NAME

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

VERSION

Version 0.01

SYNOPSIS

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

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

EXPORT

• "frac($x)"

• "frac360($x)"

• "dms($x)"

• "hms($x)"

• "zdms($x)"

• "ddd($deg[, $min[, $sec]])"

• "polynome($t, @terms)"

• "to_range($x, $range)"

• "reduce_deg($x)"

• "reduce_rad($x)"

• "opposite_deg($x)"

• "opposite_rad($x)"

• "angle_c($x, $y)"

• "angle_c_rad($x, $y)"

• "angle_c_rad($x, $y)"

• "angle_s($x1, $y1, $x2, $y2)"

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

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

• "cart($r, $theta, $phi)"

• "polar($x, $y, $z)"

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 sexadecimal 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 sexadecimal values to decimal.

Arguments

1 to 3 sexadecimal 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 sphera. 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 certesian (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

Spherical coordinates:

• $r, distance from the origin;

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

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

AUTHOR

Sergey Krushinsky, <krushi at cpan.org>

COPYRIGHT & LICENSE

Copyright 2009-2019 Sergey Krushinsky.

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

cpanm Astro::Montenbruck

perl -MCPAN -e shell
install Astro::Montenbruck