# Coverage for pygeodesy/resections.py : 99%

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''' from pygeodesy.basics import map1, _ALL_LAZY from pygeodesy.constants import EPS, EPS0, EPS02, INT0, PI, PI2, PI_2, PI_4, isnear0, \ _0_0, _0_5, _1_0, _N_1_0, _2_0, _N_2_0, _4_0, _360_0 from pygeodesy.errors import _and, _or, TriangleError, _ValueError, _xkwds from pygeodesy.fmath import favg, Fdot, fidw, fmean, hypot, hypot2_ from pygeodesy.fsums import Fsum, fsum_, fsum1, fsum1_ from pygeodesy.interns import _a_, _A_, _b_, _B_, _c_, _C_, _coincident_, _colinear_, \ _d_, _invalid_, _negative_, _not_, _rIn_, _SPACE_ # from pygeodesy.lazily import _ALL_LAZY # from .basics from pygeodesy.named import Fmt, _NamedTuple, _Pass # from pygeodesy.streprs import Fmt # from .named from pygeodesy.units import Degrees, Distance, Radians from pygeodesy.utily import acos1, asin1, sincos2, sincos2_, sincos2d, sincos2d_ from pygeodesy.vector3d import _otherV3d, Vector3d from math import cos, atan2, degrees, radians, sin, sqrt __all__ = _ALL_LAZY.resections __version__ = '22.09.24' _concyclic_ = 'concyclic' _PA_ = 'PA' _PB_ = 'PB' _PC_ = 'PC' _pointH_ = 'pointH' _pointP_ = 'pointP' _R3__ = 'R3 ' _radA_ = 'radA' _radB_ = 'radB' _radC_ = 'radC' class Collins5Tuple(_NamedTuple): '''5-Tuple C{(pointP, pointH, a, b, c)} with survey C{pointP}, auxiliary C{pointH}, each an instance of B{C{pointA}}'s (sub-)class and triangle sides C{a}, C{b} and C{c} in C{meter}, conventionally. ''' _Names_ = (_pointP_, _pointH_, _a_, _b_, _c_) _Units_ = (_Pass, _Pass, Distance, Distance, Distance) class ResectionError(_ValueError): '''Error raised for issues in L{pygeodesy.resections}. ''' pass class Survey3Tuple(_NamedTuple): '''3-Tuple C{(PA, PB, PC)} with distance from survey point C{P} to each of the triangle corners C{A}, C{B} and C{C} in C{meter}, conventionally. ''' _Names_ = (_PA_, _PB_, _PC_) _Units_ = ( Distance, Distance, Distance) class Tienstra7Tuple(_NamedTuple): '''7-Tuple C{(pointP, A, B, C, a, b, c)} with survey C{pointP}, interior triangle angles C{A}, C{B} and C{C} in C{degrees} and triangle sides C{a}, C{b} and C{c} in C{meter}, conventionally. ''' _Names_ = (_pointP_, _A_, _B_, _C_, _a_, _b_, _c_) _Units_ = (_Pass, Degrees, Degrees, Degrees, Distance, Distance, Distance) class TriAngle4Tuple(_NamedTuple): '''4-Tuple C{(radA, radB, radC, rIn)} with the interior angles at triangle corners C{A}, C{B} and C{C} in C{radians} and the C{InCircle} radius C{rIn} aka C{inradius} in C{meter}, conventionally. ''' _Names_ = (_radA_, _radB_, _radC_, _rIn_) _Units_ = ( Radians, Radians, Radians, Distance) class TriSide2Tuple(_NamedTuple): '''2-Tuple C{(a, radA)} with triangle side C{a} in C{meter}, conventionally and angle C{radA} at the opposite triangle corner in C{radians}. ''' _Names_ = (_a_, _radA_) _Units_ = ( Distance, Radians) class TriSide4Tuple(_NamedTuple): '''4-Tuple C{(a, b, radC, d)} with interior angle C{radC} at triangle corner C{C} in C{radians}with the length of triangle sides C{a} and C{b} and with triangle height C{d} perpendicular to triangle side C{c}, in the same units as triangle sides C{a} and C{b}. ''' _Names_ = (_a_, _b_, _radC_, _d_) _Units_ = ( Distance, Distance, Radians, Distance) def