def distanceTo(self, other, radius=R_M, wrap=False): '''Compute the distance from this to an other point. @arg other: The other point (L{LatLon}). @kwarg radius: Mean earth radius (C{meter}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Distance between this and the B{C{other}} point (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not L{LatLon}. @raise ValueError: Invalid B{C{radius}}. @example: >>> p1 = LatLon(52.205, 0.119) >>> p2 = LatLon(48.857, 2.351); >>> d = p1.distanceTo(p2) # 404300 ''' self.others(other) a1, b1 = self.philam a2, b2 = other.philam db, _ = unrollPI(b1, b2, wrap=wrap) r = vincentys_(a2, a1, db) return r * Radius(radius)
def _rads(n, points, closed): # angular edge lengths in radians i, m = _imdex2(closed, n) a1, b1 = points[i].philam for i in range(m, n): a2, b2 = points[i].philam db, b2 = unrollPI(b1, b2, wrap=wrap) yield vincentys_(a2, a1, db) a1, b1 = a2, b2
def intermediateTo(self, other, fraction, height=None, wrap=False): '''Locate the point at given fraction between this and an other point. @arg other: The other point (L{LatLon}). @arg fraction: Fraction between both points (float, between 0.0 for this and 1.0 for the other point). @kwarg height: Optional height, overriding the fractional height (C{meter}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Intermediate point (L{LatLon}). @raise TypeError: The B{C{other}} point is not L{LatLon}. @raise ValueError: Invalid B{C{fraction}} or B{C{height}}. @example: >>> p1 = LatLon(52.205, 0.119) >>> p2 = LatLon(48.857, 2.351) >>> p = p1.intermediateTo(p2, 0.25) # 51.3721°N, 000.7073°E @JSname: I{intermediatePointTo}. ''' self.others(other) f = Scalar(fraction, name=_fraction_) a1, b1 = self.philam a2, b2 = other.philam db, b2 = unrollPI(b1, b2, wrap=wrap) r = vincentys_(a2, a1, db) sr = sin(r) if abs(sr) > EPS: sa1, ca1, sa2, ca2, \ sb1, cb1, sb2, cb2 = sincos2(a1, a2, b1, b2) A = sin((1 - f) * r) / sr B = sin(f * r) / sr x = A * ca1 * cb1 + B * ca2 * cb2 y = A * ca1 * sb1 + B * ca2 * sb2 z = A * sa1 + B * sa2 a = atan2(z, hypot(x, y)) b = atan2(y, x) else: # points too close a = favg(a1, a2, f=f) b = favg(b1, b2, f=f) if height is None: h = self._havg(other, f=f) else: h = Height(height) return self.classof(degrees90(a), degrees180(b), height=h)
def _intersects2(c1, rad1, c2, rad2, radius=R_M, # in .ellipsoidalBase._intersects2 height=None, wrap=True, too_d=None, LatLon=LatLon, **LatLon_kwds): # (INTERNAL) Intersect two spherical circles, see L{intersections2} # above, separated to allow callers to embellish any exceptions def _dest3(bearing, h): a, b = _destination2(a1, b1, r1, bearing) return _latlon3(degrees90(a), degrees180(b), h, intersections2, LatLon, **LatLon_kwds) r1, r2, f = _rads3(rad1, rad2, radius) if f: # swapped c1, c2 = c2, c1 # PYCHOK swap a1, b1 = c1.philam a2, b2 = c2.philam db, b2 = unrollPI(b1, b2, wrap=wrap) d = vincentys_(a2, a1, db) # radians if d < max(r1 - r2, EPS): raise ValueError(_near_concentric_) x = fsum_(r1, r2, -d) # overlap if x > EPS: sd, cd, sr1, cr1, _, cr2 = sincos2(d, r1, r2) x = sd * sr1 if abs(x) < EPS: raise ValueError(_invalid_) x = acos1((cr2 - cd * cr1) / x) # 0 <= x <= PI elif x < 0: t = (d * radius) if too_d is None else too_d raise ValueError(_too_distant_fmt_ % (t,)) if height is None: # "radical height" f = _radical2(d, r1, r2).ratio h = Height(favg(c1.height, c2.height, f=f)) else: h = Height(height) b = bearing_(a1, b1, a2, b2, final=False, wrap=wrap) if x < _EPS_I2: # externally ... r = _dest3(b, h) elif x > _PI_EPS_I2: # internally ... r = _dest3(b + PI, h) else: return _dest3(b + x, h), _dest3(b - x, h) return r, r # ... abutting circles
