++ed by:
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Author image Sergey Krushinsky
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NAME

Astro::Montenbruck::Core::MathUtils - Core mathematical routines used by Astro::Montenbruck modules.

VERSION

Version 0.01

SYNOPSIS

  use Astro::Montenbruck::Core::MathUtils qw/dms/;

  my ($d, $m, $s) = dms(55.75); # (55, 45, 0)
  ...

EXPORT

SUBROUTINES

frac($x)

Fractional part of a decimal number.

frac360($x)

Range function, similar to "to_range($x, $range)", used with polinomial function for better accuracy.

dms($x)

Given decimal hours (or degrees), return nearest hours (or degrees), int, minutes, int, and seconds, float.

Positional arguments:

  • decimal value, 0..360 for angular mode, 0..24 for time

Named arguments:

  • places (optional) amount of required sexagesimal values to be returned (1-3); default = 3 (degrees/hours, minutes, seconds)

Returns:

  • array of degrees (int), minutes (int), seconds (float)

hms($x)

Alias for "dms"

zdms($x)

Converts decimal degrees to zodiac sign number (zero based), zodiac degrees, minutes and seconds.

Positional arguments:

  • decimal value, 0..360 for angular mode, 0..24 for time

Returns:

  • array of zodiac sign (0-11), degrees (int), minutes (int), seconds (float)

ddd($deg[, $min[, $sec]])

Converts sexagesimal values to decimal.

Arguments

    1 to 3 sexagesimal values, such as: degrees, minutes and seconds, or degrees and minutes, or just degrees:

    • ddd(11)

    • ddd(11, 46)

    • ddd(11, 46, 20)

    If any non-zero argument is negative, the result is negative.

    • ddd(-11, 46, 0) = -11.766666666666667

    • ddd(11, -46, 0) = 11.766666666666667

    Negative sign in wrong position is ignored.

Returns:

  • decimal (degrees or hours)

polynome($t, @terms)

Calculates polynome: $a1 + $a2*$t + $a3*$t*$t + $a4*$t*$t*$t...

Arguments

  • $t coefficient, in astronomical routines usually time in centuries

  • any number of decimal values

Returns:

  • decimal number

to_range($x, $range)

Reduces $x to 0 >= $x < $range

Arguments

  • number to reduce

  • limit (non-inclusive), e.g: 360 for degrees, 24 for hours

Returns

  • number

reduce_deg($x)

Reduces $x to 0 >= $x < 360

reduce_rad($x)

Reduces $x to 0 >= $x < pi2

opposite_deg($x)

Returns opposite degree.

opposite_rad($x)

Returns opposite radian.

angle_c($x, $y)

Calculate shortest arc in dergees between $x and $y.

angle_c_rad($x, $y)

Calculates shortest arc in radians between $x and $y.

angle_s($x1, $y1, $x2, $y2)

Calculates arc between 2 points on a sphere. Expected arguments: 2 pairs of coordinates (X, Y) of the 2 points.

The coordinates may be ecliptic, equatorial or horizontal.

diff_angle($a, $b, $mode='degrees')

Return angle $b - $a, accounting for circular values.

Parameters $a and $b should be in the range 0..pi*2 or 0..360, depending on optional $mode argument. The result will be in the range -pi..pi or -180..180. This allows us to directly compare angles which cross through 0: 359 degress... 0 degrees... 1 degree... etc.

Positional Arguments

  • $a first angle, in radians or degrees

  • $b second angle, in radians or degrees

Named Arguments

  • $mode "degrees" (default) or "radians", case insensitive.

sine($x)

Calculate sin(phi); phi in units of 1 revolution = 360 degrees

cart($r, $theta, $phi)

Conversion of polar coordinates (r,theta,phi) into cartesian (x,y,z).

Arguments

  • $r, distance from the origin;

  • $theta (in radians) corresponding to [-90 deg, +90 deg];

  • $phi (in radians) corresponding to [-360 deg, +360 deg])

Returns

Rectangular coordinates:

  • $x, X

  • $y, Y

  • $z, Z

polar($x, $y, $z)

Conversion of cartesian coordinates (x,y,z) into polar (r,theta,phi).

Arguments

  • $x, X

  • $y, Y

  • $z, Z

Returns

  • $r, distance from the origin;

  • $theta (in radians) corresponding to [-90 deg, +90 deg];

  • $phi (in radians) corresponding to [-360 deg, +360 deg])

quad($y_minus, $y_0, $y_plus)

Quadratic interpolation

Finds a parabola through 3 points (-1 , y_minus), (0, Y_0), (1, y_plus), that do not lie on a straight line.

Arguments

Three y-values:

  • $y_minus value of function at x = -1

  • $y_0 value of function at x = 0

  • $y_plus value of function at x = 1

Returns

  • $xe, abscissa of extremum (may be outside [-1, 1])

  • $ye, Value of function at xe

  • $root1, first root found

  • $root2, second root found

  • $n_root, number of roots within the interval [-1, +1]

AUTHOR

Sergey Krushinsky, <krushi at cpan.org>

COPYRIGHT & LICENSE

Copyright 2009-2021 Sergey Krushinsky.

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.