cassini(pointA, pointB, pointC, alpha, beta, useZ=False, Clas=None, **Clas_kwds): '''3-Point resection using U{Cassini<https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>}'s method. @arg pointA: First point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg alpha: Angle subtended by triangle side B{C{pointA}} to B{C{pointC}} (C{degrees}, non-negative). @arg beta: Angle subtended by triangle side B{C{pointB}} to B{C{pointC}} (C{degrees}, non-negative). @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0} (C{bool}). @kwarg Clas: Optional class to return the survey point or C{None} for B{C{pointA}}'s (sub-)class. @kwarg Clas_kwds: Optional additional keyword argument for the survey point instance. @note: Typically, B{C{pointC}} is between B{C{pointA}} and B{C{pointB}}. @return: The survey point, an instance of B{C{Clas}} or if C{B{Clas} is None} of B{C{pointA}}'s (sub-)class. @raise ResectionError: Near-coincident, -colinear or -concyclic points or negative or invalid B{C{alpha}} or B{C{beta}}. @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointM}}. @see: U{Three Point Resection Problem<https://Dokumen.tips/documents/ three-point-resection-problem-introduction-kaestner-burkhardt-method.html>} and functions L{pygeodesy.collins5}, L{pygeodesy.pierlot} and L{pygeodesy.tienstra7}. ''' def _H(A, C, sa): s, c = sincos2d(sa) if isnear0(s): raise ValueError(_or(_coincident_, _colinear_)) t = s, c, c x = Fdot(t, A.x, C.y, -A.y).fover(s) y = Fdot(t, A.y, -C.x, A.x).fover(s) return Vector3d(x, y, 0) A = _otherV3d(useZ=useZ, pointA=pointA) B = _otherV3d(useZ=useZ, pointB=pointB) C = _otherV3d(useZ=useZ, pointC=pointC) try: sa, sb = map1(float, alpha, beta) if min(sa, sb) < 0: raise ValueError(_negative_) if fsum_(_360_0, -sa, -sb) < EPS0: raise ValueError() H1 = _H(A, C, sa) H2 = _H(B, C, -sb) x = H1.x - H2.x y = H1.y - H2.y # x, y, _ = H1.minus(H2).xyz if isnear0(x) or isnear0(y): raise ValueError(_SPACE_(_concyclic_, (x, y))) m = y / x n = x / y N = n + m if isnear0(N): raise ValueError(_SPACE_(_concyclic_, (m, n, N))) t = n, m, _1_0, _N_1_0 x = Fdot(t, C.x, H1.x, C.y, H1.y).fover(N) y = Fdot(t, H1.y, C.y, C.x, H1.x).fover(N) z = _zidw(A, B, C, x, y) if useZ else INT0 clas = Clas or pointA.classof return clas(x, y, z, **_xkwds(Clas_kwds, name=cassini.__name__)) except (TypeError, ValueError) as x: raise ResectionError(pointA=pointA, pointB=pointB, pointC=pointC, alpha=alpha, beta=beta, cause=x) def collins5(pointA, pointB, pointC, alpha, beta, useZ=False, Clas=None, **Clas_kwds): '''3-Point resection using U{Collins<https://Dokumen.tips/documents/ three-point-resection-problem-introduction-kaestner-burkhardt-method.html>}' method. @arg pointA: First point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to B{C{pointC}} (C{degrees}, non-negative). @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees}, non-negative). @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0} (C{bool}). @kwarg Clas: Optional class to return the survey and auxiliary point or C{None} for B{C{pointA}}'s (sub-)class. @kwarg Clas_kwds: Optional additional keyword argument for the survey and auxiliary point instance. @note: Typically, B{C{pointC}} is between B{C{pointA}} and B{C{pointB}}. @return: L{Collins5Tuple}C{(pointP, pointH, a, b, c)} with