def _hIDW(self, x, y):
# interpolate height at (x, y) radians or degrees
try:
ds = self._distances(x, y)
return fidw(self._hs, ds, beta=self._beta)
except (TypeError, ValueError) as x:
raise HeightError(str(x))
def _hIDW(self, lli): # PYCHOK expected
# interpolate height at point lli
try:
kwds = self._distanceTo_kwds
ds = (k.distanceTo(lli, **kwds) for k in self._ks)
return fidw(self._hs, ds, beta=self._beta)
except (TypeError, ValueError) as x:
raise HeightError(str(x))
def trilaterate(point1,
distance1,
point2,
distance2,
point3,
distance3,
radius=R_M,
height=None,
LatLon=LatLon,
useZ=False):
'''Locate a point at given distances from three other points.
See also U{Trilateration<https://WikiPedia.org/wiki/Trilateration>}.
@param point1: First point (L{LatLon}).
@param distance1: Distance to the first point (C{meter}, same units
as B{C{radius}}).
@param point2: Second point (L{LatLon}).
@param distance2: Distance to the second point (C{meter}, same units
as B{C{radius}}).
@param point3: Third point (L{LatLon}).
@param distance3: Distance to the third point (C{meter}, same units
as B{C{radius}}).
@keyword radius: Optional, mean earth radius (C{meter}).
@keyword height: Optional height at the trilaterated point, overriding
the IDW height (C{meter}, same units as B{C{radius}}).
@keyword LatLon: Optional (sub-)class to return the trilaterated
point (L{LatLon}).
@keyword useZ: Include Z component iff non-NaN, non-zero (C{bool}).
@return: Trilaterated point (B{C{LatLon}}).
@raise TypeError: If B{C{point1}}, B{C{point2}} or B{C{point3}}
is not L{LatLon}.
@raise ValueError: Invalid B{C{radius}}, some B{C{distances}} exceed
trilateration or some B{C{points}} coincide.
'''
def _nd2(p, d, name, *qs):
# return Nvector and radial distance squared
_Nvll.others(p, name=name)
for q in qs:
if p.isequalTo(q, EPS):
raise ValueError('%s %s: %r' % ('coincident', 'points', p))
return p.toNvector(), (float(d) / radius)**2
if float(radius or 0) < EPS:
raise ValueError('%s %s: %r' % ('radius', 'invalid', radius))
n1, d12 = _nd2(point1, distance1, 'point1')
n2, d22 = _nd2(point2, distance2, 'point2', point1)
n3, d32 = _nd2(point3, distance3, 'point3', point1, point2)
# the following uses x,y coordinate system with origin at n1, x axis n1->n2
y = n3.minus(n1)
x = n2.minus(n1)
d = x.length # distance n1->n2
if d > EPS_2: # and y.length > EPS_2:
X = x.unit() # unit vector in x direction n1->n2
i = X.dot(y) # signed magnitude of x component of n1->n3
Y = y.minus(X.times(i)).unit() # unit vector in y direction
j = Y.dot(y) # signed magnitude of y component of n1->n3
if abs(j) > EPS_2:
# courtesy Carlos Freitas <https://GitHub.com/mrJean1/PyGeodesy/issues/33>
x = fsum_(d12, -d22, d**2) / (2 * d) # n1->intersection x- and ...
y = fsum_(d12, -d32, i**2, j**2) / (2 * j) - (x * i / j
) # ... y-component
n = n1.plus(X.times(x)).plus(Y.times(y)) # .plus(Z.times(z))
if useZ: # include non-NaN, non-zero Z component
z = fsum_(d12, -(x**2), -(y**2))
if z > EPS:
Z = X.cross(Y) # unit vector perpendicular to plane
n = n.plus(Z.times(sqrt(z)))
if height is None:
h = fidw((point1.height, point2.height, point3.height),
map1(fabs, distance1, distance2, distance3))
else:
h = height
return n.toLatLon(
height=h,
LatLon=LatLon) # Nvector(n.x, n.y, n.z).toLatLon(...)
# no intersection, d < EPS_2 or j < EPS_2
raise ValueError('no %s for %r, %r, %r at %r, %r, %r' %
('trilaterate', point1, point2, point3, distance1,
distance2, distance3))
def _trilaterate(point1,
distance1,
point2,
distance2,
point3,
distance3,
radius=R_M,
height=None,
useZ=False,
**LatLon_LatLon_kwds):
# (INTERNAL) Locate a point at given distances from
# three other points, see LatLon.triangulate above
def _nd2(p, d, r, _i_, *qs): # .toNvector and angular distance squared
for q in qs:
if p.isequalTo(q, EPS):
raise _ValueError(points=p, txt=_coincident_)
return p.toNvector(), (Scalar(d, name=_distance_ + _i_) / r)**2
r = Radius_(radius)
n1, r12 = _nd2(point1, distance1, r, _1_)
n2, r22 = _nd2(point2, distance2, r, _2_, point1)
n3, r32 = _nd2(point3, distance3, r, _3_, point1, point2)
# the following uses x,y coordinate system with origin at n1, x axis n1->n2
y = n3.minus(n1)
x = n2.minus(n1)
z = None
d = x.length # distance n1->n2
if d > EPS_2: # and y.length > EPS_2:
X = x.unit() # unit vector in x direction n1->n2
i = X.dot(y) # signed magnitude of x component of n1->n3
Y = y.minus(X.times(i)).unit() # unit vector in y direction
j = Y.dot(y) # signed magnitude of y component of n1->n3
if abs(j) > EPS_2:
# courtesy Carlos Freitas <https://GitHub.com/mrJean1/PyGeodesy/issues/33>
x = fsum_(r12, -r22, d**2) / (2 * d) # n1->intersection x- and ...
y = fsum_(r12, -r32, i**2, j**2, -2 * x * i) / (
2 * j) # ... y-component
# courtesy AleixDev <https://GitHub.com/mrJean1/PyGeodesy/issues/43>
z = fsum_(max(r12, r22, r32), -(x**2),
-(y**2)) # XXX not just r12!
if z > EPS:
n = n1.plus(X.times(x)).plus(Y.times(y))
if useZ: # include Z component
Z = X.cross(Y) # unit vector perpendicular to plane
n = n.plus(Z.times(sqrt(z)))
if height is None:
h = fidw((point1.height, point2.height, point3.height),
map1(fabs, distance1, distance2, distance3))
else:
h = Height(height)
kwds = _xkwds(LatLon_LatLon_kwds, height=h)
return n.toLatLon(**
kwds) # Nvector(n.x, n.y, n.z).toLatLon(...)
# no intersection, d < EPS_2 or abs(j) < EPS_2 or z < EPS
t = NN(_no_, _intersection_, _SPACE_)
raise IntersectionError(point1=point1,
distance1=distance1,
point2=point2,
distance2=distance2,
point3=point3,
distance3=distance3,
txt=unstr(t, z=z, useZ=useZ))