p2, s, e2, contained)
if result is None:
return result
a.degrees = -20.0
result.rotate(a, s)
return result
intercept = s.y.raw - slope * s.x.raw
denom = slope * slope + 1.0
numer = point.x.raw + slope * (point.y.raw - intercept)
x = numer / denom
y = (slope * numer) / denom + intercept
if contained:
# Check to see if point is between start and end values
x_range = sorted([s.x.raw, e.x.raw])
y_range = sorted([s.y.raw, e.y.raw])
eps = 1e-8
x_min = x - eps
x_max = x + eps
y_min = y - eps
y_max = y + eps
out_of_bounds = (
x_range[1] < x_min or
x_max < x_range[0] or
y_range[1] < y_min or
y_max < y_range[0]
)
if out_of_bounds:
return None
start_dist = ops.sqrt_sum_of_squares(s.x.raw - x, s.y.raw - y)
end_dist = ops.sqrt_sum_of_squares(e.x.raw - x, e.y.raw - y)
x_unc = (
start_dist / length.raw * s.x.raw_uncertainty +
end_dist / length.raw * e.x.raw_uncertainty
)
x_unc = math.sqrt(x_unc ** 2 + point.x.raw_uncertainty ** 2)
y_unc = (
start_dist / length.raw * s.y.raw_uncertainty +
end_dist / length.raw * e.y.raw_uncertainty
)
y_unc = math.sqrt(y_unc ** 2 + point.y.raw_uncertainty ** 2)
return create_point(x=x, y=y, x_unc=x_unc, y_unc=y_unc)
def test_sqrtSumOfSquares(self):
"""test_sqrtSumOfSquares doc..."""
self.assertEqual(1.0, ops.sqrt_sum_of_squares(-1.0))
self.assertEqual(math.sqrt(2), ops.sqrt_sum_of_squares(1.0, 1.0))
self.assertEqual(math.sqrt(4.25), ops.sqrt_sum_of_squares(2.0, 0.5))
def test_sqrtSumOfSquares(self):
"""test_sqrtSumOfSquares doc..."""
self.assertEqual(1.0, ops.sqrt_sum_of_squares(-1.0))
self.assertEqual(math.sqrt(2), ops.sqrt_sum_of_squares(1.0, 1.0))
self.assertEqual(math.sqrt(4.25), ops.sqrt_sum_of_squares(2.0, 0.5))
