Centre and radius of a circle passing through 3 points in a plane: Difference between revisions
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{{
Write a function which returns the centre and radius of a circle passing through three point in a plane. Demonstrate the function using the points (22.83,2.07) (14.39,30.24) and (33.65,17.31)
=={{header|ALGOL 68}}==
Follows the lines of the C++ code [https://www.geeksforgeeks.org/equation-of-circle-when-three-points-on-the-circle-are-given/ at geeksforgeeks.org].
<syntaxhighlight lang="algol68">
BEGIN # find the centre and radius of a circle through 3 points #
# follows the lines of the C++ code at #
# https://www.geeksforgeeks.org/equation-of-circle-when-three-points-on-the-circle-are-given/ #
MODE POINT = STRUCT( REAL x, y );
MODE CIRCLE = STRUCT( POINT centre, REAL radius );
# returns the circle that passes through p1, p2 and p3 #
PROC find circle = ( POINT p1, p2, p3 )CIRCLE:
BEGIN
REAL x1 = x OF p1, y1 = y OF p1, x2 = x OF p2, y2 = y OF p2, x3 = x OF p3, y3 = y OF p3;
REAL x12 = x1 - x2
, x13 = x1 - x3
, y12 = y1 - y2
, y13 = y1 - y3
, y31 = y3 - y1
, y21 = y2 - y1
, x31 = x3 - x1
, x21 = x2 - x1
;
REAL sx13 = x1^2 - x3^2
, sy13 = y1^2 - y3^2
, sx21 = x2^2 - x1^2
, sy21 = y2^2 - y1^2
;
REAL f = ( ( ( sx13 + sy13 ) * x12 )
+ ( ( sx21 + sy21 ) * x13 )
)
/ ( 2 * ( ( y31 * x12 ) - ( y21 * x13 ) ) )
, g = ( ( ( sx13 + sy13 ) * y12 )
+ ( ( sx21 + sy21 ) * y13 )
)
/ ( 2 * ( ( x31 * y12 ) - ( x21 * y13 ) ) )
;
REAL c = - (x1^2) - (y1^2) - ( 2 * g * x1 ) - ( 2 * f * y1 );
( ( -g, -f ), sqrt( g^2 + f^2 - c ) )
END # find circle # ;
CIRCLE c = find circle( ( 22.83, 2.07 ), ( 14.39, 30.24 ), ( 33.65, 17.31 ) );
print( ( "Centre = ( ", fixed( x OF centre OF c, -10, 6 ) ) );
print( ( ", ", fixed( y OF centre OF c, -10, 6 ) ) );
print( ( " ), Radius = ", fixed( radius OF c, -10, 6 ), newline ) )
END
</syntaxhighlight>
{{out}}
<pre>
Centre = ( 18.978516, 16.265411 ), Radius = 14.708624
</pre>
=={{header|BASIC}}==
==={{header|BASIC256}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vbnet">call findCircle(22.83, 2.07, 14.39, 30.24, 33.65, 17.31)
end
subroutine findCircle(x1, y1, x2, y2, x3, y3)
x12 = x1 - x2
x13 = x1 - x3
y12 = y1 - y2
y13 = y1 - y3
y31 = y3 - y1
y21 = y2 - y1
x31 = x3 - x1
x21 = x2 - x1
sx13 = x1 * x1 - x3 * x3
sy13 = y1 * y1 - y3 * y3
sx21 = x2 * x2 - x1 * x1
sy21 = y2 * y2 - y1 * y1
f = (sx13 * x12 + sy13 * x12 + sx21 * x13 + sy21 * x13) / (y31 * x12 - y21 * x13) / 2
g = (sx13 * y12 + sy13 * y12 + sx21 * y13 + sy21 * y13) / (x31 * y12 - x21 * y13) / 2