survey C{pointP}, auxiliary C{pointH}, each an instance of B{C{Clas}} or if C{B{Clas} is None} of B{C{pointA}}'s (sub-)class and triangle sides C{a}, C{b} and C{c} in C{meter}, conventionally. @raise ResectionError: Near-coincident, -colinear or -concyclic points or negative or invalid B{C{alpha}} or B{C{beta}}. @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointM}}. @see: U{Collins' methode<https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>} and functions L{pygeodesy.cassini}, L{pygeodesy.pierlot} and L{pygeodesy.tienstra7}. ''' def _azi_len2(A, B, pi2): v = B.minus(A) r = atan2(v.x, v.y) if pi2 and r < 0: r += pi2 return r, v.length def _cV3(d, r, A, B, C, useZ, V3, **kwds): s, c = sincos2(r) x = A.x + d * s y = A.y + d * c z = _zidw(A, B, C, x, y) if useZ else INT0 return V3(x, y, z, **kwds) A = _otherV3d(useZ=useZ, pointA=pointA) B = _otherV3d(useZ=useZ, pointB=pointB) C = _otherV3d(useZ=useZ, pointC=pointC) try: ra, rb = radians(alpha), radians(beta) if min(ra, rb) < 0: raise ValueError(_negative_) sra, srH = sin(ra), sin(ra + rb - PI) # rH = PI - ((PI - ra) + (PI - rb)) if isnear0(sra) or isnear0(srH): raise ValueError(_or(_coincident_, _colinear_, _concyclic_)) clas = Clas or pointA.classof kwds = _xkwds(Clas_kwds, name=collins5.__name__) # za, a = _azi_len2(C, B, PI2) zb, b = _azi_len2(C, A, PI2) zc, c = _azi_len2(A, B, 0) # d = c * sin(PI - rb) / srH # B.minus(H).length d = c * sin(PI - ra) / srH # A.minus(H).length r = zc + PI - rb # zh = zc + (PI - rb) H = _cV3(d, r, A, B, C, useZ, Vector3d) zh, _ = _azi_len2(C, H, PI2) # d = a * sin(za - zh) / sin(rb) # B.minus(P).length d = b * sin(zb - zh) / sra # A.minus(P).length r = zh - ra # zb - PI + (PI - ra - (zb - zh)) P = _cV3(d, r, A, B, C, useZ, clas, **kwds) H = clas(H.x, H.y, H.z, **kwds) a = B.minus(C).length return Collins5Tuple(P, H, a, b, c, name=collins5.__name__) except (TypeError, ValueError) as x: raise ResectionError(pointA=pointA, pointB=pointB, pointC=pointC, alpha=alpha, beta=beta, cause=x) def pierlot(point1, point2, point3, alpha12, alpha23, useZ=False, Clas=None, **Clas_kwds): '''3-Point resection using U{Pierlot<http://www.Telecom.ULg.ac.Be/publi/publications/ pierlot/Pierlot2014ANewThree>}'s method C{ToTal}. @arg point1: First point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg alpha12: Angle subtended from B{C{point1}} to B{C{point2}} (C{degrees}). @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} (C{degrees}). @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0} (C{bool}). @kwarg Clas: Optional class to return the survey point or C{None} for B{C{point1}}'s (sub-)class. @kwarg Clas_kwds: Optional additional keyword arguments for the survey point instance. @note: Points B{C{point1}}, B{C{point2}} and B{C{point3}} are ordered counter-clockwise, typically. @return: The survey (or robot) point, an instance of B{C{Clas}} or if C{B{Clas} is None} of B{C{point1}}'s (sub-)class. @raise ResectionError: Near-coincident, -colinear or -concyclic points or invalid B{C{alpha12}} or B{C{alpha23}}. @raise TypeError: Invalid B{C{point1}}, B{C{point2}} or B{C{point3}}. @see: U{V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation Algorithm for Mobile Robot Positioning"<https://ORBi.ULiege.Be/ bitstream/2268/157469/1/Pierlot2014ANewThree.pdf>}, U{Vincent Pierlot, Marc Van Droogenbroeck, "18 Triangulation Algorithms for 2D Positioning (also known as the Resection Problem)"<http://www.Telecom.ULg.ac.Be/ triangulation>} and functions L{pygeodesy.cassini}, L{pygeodesy.collins5} and L{pygeodesy.tienstra7}. ''' B1 = _otherV3d(useZ=useZ, point1=point1) B2 = _otherV3d(useZ=useZ, point2=point2) B3 = _otherV3d(useZ=useZ, point3=point3) try: # (INTERNAL) Raises error for (pseudo-)singularities s12, c12, s23, c23 = sincos2d_(alpha12, alpha23) if isnear0(s12) or isnear0(s23): raise ValueError(_or(_coincident_, _colinear_)) cot12 = c12 / s12 cot23 = c23 / s23 # cot31 = (1 - cot12 * cot23) / (cot12 + cot32) d = fsum1_(c12 * s23, s12 * c23) if isnear0(d): raise ValueError(_or(_colinear_, _coincident_)) cot31 = Fsum(_1_0, s12 * s23, -c12 * c23, _N_1_0).fover(d) x1_, y1_, _ = B1.minus(B2).xyz x3_, y3_, _ = B3.minus(B2).xyz # x23 = x3_ - cot23 * y3_ # y23 = y3_ + cot23 * x3_ X12_23 = Fsum(x1_, cot12 * y1_, -x3_, cot23 * y3_) Y12_23 = Fsum(y1_, -cot12 * x1_, -y3_, -cot23 * x3_) X31_23 = Fsum(x1_, -cot31 * y1_, cot31 * y3_, cot23 * y3_) Y31_23 = Fsum(y1_, cot31 * x1_, -cot31 * x3_, -cot23 * x3_) d = float(X31_23 * Y12_23 - X12_23 * Y31_23) if isnear0(d): raise ValueError(_or(_coincident_, _colinear_, _concyclic_)) K = Fsum(x3_ * x1_, cot31 * (y3_ * x1_), y3_ * y1_, -cot31 * (x3_ * y1_)) x = (B2.x * d + K * Y12_23).fover(d) y = (B2.y * d - K * X12_23).fover(d) z = _zidw(B1, B2, B3, x, y) if useZ else INT0 clas = Clas or point1.classof return clas(x, y, z, **_xkwds(Clas_kwds, name=pierlot.__name__)) except (TypeError, ValueError) as x: raise ResectionError(point1=point1, point2=point2, point3=point3, alpha12=alpha12, alpha23=alpha23, cause=x) def snellius3(a, b, degC, alpha, beta): '''Snellius' surveying using U{Snellius Pothenot<https://WikiPedia.org/wiki/Snellius–Pothenot_problem>}. @arg a: Length of the triangle side between corners C{B} and C{C} and opposite of triangle corner C{A} (C{scalar}, non-negative C{meter}, conventionally). @arg b: Length of the triangle side between corners C{C} and C{A} and opposite of triangle corner C{B} (C{scalar}, non-negative C{meter}, conventionally). @arg degC: Angle at triangle corner C{C}, opposite triangle side C{c} (non-negative C{degrees}). @arg alpha: Angle subtended by triangle side B{C{b}} (non-negative C{degrees}). @arg beta: Angle subtended by triangle side B{C{a}} (non-negative C{degrees}). @return: L{Survey3Tuple}C{(PA, PB, PC)} with distance from survey point C{P} to each of the triangle corners C{A}, C{B} and C{C}, same units as triangle sides B{C{a}}, B{C{b}} and B{C{c}}. @raise TriangleError: Invalid B{C{a}}, B{C{b}} or B{C{degC}} or negative B{C{alpha}} or B{C{beta}}. @see: Function L{pygeodesy.wildberger3}. ''' try: a, b, degC, alpha, beta = map1(float, a, b, degC, alpha, beta) ra, rb, rC = map1(radians, alpha, beta, degC) if min(ra, rb, rC, a, b) < 0: raise ValueError(_negative_) r = fsum_(ra, rb, rC) * _0_5 k = PI - r if min(k, r) < 0: raise ValueError(_or(_coincident_, _colinear_)) sa, sb = sin(ra), sin(rb) p = atan2(a * sa, b * sb) sp, cp, sr, cr = sincos2_(PI_4 - p, r) w = atan2(sp * sr, cp * cr) x = k + w y = k - w s = abs(sa) if abs(sb) > s: pc = abs(a * sin(y) / sb) elif s: pc = abs(b * sin(x) / sa) else: raise ValueError(_or(_colinear_, _coincident_)) pa = _triSide(b, pc, fsum_(PI, -ra, -x)) pb = _triSide(a, pc, fsum_(PI, -rb, -y)) return Survey3Tuple(pa, pb, pc, name=snellius3.