1

2# -*- coding: utf-8 -*-

3

4 u'''(INTERNAL) Private L{geodesicx} base class, functions and constants.

5

6 Copyright (C) U{Charles Karney<mailto:Charles@Karney.com>} (2008-2023)

7 and licensed under the MIT/X11 License. For more information, see the

8 U{GeographicLib<https://GeographicLib.SourceForge.io>} documentation.

9'''

10

11# from pygeodesy.basics import isodd # from .karney

12 from pygeodesy.constants import _0_0, _2_0

13 from pygeodesy.errors import _not_, _or

14# from pygeodesy.interns import _not_ # from .errors

15 from pygeodesy.karney import _CapsBase, GeodesicError, isodd, _hypot, _sum2_

16

17 from math import ldexp as _ldexp

18

19__all__ = ()

20__version__ = '23.05.15'

21

22# valid C{nC4}s and C{C4order}s, see _xnC4 below

23_nC4s = {24: 2900, 27: 4032, 30: 5425}

24

25

26 class _GeodesicBase(_CapsBase): # in .geodsolve

27 '''(INTERNAL) Base class for C{[_]Geodesic*Exact}.

28 '''

29# def toRepr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature

30# '''Return this C{GeodesicExact*} items string.

31#

32# @kwarg prec: The C{float} precision, number of decimal digits (0..9).

33# Trailing zero decimals are stripped for B{C{prec}} values

34# of 1 and above, but kept for negative B{C{prec}} values.

35# @kwarg sep: Separator to join (C{str}).

36#

37# @return: C{GeodesicExact*} (C{str}).

38# '''

39# return Fmt.PAREN(self.named, self.toStr(prec=prec, sep=sep))

40 pass

41

42

43 def _cosSeries(c4s, sx, cx): # PYCHOK shared .geodesicx.gx and -.gxline

44 '''(INTERNAL) I{Karney}'s cosine series expansion using U{Clenshaw

45 summation<https://WikiPedia.org/wiki/Clenshaw_algorithm>}.

46 '''

47 ar = _2_0 * (cx - sx) * (cx + sx) # 2 * cos(2 * x)

48 y0 = t0 = y1 = t1 = _0_0

49 n = len(c4s) # c4s = list(c4s)

50 if isodd(n):

51 n -= 1

52 y0 = c4s[n] # c4s.pop()

53 _s2_ = _sum2_

54 for n in range(n - 1, 0, -2): # reversed

55 # y1 = ar * y0 - y1 + c4s.pop()

56 # y0 = ar * y1 - y0 + c4s.pop()

57 y1, t1 = _s2_(ar * y0, ar * t0, -y1, -t1, c4s[n])

58 y0, t0 = _s2_(ar * y1, ar * t1, -y0, -t0, c4s[n - 1])

59 s, _ = _s2_(cx * y0, cx * t0, -cx * y1, -cx * t1)

60 return s # cx * (y0 - y1)

61

62

63_f = float # in _f2 and .geodesicx._C4_24, _27 and _30

64

65

66 def _f2(hi, lo): # in .geodesicx._C4_24, _27 and _30

67 '''(INTERNAL) For C{_coeffs}.

68 '''

69 return _ldexp(_f(hi), 52) + _f(lo)

70

71

72 def _sincos12(sin1, cos1, sin2, cos2, sineg0=False): # PYCHOK shared

73 '''(INTERNAL) Compute the sine and cosine of angle

74 M{ang12 = atan2(sin2, cos2) - atan2(sin1, cos1)}.

75

76 Use C{-sin1} to get C{sin12} and C{cos12} of the sum

77 M{ang12 = atan2(sin2, cos2) + atan2(sin1, cos1)}.

78

79 @kwarg sineg0: If C{True}, make negative C{sin12} zero (C{bool}).

80

81 @return: 2-Tuple C{(sin12, cos12)}.

82 '''

83 s = sin2 * cos1 - sin1 * cos2

84 c = cos2 * cos1 + sin1 * sin2

85 if sineg0 and s < 0:

86 s = _0_0 # max(s, _0_0) or NEG0?

87 return s, c

88

89

90 def _sin1cos2(sin1, cos1, sin2, cos2): # PYCHOK shared

91 '''(INTERNAL) Compute the C{sin1 * cos2} sine and its cosine.

92

93 @return: 2-Tuple C{(sin1 * cos2, hypot(sin1 * sin2, cos1)}.

94 '''

95 s = sin1 * cos2

96 c = _hypot(sin1 * sin2, cos1)

97 return s, c # _norm2(s, c)

98

99

100 def _xnC4(**name_nC4):

101 '''(INTERNAL) Validate C{C4order}.

102 '''

103 n, nC4 = name_nC4.popitem()

104 if nC4 not in _nC4s or not isinstance(nC4, int):

105 raise GeodesicError(n, nC4, txt=_not_(_or(*map(str, _nC4s))))

106 return _nC4s[nC4]

107

108

109# **) MIT License

110#

111# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

112#

113# Permission is hereby granted, free of charge, to any person obtaining a

114# copy of this software and associated documentation files (the "Software"),

115# to deal in the Software without restriction, including without limitation

116# the rights to use, copy, modify, merge, publish, distribute, sublicense,

117# and/or sell copies of the Software, and to permit persons to whom the

118# Software is furnished to do so, subject to the following conditions:

119#

120# The above copyright notice and this permission notice shall be included

121# in all copies or substantial portions of the Software.

122#

123# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

124# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

125# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

126# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

127# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

128# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

129# OTHER DEALINGS IN THE SOFTWARE.