def distance(self, p1, p2): '''Return the L{vincentys_} distance in C{radians}. ''' r, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) return vincentys_(p2.phi, p1.phi, r)
def _distances(self, x, y): # (x, y) radians for xk, yk in zip(self._xs, self._ys): d, _ = unrollPI(xk, x, wrap=self._wrap) yield vincentys_(yk, y, d)
def distance(self, p1, p2): '''Return the L{vincentys_} distance in C{radians}. ''' d, _ = unrollPI(p1.b, p2.b, wrap=self._wrap) return vincentys_(p2.a, p1.a, d)
def intersections2( center1, rad1, center2, rad2, radius=R_M, # MCCABE 13 height=None, wrap=False, LatLon=LatLon, **LatLon_kwds): '''Compute the intersection points of two circles each defined by a center point and radius. @arg center1: Center of the first circle (L{LatLon}). @arg rad1: Radius of the second circle (C{meter} or C{radians}, see B{C{radius}}). @arg center2: Center of the second circle (L{LatLon}). @arg rad2: Radius of the second circle (C{meter} or C{radians}, see B{C{radius}}). @kwarg radius: Mean earth radius (C{meter} or C{None} if both B{C{rad1}} and B{C{rad2}} are given in C{radians}). @kwarg height: Optional height for the intersection point, overriding the mean height (C{meter}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg LatLon: Optional class to return the intersection points (L{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if B{C{LatLon=None}}. @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance or L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None}. The intersection points are the same instance for abutting circles. @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting circles. @raise TypeError: If B{C{center1}} or B{C{center2}} not L{LatLon}. @raise ValueError: Invalid B{C{rad1}}, B{C{rad2}}, B{C{radius}} or B{C{height}}. @note: Courtesy U{Samuel Čavoj<https://GitHub.com/mrJean1/PyGeodesy/issues/41>}. @see: This U{Answer<https://StackOverflow.com/questions/53324667/ find-intersection-coordinates-of-two-circles-on-earth/53331953>}. ''' def _destination1(bearing): a, b = _destination2(a1, b1, r1, bearing) return _latlon3(degrees90(a), degrees180(b), h, intersections2, LatLon, **LatLon_kwds) _Trll.others(center1, name='center1') _Trll.others(center2, name='center2') a1, b1 = center1.philam a2, b2 = center2.philam r1, r2, x = _rads3(rad1, rad2, radius) if x: a1, b1, a2, b2 = a2, b2, a1, b1 db, _ = unrollPI(b1, b2, wrap=wrap) d = vincentys_(a2, a1, db) # radians if d < max(r1 - r2, EPS): raise IntersectionError(center1=center1, rad1=rad1, center2=center2, rad2=rad2, txt=_near_concentric_) x = fsum_(r1, r2, -d) if x > EPS: try: sd, cd, s1, c1, _, c2 = sincos2(d, r1, r2) x = sd * s1 if abs(x) < EPS: raise ValueError x = acos1((c2 - cd * c1) / x) except ValueError: raise IntersectionError(center1=center1, rad1=rad1, center2=center2, rad2=rad2) elif x < 0: raise IntersectionError(center1=center1, rad1=rad1, center2=center2, rad2=rad2, txt=_too_distant_) b = bearing_(a1, b1, a2, b2, final=False, wrap=wrap) if height is None: h = fmean((center1.height, center2.height)) else: Height(height) if abs(x) > EPS: return _destination1(b + x), _destination1(b - x) else: # abutting circles x = _destination1(b) return x, x