__name__) except (TypeError, ValueError) as x: raise TriangleError(a=a, b=b, degC=degC, alpha=alpha, beta=beta, cause=x) def tienstra7(pointA, pointB, pointC, alpha, beta=None, gamma=None, useZ=False, Clas=None, **Clas_kwds): '''3-Point resection using U{Tienstra<https://WikiPedia.org/wiki/Tienstra_formula>}'s formula. @arg pointA: First point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees}, non-negative). @kwarg beta: Angle subtended by triangle side C{b} from B{C{pointA}} to B{C{pointC}} (C{degrees}, non-negative) or C{None} if C{B{gamma} is not None}. @kwarg gamma: Angle subtended by triangle side C{c} from B{C{pointA}} to B{C{pointB}} (C{degrees}, non-negative) or C{None} if C{B{beta} is not None}. @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0} (C{bool}). @kwarg Clas: Optional class to return the survey point or C{None} for B{C{pointA}}'s (sub-)class. @kwarg Clas_kwds: Optional additional keyword arguments for the survey point instance. @note: Points B{C{pointA}}, B{C{pointB}} and B{C{pointC}} are ordered clockwise. @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP}, an instance of B{C{Clas}} or if C{B{Clas} is None} of B{C{pointA}}'s (sub-)class, with triangle angles C{A} at B{C{pointA}}, C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and with triangle sides C{a}, C{b} and C{c} in C{meter}, conventionally. @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}. @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointC}}. @see: U{3-Point Resection Solver<http://MesaMike.org/geocache/GC1B0Q9/tienstra/>}, U{V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation..." <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree/>}, U{18 Triangulation Algorithms...<http://www.Telecom.ULg.ac.Be/triangulation/>} and functions L{pygeodesy.cassini}, L{pygeodesy.collins5} and L{pygeodesy.pierlot}. ''' def _deg_ks(r, s, ks, N): if isnear0(fsum_(PI, r, -s)): # r + (PI2 - s) == PI raise ValueError(Fmt.PARENSPACED(concyclic=N)) # k = 1 / (cot(r) - cot(s)) # = 1 / (cos(r) / sin(r) - cos(s) / sin(s)) # = 1 / (cos(r) * sin(s) - cos(s) * sin(r)) / (sin(r) * sin(s)) # = sin(r) * sin(s) / (cos(r) * sin(s) - cos(s) * sin(r)) sr, cr, ss, cs = sincos2_(r, s) c = cr * ss - cs * sr if isnear0(c): raise ValueError(Fmt.PARENSPACED(cotan=N)) ks.append(sr * ss / c) return Degrees(degrees(r), name=N) # C degrees A = _otherV3d(useZ=useZ, pointA=pointA) B = _otherV3d(useZ=useZ, pointB=pointB) C = _otherV3d(useZ=useZ, pointC=pointC) try: sa, sb, sc = map1(radians, alpha, (beta or 0), (gamma or 0)) if beta is None: if gamma is None: raise ValueError(_and(Fmt.EQUAL(beta=beta), Fmt.EQUAL(gamma=gamma))) sb = fsum_(PI2, -sa, -sc) elif gamma is None: sc = fsum_(PI2, -sa, -sb) else: # subtended angles must add to 360 degrees r = fsum1_(sa, sb, sc) if abs(r - PI2) > EPS: raise ValueError(Fmt.EQUAL(sum=degrees(r))) if min(sa, sb, sc) < 0: raise ValueError(_negative_) # triangle sides a = B.minus(C).length b = A.minus(C).length c = A.minus(B).length ks = [] # 3 Ks and triangle angles dA = _deg_ks(_triAngle(b, c, a), sa, ks, _A_) dB = _deg_ks(_triAngle(a, c, b), sb, ks, _B_) dC = _deg_ks(_triAngle(a, b, c), sc, ks, _C_) k = fsum1(ks, floats=True) if isnear0(k): raise ValueError(Fmt.EQUAL(K=k)) x = Fdot(ks, A.x, B.x, C.x).fover(k) y = Fdot(ks, A.y, B.y, C.y).fover(k) z = _zidw(A, B, C, x, y) if useZ else INT0 n = tienstra7.