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# -*- coding: utf-8 -*- 

 

u'''#-Point resection functions L{ciassini}, L{collins}, L{pierot} and L{tienstra}. 

''' 

 

from pygeodesy.basics import isnear0, map1 

from pygeodesy.errors import _and, _or, _ValueError 

from pygeodesy.fmath import fdot, fidw, fmean, fsum_, fsum1, fsum1_ 

from pygeodesy.formy import triAngle 

from pygeodesy.interns import EPS, EPS0, PI, PI2, _a_, \ 

_A_, _B_, _C_, _coincident_, _colinear_, \ 

_invalid_, _negative_, _SPACE_, \ 

_1_0, _N_1_0, _360_0 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import Fmt, _NamedTuple, _Pass 

# from pygeodesy.streprs import Fmt # from .named 

from pygeodesy.units import Degrees, Distance 

from pygeodesy.utily import sincos2, sincos2_, sincos2d 

from pygeodesy.vector3d import _otherV3d, Vector3d # PYCHOK unused 

 

from math import atan2, degrees, radians, sin 

 

__all__ = _ALL_LAZY.resections 

__version__ = '21.10.23' 

 

_b_ = 'b' 

_c_ = 'c' 

_concyclic_ = 'concyclic' 

_pointH_ = 'pointH' 

_pointP_ = 'pointP' 

 

 

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 resection issues. 

''' 

pass 

 

 

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) 

 

 

def cassini(pointA, pointB, pointC, alpha, beta, useZ=False): 

'''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=0} (C{bool}). 

 

@note: B{C{PointC}} is between B{C{pointA}} and B{C{pointB}}, typically. 

 

@return: Survey point, an instance 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.collins} and L{pygeodesy.tienstra}. 

''' 

try: 

return _cassini(_otherV3d(useZ=useZ, pointA=pointA), 

_otherV3d(useZ=useZ, pointB=pointB), 

_otherV3d(useZ=useZ, pointC=pointC), 

alpha, beta, useZ=useZ, clas=pointA.classof) 

except (TypeError, ValueError) as x: 

raise ResectionError(pointA=pointA, pointB=pointB, pointC=pointC, 

alpha=alpha, beta=beta, txt=str(x)) 

 

 

def _cassini(A, B, C, alpha, beta, useZ=False, clas=Vector3d): 

# (INTERNAL) Cassini's 3-point resection, note pointC == -M in reference 

 

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) / s 

y = fdot(t, A.y, -C.x, A.x) / s 

return Vector3d(x, y, 0) 

 

sa, sb = map1(float, alpha, beta) 

if min(sa, sb) < 0: 

raise ValueError(_negative_) 

if fsum_(_360_0, -sa, -sb) < EPS0: 

raise ValueError(_invalid_) 

 

h1 = _H(A, C, sa) 

h2 = _H(B, C, -sb) 

 

x = h1.x - h2.x 

y = h1.y - h2.y 

if isnear0(x) or isnear0(y): 

raise ValueError(_SPACE_(_concyclic_, (x, y))) 

 

n = x / y 

m = y / x 

N = n + m 

if isnear0(N): 

raise ValueError(_SPACE_(_concyclic_, (N, n, m))) 

 

t = n, m, _1_0, _N_1_0 

x = fdot(t, C.x, h1.x, C.y, h1.y) / N 

y = fdot(t, h1.y, C.y, C.x, h1.x) / N 

z = _zidw(A, B, C, x, y) if useZ else 0 

return clas(x, y, z, name=cassini.__name__) 

 

 

def collins(pointA, pointB, pointC, alpha, beta, useZ=False): 

'''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 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=0} (C{bool}). 

 

@note: B{C{PointC}} is between B{C{pointA}} and B{C{pointB}}, typically. 

 

@return: L{Collins5Tuple}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}. 

 

@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} and L{pygeodesy.tienstra}. 

''' 

try: 

return _collins(_otherV3d(useZ=useZ, pointA=pointA), 

_otherV3d(useZ=useZ, pointB=pointB), 

_otherV3d(useZ=useZ, pointC=pointC), 

alpha, beta, useZ=useZ, clas=pointA.classof) 

except (TypeError, ValueError) as x: 

raise ResectionError(pointA=pointA, pointB=pointB, pointC=pointC, 

alpha=alpha, beta=beta, txt=str(x)) 

 

 

def _collins(A, B, C, alpha, beta, useZ=False, clas=Vector3d): 

# (INTERNAL) Collins' 3-point resection, note C{pointC} center 

 

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, **name): 

s, c = sincos2(r) 

x = A.x + d * s 

y = A.y + d * c 

z = _zidw(A, B, C, x, y) if useZ else 0 

return V3(x, y, z, **name) 

 

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_)) 

 

# 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, name=collins.__name__) 

 

H = clas(H.x, H.y, H.z, name=collins.__name__) 

a = B.minus(C).length 

return Collins5Tuple(P, H, a, b, c) 

 

 

def tienstra(pointA, pointB, pointC, alpha, beta=None, gamma=None, useZ=False): 

'''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 B{C{pointB}} to B{C{pointC}} 

(C{degrees}, non-negative). 

@kwarg beta: Angle subtended by triangle side 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 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=0} (C{bool}). 

 

@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{pointA}}'s (sub-)class and triangle angles C{A}, 

C{B} and C{C} in C{degrees} and triangle sides C{a}, C{b} and C{c}. 

 

@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://Telecom.ULG.ac.BE/publi/publications/pierlot/Pierlot2014ANewThree/>}, 

U{18 Triangulation Algorithms...<http://Telecom.ULG.ac.BE/triangulation/>} and 

functions L{pygeodesy.cassini} and L{pygeodesy.collins}. 

''' 

try: 

return _tienstra(_otherV3d(useZ=useZ, pointA=pointA), 

_otherV3d(useZ=useZ, pointB=pointB), 

_otherV3d(useZ=useZ, pointC=pointC), 

alpha, beta, gamma, useZ=useZ, clas=pointA.classof) 

except (TypeError, ValueError) as x: 

raise ResectionError(pointA=pointA, pointB=pointB, pointC=pointC, 

alpha=alpha, beta=beta, gamma=gamma, txt=str(x)) 

 

 

def _tienstra(A, B, C, alpha, beta, gamma, useZ=False, clas=Vector3d): 

# (INTERNAL) Tienstra's 3-point resection 

 

def _deg_ks(r, s, ks, N): 

if isnear0(fsum1_(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 

 

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 = fsum1_(PI2, -sa, -sc) 

elif gamma is None: 

sc = fsum1_(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 

aA = _deg_ks(triAngle(b, c, a), sa, ks, _A_) 

aB = _deg_ks(triAngle(a, c, b), sb, ks, _B_) 

aC = _deg_ks(triAngle(a, b, c), sc, ks, _C_) 

 

k = fsum1(ks) 

if isnear0(k): 

raise ValueError(Fmt.EQUAL(K=k)) 

x = fdot(ks, A.x, B.x, C.x) / k 

y = fdot(ks, A.y, B.y, C.y) / k 

z = _zidw(A, B, C, x, y) if useZ else 0 

P = clas(x, y, z, name=tienstra.__name__) 

return Tienstra7Tuple(P, aA, aB, aC, a, b, c) 

 

 

def _zidw(A, B, C, x, y): 

# interpolate z or coplanar with A, B and C? 

t = A.z, B.z, C.z 

v = Vector3d(x, y, fmean(t)) 

return fidw(t, (v.minus(A).length, v.minus(B).length, v.minus(C).length)) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2021 -- 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.