def intersection(start1, end1, start2, end2, height=None, wrap=False, LatLon=LatLon, **LatLon_kwds): '''Compute the intersection point of two paths both defined by two points or a start point and bearing from North. @arg start1: Start point of the first path (L{LatLon}). @arg end1: End point ofthe first path (L{LatLon}) or the initial bearing at the first start point (compass C{degrees360}). @arg start2: Start point of the second path (L{LatLon}). @arg end2: End point of the second path (L{LatLon}) or the initial bearing at the second start point (compass C{degrees360}). @kwarg height: Optional height for the intersection point, overriding the mean height (C{meter}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg LatLon: Optional class to return the intersection point (L{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if B{C{LatLon=None}}. @return: The intersection point (B{C{LatLon}}) or a L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None}. An alternate intersection point might be the L{antipode} to the returned result. @raise IntersectionError: Intersection is ambiguous or infinite or the paths are coincident, colinear or parallel. @raise TypeError: A B{C{start}} or B{C{end}} point not L{LatLon}. @raise ValueError: Invalid B{C{height}}. @example: >>> p = LatLon(51.8853, 0.2545) >>> s = LatLon(49.0034, 2.5735) >>> i = intersection(p, 108.547, s, 32.435) # '50.9078°N, 004.5084°E' ''' _Trll.others(start1, name=_start1_) _Trll.others(start2, name=_start2_) hs = [start1.height, start2.height] a1, b1 = start1.philam a2, b2 = start2.philam db, b2 = unrollPI(b1, b2, wrap=wrap) r12 = vincentys_(a2, a1, db) if abs(r12) < EPS: # [nearly] coincident points a, b = favg(a1, a2), favg(b1, b2) # see <https://www.EdWilliams.org/avform.htm#Intersection> elif isscalar(end1) and isscalar(end2): # both bearings sa1, ca1, sa2, ca2, sr12, cr12 = sincos2(a1, a2, r12) x1, x2 = (sr12 * ca1), (sr12 * ca2) if abs(x1) < EPS or abs(x2) < EPS: raise IntersectionError(start1=start1, end1=end1, start2=start2, end2=end2, txt='parallel') # handle domain error for equivalent longitudes, # see also functions asin_safe and acos_safe at # <https://www.EdWilliams.org/avform.htm#Math> t1, t2 = map1(acos1, (sa2 - sa1 * cr12) / x1, (sa1 - sa2 * cr12) / x2) if sin(db) > 0: t12, t21 = t1, PI2 - t2 else: t12, t21 = PI2 - t1, t2 t13, t23 = map1(radiansPI2, end1, end2) x1, x2 = map1( wrapPI, t13 - t12, # angle 2-1-3 t21 - t23) # angle 1-2-3 sx1, cx1, sx2, cx2 = sincos2(x1, x2) if sx1 == 0 and sx2 == 0: # max(abs(sx1), abs(sx2)) < EPS raise IntersectionError(start1=start1, end1=end1, start2=start2, end2=end2, txt='infinite') sx3 = sx1 * sx2 # if sx3 < 0: # raise IntersectionError(start1=start1, end1=end1, # start2=start2, end2=end2, txt=_ambiguous_) x3 = acos1(cr12 * sx3 - cx2 * cx1) r13 = atan2(sr12 * sx3, cx2 + cx1 * cos(x3)) a, b = _destination2(a1, b1, r13, t13) # choose antipode for opposing bearings if _xb(a1, b1, end1, a, b, wrap) < 0 or \ _xb(a2, b2, end2, a, b, wrap) < 0: a, b = antipode_(a, b) # PYCHOK PhiLam2Tuple else: # end point(s) or bearing(s) x1, d1 = _x3d2(start1, end1, wrap, _1_, hs) x2, d2 = _x3d2(start2, end2, wrap, _2_, hs) x = x1.cross(x2) if x.length < EPS: # [nearly] colinear or parallel paths raise IntersectionError(start1=start1, end1=end1, start2=start2, end2=end2, txt=_colinear_) a, b = x.philam # choose intersection similar to sphericalNvector d1 = _xdot(d1, a1, b1, a, b, wrap) if d1: d2 = _xdot(d2, a2, b2, a, b, wrap) if (d2 < 0 and d1 > 0) or (d2 > 0 and d1 < 0): a, b = antipode_(a, b) # PYCHOK PhiLam2Tuple h = fmean(hs) if height is None else Height(height) return _latlon3(degrees90(a), degrees180(b), h, intersection, LatLon, **LatLon_kwds)