c = -x1 * x1 - y1 * y1 - 2 * g * x1 - 2 * f * y1
h = -g
k = -f
r = sqr(h * h + k * k - c)
print "Centre is at ("; h; ", "; k; ")"
print "Radius is "; r
print
print "Check radius as the distance between the centre and the first point:"
print sqr((22.83 - h) ^ 2 + (2.07 - k) ^ 2)
end subroutine</syntaxhighlight>
{{out}}
<pre>Centre is at (18.9785156601, 16.2654107977)
Radius is 14.708624
Check radius as the distance between the centre and the first point:
14.708624</pre>
==={{header|Chipmunk Basic}}===
{{trans|FreeBASIC}}
{{works with|Chipmunk Basic|3.6.4}}
<syntaxhighlight lang="vbnet">100 sub findcircle(x1,y1,x2,y2,x3,y3)
110 x12 = x1-x2
120 x13 = x1-x3
130 y12 = y1-y2
140 y13 = y1-y3
150 y31 = y3-y1
160 y21 = y2-y1
170 x31 = x3-x1
180 x21 = x2-x1
190 '
200 sx13 = x1*x1-x3*x3
210 sy13 = y1*y1-y3*y3
220 sx21 = x2*x2-x1*x1
230 sy21 = y2*y2-y1*y1
240 '
250 f = (sx13*x12+sy13*x12+sx21*x13+sy21*x13)/(y31*x12-y21*x13)/2
260 g = (sx13*y12+sy13*y12+sx21*y13+sy21*y13)/(x31*y12-x21*y13)/2
270 '
280 c = -x1*x1-y1*y1-2*g*x1-2*f*y1
290 h = -g
300 k = -f
310 r = sqr(h*h+k*k-c)
320 '
330 print "Centre is at ( ";h;", ";k;")"
340 print "Radius is ";r
350 print
360 print "Check radius as the distance between the centre and the first point:"
370 print sqr((22.83-h)^2+(2.07-k)^2)
380 end sub
390 cls
400 findcircle(22.83,2.07,14.39,30.24,33.65,17.31)
410 end</syntaxhighlight>
==={{header|Gambas}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vbnet">Sub findCircle(x1 As Float, y1 As Float, x2 As Float, y2 As Float, x3 As Float, y3 As Float)
Dim x12 As Float = x1 - x2
Dim x13 As Float = x1 - x3
Dim y12 As Float = y1 - y2
Dim y13 As Float = y1 - y3
Dim y31 As Float = y3 - y1
Dim y21 As Float = y2 - y1
Dim x31 As Float = x3 - x1
Dim x21 As Float = x2 - x1
Dim sx13 As Float = x1 * x1 - x3 * x3
Dim sy13 As Float = y1 * y1 - y3 * y3
Dim sx21 As Float = x2 * x2 - x1 * x1
Dim sy21 As Float = y2 * y2 - y1 * y1
Dim f As Float = (sx13 * x12 + sy13 * x12 + sx21 * x13 + sy21 * x13) / (y31 * x12 - y21 * x13) / 2
Dim g As Float = (sx13 * y12 + sy13 * y12 + sx21 * y13 + sy21 * y13) / (x31 * y12 - x21 * y13) / 2
Dim c As Float = -x1 * x1 - y1 * y1 - 2 * g * x1 - 2 * f * y1
Dim h As Float = -g
Dim k As Float = -f
Dim r As Float = Sqr(h * h + k * k - c)
Print "Centre is at (" & h & ", " & k & ")"
Print "Radius is "; r
Print
Print "Check radius as the distance between the centre and the first point:"
Print Sqr((22.83 - h) ^ 2 + (2.07 - k) ^ 2)
End Sub
Public Sub Main()