__name__ clas = Clas or pointA.classof P = clas(x, y, z, **_xkwds(Clas_kwds, name=n)) return Tienstra7Tuple(P, dA, dB, dC, a, b, c, name=n) except (TypeError, ValueError) as x: raise ResectionError(pointA=pointA, pointB=pointB, pointC=pointC, alpha=alpha, beta=beta, gamma=gamma, cause=x) def triAngle(a, b, c): '''Compute one angle of a triangle. @arg a: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg b: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg c: Opposite triangle side length (C{scalar}, non-negative C{meter}, conventionally). @return: Angle in C{radians} at triangle corner C{C}, opposite triangle side B{C{c}}. @raise TriangleError: Invalid or negative B{C{a}}, B{C{b}} or B{C{c}}. @see: Functions L{pygeodesy.triAngle4} and L{pygeodesy.triSide}. ''' try: return _triAngle(a, b, c) except (TypeError, ValueError) as x: raise TriangleError(a=a, b=b, c=c, tx=str(x), cause=x) def _triAngle(a, b, c): # (INTERNAL) To allow callers to embellish errors a, b, c = map1(float, a, b, c) if a < b: a, b = b, a if b < 0 or c < 0: raise ValueError(_negative_) if a < EPS0: raise ValueError(_coincident_) b_a = b / a if b_a < EPS0: raise ValueError(_coincident_) return acos1(fsum_(_1_0, b_a**2, -(c / a)**2) / (b_a * _2_0)) def triAngle4(a, b, c): '''Compute the angles of a triangle. @arg a: Length of the triangle side opposite of triangle corner C{A} (C{scalar}, non-negative C{meter}, conventionally). @arg b: Length of the triangle side opposite of triangle corner C{B} (C{scalar}, non-negative C{meter}, conventionally). @arg c: Length of the triangle side opposite of triangle corner C{C} (C{scalar}, non-negative C{meter}, conventionally). @return: L{TriAngle4Tuple}C{(radA, radB, radC, rIn)} with angles C{radA}, C{radB} and C{radC} at triangle corners C{A}, C{B} and C{C}, all in C{radians} and the C{InCircle} radius C{rIn} aka C{inradius}, same units as triangle sides B{C{a}}, B{C{b}} and B{C{c}}. @raise TriangleError: Invalid or negative B{C{a}}, B{C{b}} or B{C{c}}. @see: Function L{pygeodesy.triAngle}. ''' try: a, b, c = map1(float, a, b, c) ab = a < b if ab: a, b = b, a bc = b < c if bc: b, c = c, b if c > EPS0: # c = min(a, b, c) s = float(Fsum(a, b, c) * _0_5) if s < EPS0: raise ValueError(_negative_) sa, sb, sc = (s - a), (s - b), (s - c) r = sa * sb * sc / s if r < EPS02: raise ValueError(_coincident_) r = sqrt(r) rA = atan2(r, sa) * _2_0 rB = atan2(r, sb) * _2_0 rC = fsum_(PI, -rA, -rB) if min(rA, rB, rC) < 0: raise ValueError(_colinear_) elif c < 0: raise ValueError(_negative_) else: # 0 <= c <= EPS0 rA = rB = PI_2 rC = r = _0_0 if bc: rB, rC = rC, rB if ab: rA, rB = rB, rA return TriAngle4Tuple(rA, rB, rC, r, name=triAngle4.