Length of an arc between two angles: Difference between revisions
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Writeln(Format('%.7f', [arc_length(10, 10, 120)])); |
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Revision as of 22:38, 18 July 2020
- 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.
AWK
<lang AWK>
- syntax: GAWK -f LENGTH_OF_AN_ARC_BETWEEN_TWO_ANGLES.AWK
- converted from PHIX
BEGIN {
printf("%.7f\n",arc_length(10,10,120)) exit(0)
} function arc_length(radius,angle1,angle2) {
return (360 - abs(angle2-angle1)) * 3.14159265 / 180 * radius
} function abs(x) { if (x >= 0) { return x } else { return -x } } </lang>
- Output:
43.6332313
Delphi
<lang Delphi> program Length_of_an_arc;
{$APPTYPE CONSOLE} {$R *.res}
uses
System.SysUtils;
function arc_length(radius, angle1, angle2: Double): Double; begin
Result := (360 - abs(angle2 - angle1)) * PI / 180 * radius;
end;
begin
Writeln(Format('%.7f', [arc_length(10, 10, 120)])); Readln;
end. </lang>
- Output:
43.6332313
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
Fortran
The Fortran subroutine contains the MAX(DIF, 360. - DIF) operation. Other solutions presented here correspond to different interpretations of the problem. This subroutine computes the length of the major arc, which is not necessarily equal to distance traveling counter-clockwise. <lang fortran>*-----------------------------------------------------------------------
- given: polar coordinates of two points on a circle of known radius
- find: length of the major arc between these points
- ___Name_____Type___I/O___Description___________________________________
- RAD Real In Radius of circle, any unit of measure
- ANG1 Real In Angle of first point, degrees
- ANG2 Real In Angle of second point, degrees
- MAJARC Real Out Length of major arc, same units as RAD
- -----------------------------------------------------------------------
FUNCTION MAJARC (RAD, ANG1, ANG2) IMPLICIT NONE REAL RAD, ANG1, ANG2, MAJARC
REAL FACT ! degrees to radians PARAMETER (FACT = 3.1415926536 / 180.) REAL DIF
- Begin
MAJARC = 0. IF (RAD .LE. 0.) RETURN DIF = MOD(ABS(ANG1 - ANG2), 360.) ! cyclic difference DIF = MAX(DIF, 360. - DIF) ! choose the longer path MAJARC = RAD * DIF * FACT ! L = r theta RETURN END ! of majarc
- -----------------------------------------------------------------------
PROGRAM TMA IMPLICIT NONE INTEGER J REAL ANG1, ANG2, RAD, MAJARC, ALENG REAL DATARR(3,3) DATA DATARR / 120., 10., 10., $ 10., 120., 10., $ 180., 270., 10. /
DO J = 1, 3 ANG1 = DATARR(1,J) ANG2 = DATARR(2,J) RAD = DATARR(3,J) ALENG = MAJARC (RAD, ANG1, ANG2) PRINT *, 'first angle: ', ANG1, ' second angle: ', ANG2, $ ' radius: ', RAD, ' Length of major arc: ', ALENG END DO END
</lang>
- Output:
first angle: 120.000000 second angle: 10.0000000 radius: 10.0000000 Length of major arc: 43.6332321 first angle: 10.0000000 second angle: 120.000000 radius: 10.0000000 Length of major arc: 43.6332321 first angle: 180.000000 second angle: 270.000000 radius: 10.0000000 Length of major arc: 47.1238899
Go
<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>
Kotlin
<lang scala>import kotlin.math.PI import kotlin.math.abs
fun arcLength(radius: Double, angle1: Double, angle2: Double): Double {
return (360.0 - abs(angle2 - angle1)) * PI * radius / 180.0
}
fun main() {
val al = arcLength(10.0, 10.0, 120.0) println("arc length: $al")
}</lang>
- Output:
arc length: 43.63323129985823
Perl
<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
<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
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
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
<lang zkl>fcn arcLength(radius, angle1, angle2){
(360.0 - (angle2 - angle1).abs()).toRad()*radius
} println(arcLength(10,10,120));</lang>
- Output:
43.6332