findCircle(22.83, 2.07, 14.39, 30.24, 33.65, 17.31)
End </syntaxhighlight>
{{out}}
<pre>Centre is at (18.9785156601488, 16.2654107977159)
Radius is 14,7086239783342
Check radius as the distance between the centre and the first point:
14,7086239783342</pre>
==={{header|PureBasic}}===
<syntaxhighlight lang="basic">Procedure.d findCircle(x1, y1, x2, y2, x3, y3)
Define.d x12, x13, y12, y13, y31, y21, x31, x21, sx13, sy13, sx21, sy21
Define.d f, g, c, h, k, r
x12 = x1 - x2
x13 = x1 - x3
y12 = y1 - y2
y13 = y1 - y3
y31 = y3 - y1
y21 = y2 - y1
x31 = x3 - x1
x21 = x2 - x1
sx13 = x1 * x1 - x3 * x3
sy13 = y1 * y1 - y3 * y3
sx21 = x2 * x2 - x1 * x1
sy21 = y2 * y2 - y1 * y1
f = (sx13 * x12 + sy13 * x12 + sx21 * x13 + sy21 * x13) / (y31 * x12 - y21 * x13) / 2
g = (sx13 * y12 + sy13 * y12 + sx21 * y13 + sy21 * y13) / (x31 * y12 - x21 * y13) / 2
c = -x1 * x1 - y1 * y1 - 2 * g * x1 - 2 * f * y1
h = -g
k = -f
r = Sqr(h * h + k * k - c)
PrintN("Centre is at (" + Str(h) + ", " + Str(k) + ")")
PrintN("Radius is " + Str(r))
PrintN("")
PrintN("Check radius as the distance between the centre and the first point: " + Str(Sqr(Pow((22.83 - h), 2) + Pow((2.07 - k), 2))))
EndProcedure
OpenConsole()
findCircle(22.83, 2.07, 14.39, 30.24, 33.65, 17.31)
PrintN(#CRLF$ + "--- terminado, pulsa RETURN---"): Input()
PrintN(#CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()</syntaxhighlight>
==={{header|Yabasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="qbasic">findCircle(22.83, 2.07, 14.39, 30.24, 33.65, 17.31)
END
SUB findCircle(x1, y1, x2, y2, x3, y3)
x12 = x1 - x2
x13 = x1 - x3
y12 = y1 - y2
y13 = y1 - y3
y31 = y3 - y1
y21 = y2 - y1
x31 = x3 - x1
x21 = x2 - x1
sx13 = x1 * x1 - x3 * x3
sy13 = y1 * y1 - y3 * y3
sx21 = x2 * x2 - x1 * x1
sy21 = y2 * y2 - y1 * y1
f = (sx13 * x12 + sy13 * x12 + sx21 * x13 + sy21 * x13) / (y31 * x12 - y21 * x13) / 2
g = (sx13 * y12 + sy13 * y12 + sx21 * y13 + sy21 * y13) / (x31 * y12 - x21 * y13) / 2
c = -x1 * x1 - y1 * y1 - 2 * g * x1 - 2 * f * y1
h = -g
k = -f
r = SQRT(h * h + k * k - c)
PRINT "Centre is at (", h, ", ", k, ")"
PRINT "Radius is ", r
PRINT
PRINT "Check radius as the distance between the centre and the first point:"
PRINT SQRT((22.83 - h) ^ 2 + (2.07 - k) ^ 2)
END SUB</syntaxhighlight>
{{out}}
<pre>Centre is at (18.9785, 16.2654)
Radius is 14.7086
Check radius as the distance between the centre and the first point:
14.7086</pre>
=={{header|C++}}==
This follows the lines of the C++ code [https://www.geeksforgeeks.org/equation-of-circle-when-three-points-on-the-circle-are-given/ here].