__name__) except (TypeError, ValueError) as x: raise TriangleError(a=a, b=b, c=c, cause=x) def triSide(a, b, radC): '''Compute one side of a triangle. @arg a: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg b: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg radC: Angle included by sides B{C{a}} and B{C{b}}, opposite triangle side C{c} (C{radians}). @return: Length of triangle side C{c}, opposite triangle corner C{C} and angle B{C{radC}}, same units as B{C{a}} and B{C{b}}. @raise TriangleError: Invalid B{C{a}}, B{C{b}} or B{C{radC}}. @see: Functions L{pygeodesy.sqrt_a}, L{pygeodesy.triAngle}, L{pygeodesy.triSide2} and L{pygeodesy.triSide4}. ''' try: return _triSide(a, b, radC) except (TypeError, ValueError) as x: raise TriangleError(a=a, b=b, radC=radC, cause=x) def _triSide(a, b, radC): # (INTERNAL) To allow callers to embellish errors a, b, r = map1(float, a, b, radC) if min(a, b, r) < 0: raise ValueError(_negative_) if a < b: a, b = b, a if a > EPS0: ba = b / a c2 = fsum_(_1_0, ba**2, _N_2_0 * ba * cos(r)) if c2 > EPS02: return a * sqrt(c2) elif c2 < 0: raise ValueError(_invalid_) return hypot(a, b) def triSide2(b, c, radB): '''Compute one side and the opposite angle of a triangle. @arg b: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg c: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg radB: Angle included by sides B{C{a}} and B{C{c}}, opposite triangle side C{b} (C{radians}). @return: L{TriSide2Tuple}C{(a, radA)} with triangle angle C{radA} in C{radians} and length of the opposite triangle side C{a}, same units as B{C{b}} and B{C{c}}. @raise TriangleError: Invalid B{C{b}} or B{C{c}} or either B{C{b}} or B{C{radB}} near zero. @see: Functions L{pygeodesy.sqrt_a}, L{pygeodesy.triSide} and L{pygeodesy.triSide4}. ''' try: return _triSide2(b, c, radB) except (TypeError, ValueError) as x: raise TriangleError(b=b, c=c, radB=radB, cause=x) def _triSide2(b, c, radB): # (INTERNAL) To allow callers to embellish errors b, c, rB = map1(float, b, c, radB) if min(b, c, rB) < 0: raise ValueError(_negative_) sB, cB = sincos2(rB) if isnear0(sB): if not isnear0(b): raise ValueError(_invalid_) if cB < 0: a, rA = (b + c), PI else: a, rA = abs(b - c), _0_0 elif isnear0(b): raise ValueError(_invalid_) else: rA = fsum_(PI, -rB, -asin1(c * sB / b)) a = sin(rA) * b / sB return TriSide2Tuple(a, rA, name=triSide2.__name__) def triSide4(radA, radB, c): '''Compute two sides and the height of a triangle. @arg radA: Angle at triangle corner C{A}, opposite triangle side C{a} (non-negative C{radians}). @arg radB: Angle at triangle corner C{B}, opposite triangle side C{b} (non-negative C{radians}). @arg c: Length of triangle side between triangle corners C{A} and C{B}, (C{scalar}, non-negative C{meter}, conventionally). @return: L{TriSide4Tuple}C{(a, b, radC, d)} with triangle sides C{a} and C{b} and triangle height C{d} perpendicular to triangle side B{C{c}}, all in the same units as B{C{c}} and interior angle C{radC} in C{radians} at triangle corner C{C}, opposite triangle side B{C{c}}. @raise TriangleError: Invalid or negative B{C{radA}}, B{C{radB}} or B{C{c}}. @see: U{Triangulation, Surveying<https://WikiPedia.org/wiki/Triangulation_(surveying)>} and functions L{pygeodesy.sqrt_a}, L{pygeodesy.triSide} and L{pygeodesy.triSide2}. ''' try: rA, rB, c = map1(float, radA, radB, c) rC = fsum_(PI, -rA, -rB) if min(rC, rA, rB, c) < 0: raise ValueError(_negative_) sa, ca, sb, cb = sincos2_(rA, rB) sc = fsum1_(sa * cb, sb * ca) if sc < EPS0 or min(sa, sb) < 0: raise ValueError(_invalid_) sc = c / sc return TriSide4Tuple((sa * sc), (sb * sc), rC, (sa * sb * sc), name=triSide4.