Astro:...thUtils(3pm)

💖 NAME 💖

Astro::Montenbruck::Core::MathUtils — the core mathematical routines that all the Astro::Montenbruck modules lean on. The whole math brain trust, basically. This is page Astro:...thUtils(3pm), from the User Contributed Perl Documentation collection ✨

🌸 VERSION 🌸

Version 0.01 — baby version, but she works 💅

🦋 SYNOPSIS 🦋

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

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

Like, that's it. That's the whole vibe. You pull in dms, you throw it a decimal, you get back a tidy little (55, 45, 0) trio 🎀

✨ EXPORT ✨

Here's the full squad of functions this module hands out. Yes, some of them are listed more than once — that's just how the source says it, so we're keeping it exactly the same, no edits, periodt 💀

• 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)

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🔥 SUBROUTINES 🔥

🌈 frac($x)

Gives you the fractional part of a decimal number. The little decimal crumbs at the end of the number, she isolates them. Obsessed 🫶

🌈 frac360($x)

A range function, similar to to_range($x, $range) — it's the one used together with the polynomial function so you get better accuracy. Teamwork makes the dream work ✨

🌈 dms($x)

Okay so you give this one decimal hours (or degrees) and it hands back the nearest hours (or degrees) as an int, minutes as an int, and seconds as a float. Sexagesimal-era glow-up 💫

Positional arguments:

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

Named arguments:

• places (optional) — how many sexagesimal values you actually want returned (1-3); default = 3 (degrees/hours, minutes, seconds)

Returns:

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

🌈 hms($x)

Just an alias for dms. Same function, different name, main character energy either way 👑

🌈 zdms($x)

Takes decimal degrees and converts them into zodiac sign number (zero based), zodiac degrees, minutes and seconds. Astrology girlies stay winning 🍓

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]])

The glow-down — converts sexagesimal values back to decimal. Reverse card, uno 🎴

Arguments

1 to 3 sexagesimal values, like: degrees, minutes and seconds, or degrees and minutes, or literally just degrees:

• ddd(11)
• ddd(11, 46)
• ddd(11, 46, 20)

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

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

Negative sign in the wrong position is ignored. She just ignores it. No note, no error, just vibes 🙈

Returns:

• decimal (degrees or hours)

🌈 polynome($t, @terms)

Calculates the polynome: $a1 + $a2*$t + $a3*$t*$t + $a4*$t*$t*$t... — like, all the way down the line 💅

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. Keeping it in the box, respectfully 🎁

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. The 180° twin, if you will 🪞

🌈 opposite_rad($x)

Returns opposite radian. Same twin energy, but in radians 💜

🌈 angle_c($x, $y)

Calculate shortest arc in dergees — wait, degrees 😭 — between $x and $y. Shortest path only, she does not take the scenic route.

(The original really did spell it "dergees". We cherish her.)

🌈 angle_c_rad($x, $y)

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

🌈 angle_s($x1, $y1, $x2, $y2)

Calculates the 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 — she's not picky, she's flexible.

🌈 diff_angle($a, $b, $mode='degrees')

Returns the angle $b - $a, accounting for circular values. Circular math is so real.

Parameters $a and $b should be in the range 0..pi*2 or 0..360, depending on the optional $mode argument. The result will be in the range -pi..pi or -180..180. This is what lets us directly compare angles which cross through 0: 359 degress... 0 degrees... 1 degree... etc. The wrap-around is fully handled, no cap ✨

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. One full lap, one sine cycle 🌀

🌈 cart($r, $theta, $phi)

Conversion of polar coordinates (r,theta,phi) into cartesian (x,y,z). Glow-up from round to boxy 📦

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). The reverse transformation, we love a two-way street 💖

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. Curve fitting time, bestie 📈

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]

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🧚 AUTHOR 🧚

Sergey Krushinsky, <krushi at cpan.org> — the icon who wrote all of this 💜

👑 COPYRIGHT & LICENSE 👑

Copyright (C) 2009-2022 by Sergey Krushinsky

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself. Free software, free spirit, we stan 🫶

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And that's the whole page, bestie — sign-off time: this was doc'd up as perl v5.42.2, dated 2026-02-15, and it's the Astro:...thUtils(3pm) page. Go do some math, slay 💅✨