Length of an arc between two angles

Length of an arc between two angles is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

Write a method (function, procedure etc.) in your language which calculates the length of the major arc of a circle of given radius between two angles.

In this diagram the major arc is colored green.

Illustrate the use of your method by calculating the length of the major arc of a circle of radius 10 units, between angles of 10 and 120 degrees.

Factor

<lang factor>USING: kernel math math.constants math.trig prettyprint ;

arc-length ( radius angle angle -- x )

   - abs deg>rad 2pi swap - * ;

10 10 120 arc-length .</lang>

Output:

43.63323129985824

Go

Translation of: Julia

<lang go>package main

import (

   "fmt"
   "math"

)

func arcLength(radius, angle1, angle2 float64) float64 {

   return (360 - math.Abs(angle2-angle1)) * math.Pi * radius / 180

}

func main() {

   fmt.Println(arcLength(10, 10, 120))

}</lang>

Output:

43.63323129985823

Julia

The task seems to be to find the distance along the circumference of the circle which is NOT swept out between the two angles. <lang julia> arclength(r, angle1, angle2) = (360 - abs(angle2 - angle1)) * π/180 * r @show arclength(10, 10, 120) # --> arclength(10, 10, 120) = 43.63323129985823 </lang>

Perl

Translation of: Raku

<lang perl>use strict; use warnings; use utf8; binmode STDOUT, ":utf8"; use POSIX 'fmod';

use constant π => 2 * atan2(1, 0); use constant τ => 2 * π;

sub d2r { $_[0] * τ / 360 }

sub arc {

   my($a1, $a2, $r) = (d2r($_[0]), d2r($_[1]), $_[2]);
   my @a = map { fmod( ($_ + τ), τ) } ($a1, $a2);
   printf "Arc length: %8.5f  Parameters: (%9.7f, %10.7f, %10.7f)\n",
      (fmod(($a[0]-$a[1] + τ), τ) * $r), $a2, $a1, $r;

}

arc(@$_) for

   [ 10, 120,   10],
   [ 10, 120,    1],
   [120,  10,    1],
   [-90, 180, 10/π],
   [-90,   0, 10/π],
   [ 90,   0, 10/π];</lang>

Output:

Arc length: 43.63323  Parameters: (2.0943951, 0.1745329, 10.0000000)
Arc length: 43.63323  Parameters: (2.0943951,  0.1745329, 10.0000000)
Arc length:  4.36332  Parameters: (2.0943951,  0.1745329,  1.0000000)
Arc length:  1.91986  Parameters: (0.1745329,  2.0943951,  1.0000000)
Arc length: 15.00000  Parameters: (0.0000000, -1.5707963,  3.1830989)
Arc length:  5.00000  Parameters: (0.0000000,  1.5707963,  3.1830989)

Phix

Translation of: Julia

<lang Phix>function arclength(atom r, angle1, angle2)

   return (360 - abs(angle2 - angle1)) * PI/180 * r

end function ?arclength(10, 10, 120) -- 43.6332313</lang>

Raku

Works with: Rakudo version 2020.02

Taking a slightly different approach. Rather than the simplest thing that could possibly work, implements a reusable arc-length routine. Standard notation for angles has the zero to the right along an 'x' axis with a counter-clockwise rotation for increasing angles. This version follows convention and assumes the first given angle is "before" the second when rotating counter-clockwise. In order to return the major swept angle in the task example, you need to supply the "second" angle first. (The measurement will be from the first given angle counter-clockwise to the second.)

If you don't supply a radius, returns the radian arc angle which may then be multiplied by the radius to get actual circumferential length.

Works in radian angles by default but provides a postfix ° operator to convert degrees to radians and a postfix ᵍ to convert gradians to radians.

<lang perl6>sub arc ( Real \a1, Real \a2, :r(:$radius) = 1 ) {

   ( ([-] (a2, a1).map((* + τ) % τ)) + τ ) % τ × $radius

}

sub postfix:<°> (\d) { d × τ / 360 } sub postfix:<ᵍ> (\g) { g × τ / 400 }

say 'Task example: from 120° counter-clockwise to 10° with 10 unit radius'; say arc(:10radius, 120°, 10°), ' engineering units';

say "\nSome test examples:"; for \(120°, 10°), # radian magnitude (unit radius)

   \(10°, 120°), # radian magnitude (unit radius)
   \(:radius(10/π), 180°, -90°), # 20 unit circumference for ease of comparison
   \(0°, -90°, :r(10/π),),       #  ↓  ↓  ↓  ↓  ↓  ↓  ↓
   \(:radius(10/π), 0°, 90°),
   \(π/4, 7*π/4, :r(10/π)),
   \(175ᵍ, -45ᵍ, :r(10/π)) {  # test gradian parameters
   printf "Arc length: %8s  Parameters: %s\n", arc(|$_).round(.000001), $_.raku

}</lang>

Output:

Task example: from 120° counter-clockwise to 10° with 10 unit radius
43.63323129985824 engineering units

Some test examples:
Arc length: 4.363323  Parameters: \(2.0943951023931953e0, 0.17453292519943295e0)
Arc length: 1.919862  Parameters: \(0.17453292519943295e0, 2.0943951023931953e0)
Arc length:        5  Parameters: \(3.141592653589793e0, -1.5707963267948966e0, :radius(3.183098861837907e0))
Arc length:       15  Parameters: \(0e0, -1.5707963267948966e0, :r(3.183098861837907e0))
Arc length:        5  Parameters: \(0e0, 1.5707963267948966e0, :radius(3.183098861837907e0))
Arc length:       15  Parameters: \(0.7853981633974483e0, 5.497787143782138e0, :r(3.183098861837907e0))
Arc length:        9  Parameters: \(2.7488935718910685e0, -0.7068583470577035e0, :r(3.183098861837907e0))

REXX

Translation of: Julia

This REXX version handles angles (in degrees) that may be   >   360º. <lang rexx>/*REXX program calculates the length of an arc between two angles (stated in degrees).*/ parse arg radius angle1 angle2 . /*obtain optional arguments from the CL*/ if radius== | radius=="," then radius= 10 /*Not specified? Then use the default.*/ if angle1== | angle1=="," then angle1= 10 /* " " " " " " */ if angle2== | angle2=="," then angle2= 120 /* " " " " " " */

say ' circle radius = ' radius say ' angle 1 = ' angle1"º" /*angles may be negative or > 360º.*/ say ' angle 2 = ' angle2"º" /* " " " " " " " */ say say ' arc length = ' arcLength(radius, angle1, angle2) exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ arcLength: procedure; parse arg r,a1,a2; #=360; return (#-abs(a1//#-a2//#)) * pi()/180 * r /*──────────────────────────────────────────────────────────────────────────────────────*/ pi: pi= 3.1415926535897932384626433832795; return pi /*use 32 digs (overkill).*/</lang>

output   when using the default inputs:

     circle radius =  10
           angle 1 =  10º
           angle 2 =  120º

        arc length =  43.6332313

zkl

Translation of: Julia

<lang zkl>fcn arcLength(radius, angle1, angle2){

  (360.0 - (angle2 - angle1).abs()).toRad()*radius

} println(arcLength(10,10,120));</lang>

Output:

43.6332