__name__) except (TypeError, ValueError) as x: raise TriangleError(radA=radA, radB=radB, c=c, cause=x) def wildberger3(a, b, c, alpha, beta, R3=min): '''Snellius' surveying using U{Rational Trigonometry<https://WikiPedia.org/wiki/Snellius–Pothenot_problem>}. @arg a: Length of the triangle side between corners C{B} and C{C} and opposite of triangle corner C{A} (C{scalar}, non-negative C{meter}, conventionally). @arg b: Length of the triangle side between corners C{C} and C{A} and opposite of triangle corner C{B} (C{scalar}, non-negative C{meter}, conventionally). @arg c: Length of the triangle side between corners C{A} and C{B} and opposite of triangle corner C{C} (C{scalar}, non-negative C{meter}, conventionally). @arg alpha: Angle subtended by triangle side B{C{b}} (C{degrees}, non-negative). @arg beta: Angle subtended by triangle side B{C{a}} (C{degrees}, non-negative). @kwarg R3: Callable to determine C{R3} from C{(R3 - C)**2 = D}, typically standard function C{min} or C{max}, invoked with 2 arguments. @return: L{Survey3Tuple}C{(PA, PB, PC)} with distance from survey point C{P} to each of the triangle corners C{A}, C{B} and C{C}, same units as B{C{a}}, B{C{b}} and B{C{c}}. @raise TriangleError: Invalid B{C{a}}, B{C{b}} or B{C{c}} or negative B{C{alpha}} or B{C{beta}} or B{C{R3}} not C{callable}. @see: U{Wildberger, Norman J.<https://math.sc.Chula.ac.TH/cjm/content/ survey-article-greek-geometry-rational-trigonometry-and-snellius-–-pothenot-surveying>}, U{Devine Proportions, page 252<http://www.ms.LT/derlius/WildbergerDivineProportions.pdf>} and function L{pygeodesy.snellius3}. ''' def _s(x): return sin(x)**2 def _vpa(r1, r3, q2, q3, s3): r = r1 * r3 * _4_0 n = (r - Fsum(r1, r3, -q2).fpow(2)).fover(s3) if n < 0 or isnear0(r): raise ValueError(_coincident_) return sqrt((n / r) * q3) if n else _0_0 try: a, b, c, da, db = map1(float, a, b, c, alpha, beta) if min(a, b, c, da, db) < 0: raise ValueError(_negative_) ra, rb = radians(da), radians(db) s1, s2, s3 = s = map1(_s, rb, ra, ra + rb) # rb, ra! if min(s) < EPS02: raise ValueError(_or(_coincident_, _colinear_)) q1, q2, q3 = q = a**2, b**2, c**2 if min(q) < EPS02: raise ValueError(_coincident_) r1 = s2 * q3 / s3 # s2! r2 = s1 * q3 / s3 # s1! Qs = Fsum(*q) # == hypot2_(a, b, c) Ss = Fsum(*s) # == fsum1(s, floats=True) s += Qs * _0_5, # tuple! C0 = Fdot(s, q1, q2, q3, -Ss) r3 = C0.fover(-s3) d0 = Qs.fpow(2).fsub_(hypot2_(*q) * _2_0).fmul(s1 * s2).fover(s3) if d0 > EPS02: # > c0 d0 = sqrt(d0) if not callable(R3): raise ValueError(_R3__ + _not_(callable.__name__)) r3 = R3(float(C0 + d0), float(C0 - d0)) # XXX min or max elif d0 < 0: raise ValueError(_negative_) pa = _vpa(r1, r3, q2, q3, s3) pb = _vpa(r2, r3, q1, q3, s3) pc = favg(_triSide2(b, pa, ra).a, _triSide2(a, pb, rb).a) return Survey3Tuple(pa, pb, pc, name=wildberger3.__name__) except (TypeError, ValueError) as x: raise TriangleError(a=a, b=b, c=c, alpha=alpha, beta=beta, R3=R3, cause=x) def _zidw(A, B, C, x, y): # interpolate z or coplanar with A, B and C? t = A.z, B.z, C.z m = Vector3d(x, y, fmean(t)).minus return fidw(t, (m(T).length for T in (A, B, C))) # **) MIT License # # Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.