Length of an arc between two angles

From Rosetta Code
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[edit]

USING: kernel math math.constants math.trig prettyprint ;
 
: arc-length ( radius angle angle -- x )
- abs deg>rad 2pi swap - * ;
 
10 10 120 arc-length .
Output:
43.63323129985824

Go[edit]

Translation of: Julia
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))
}
Output:
43.63323129985823

Julia[edit]

The task seems to be to find the distance along the circumference of the circle which is NOT swept out between the two angles.

 
arclength(r, angle1, angle2) = (360 - abs(angle2 - angle1)) * π/180 * r
@show arclength(10, 10, 120) # --> arclength(10, 10, 120) = 43.63323129985823
 

Perl[edit]

Translation of: Raku
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];
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[edit]

Translation of: Julia
function arclength(atom r, angle1, angle2)
return (360 - abs(angle2 - angle1)) * PI/180 * r
end function
?arclength(10, 10, 120) -- 43.6332313

Raku[edit]

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.

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 × 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)),
\(175, -45, :r(10/π)) { # test gradian parameters
printf "Arc length: %8s Parameters: %s\n", arc(|$_).round(.000001), $_.raku
}
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[edit]

Translation of: Julia

This REXX version handles angles (in degrees) that may be   >   360º.

/*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).*/
output   when using the default inputs:
     circle radius =  10
           angle 1 =  10º
           angle 2 =  120º

        arc length =  43.6332313

zkl[edit]

Translation of: Julia
fcn arcLength(radius, angle1, angle2){
(360.0 - (angle2 - angle1).abs()).toRad()*radius
}
println(arcLength(10,10,120));
Output:
43.6332