<syntaxhighlight lang="c++">#include <iostream>
#include <math.h>
using namespace std;
void findCircle(float x1, float y1, float x2, float y2, float x3, float y3) {
float x12 = x1 - x2;
float x13 = x1 - x3;
float y12 = y1 - y2;
float y13 = y1 - y3;
float y31 = y3 - y1;
float y21 = y2 - y1;
float x31 = x3 - x1;
float x21 = x2 - x1;
float sx13 = pow(x1, 2) - pow(x3, 2);
float sy13 = pow(y1, 2) - pow(y3, 2);
float sx21 = pow(x2, 2) - pow(x1, 2);
float sy21 = pow(y2, 2) - pow(y1, 2);
float f = ((sx13) * (x12) + (sy13) * (x12) + (sx21) * (x13) + (sy21) * (x13))
/ (2 * ((y31) * (x12) - (y21) * (x13)));
float g = ((sx13) * (y12) + (sy13) * (y12) + (sx21) * (y13) + (sy21) * (y13))
/ (2 * ((x31) * (y12) - (x21) * (y13)));
float c = -pow(x1, 2) - pow(y1, 2) - 2 * g * x1 - 2 * f * y1;
float h = -g;
float k = -f;
float r = sqrt(h * h + k * k - c);
cout << "Centre is at (" << h << ", " << k << ")" << endl;
cout << "Radius is " << r;
}
int main() {
findCircle(22.83, 2.07, 14.39, 30.24, 33.65, 17.31);
return 0;
}</syntaxhighlight>
=={{header|Dart}}==
{{trans|C++}}
<syntaxhighlight lang="dart">import 'dart:math';
void findCircle(
double x1, double y1, double x2, double y2, double x3, double y3) {
double x12 = x1 - x2;
double x13 = x1 - x3;
double y12 = y1 - y2;
double y13 = y1 - y3;
double y31 = y3 - y1;
double y21 = y2 - y1;
double x31 = x3 - x1;
double x21 = x2 - x1;
double sx13 = x1 * x1 - x3 * x3;
double sy13 = y1 * y1 - y3 * y3;
double sx21 = x2 * x2 - x1 * x1;
double sy21 = y2 * y2 - y1 * y1;
double f = (sx13 * x12 + sy13 * x12 + sx21 * x13 + sy21 * x13) /
(2 * (y31 * x12 - y21 * x13));
double g = (sx13 * y12 + sy13 * y12 + sx21 * y13 + sy21 * y13) /
(2 * (x31 * y12 - x21 * y13));
double c = -pow(x1, 2) - pow(y1, 2) - 2 * g * x1 - 2 * f * y1;
double h = -g;
double k = -f;
double r = sqrt(h * h + k * k - c);
print("Centre is at ($h, $k)");
print("\nCheck radius as the distance between the centre and the first point: $r");
}
void main() {
findCircle(22.83, 2.07, 14.39, 30.24, 33.65, 17.31);
}</syntaxhighlight>
{{out}}
<pre>Centre is at (18.978515660148815, 16.265410797715866)
Check radius as the distance between the centre and the first point: 14.70862397833418</pre>
=={{header|EasyLang}}==
{{trans|Wren}}
<syntaxhighlight>
proc circ x1 y1 x2 y2 x3 y3 . cx cy cr .
x12 = x1 - x2
x13 = x1 - x3
y12 = y1 - y2
y13 = y1 - y3
y31 = y3 - y1
y21 = y2 - y1
x31 = x3 - x1
x21 = x2 - x1
sx13 = x1 * x1 - x3 * x3
sy13 = y1 * y1 - y3 * y3
sx21 = x2 * x2 - x1 * x1
sy21 = y2 * y2 - y1 * y1
f = (sx13 * x12 + sy13 * x12 + sx21 * x13 + sy21 * x13) / (y31 * x12 - y21 * x13) / 2
g = (sx13 * y12 + sy13 * y12 + sx21 * y13 + sy21 * y13) / (x31 * y12 - x21 * y13) / 2
c = -x1 * x1 - y1 * y1 - 2 * g * x1 - 2 * f * y1
cx = -g
cy = -f
cr = sqrt (cx * cx + cy * cy - c)
.
circ 22.83 2.07 14.39 30.24 33.65 17.31 cx cy cr
print "Centre: (" & cx & ", " & cy & ") Radius: " & cr
</syntaxhighlight>
{{out}}
<pre>
Centre: (18.98, 16.27) Radius: 14.71
</pre>
=={{header|F_Sharp|F#}}==
Line 7 ⟶ 387:
let c (a,b) (c,d) (e,f)=(0.5*((a*a+b*b)*(f-d)+(c*c+d*d)*(b-f)+(e*e+f*f)*(d-b))/(a*(f-d)+c*(b-f)+e*(d-b)),
0.5*((a*a+b*b)*(e-c)+(c*c+d*d)*(a-e)+(e*e+f*f)*(c-a))/(b*(e-c)+d*(a-e)+f*(c-a)))
let d n g = let n,g=fst n-fst g,snd n-snd g in sqrt(n*n+g*g)
let circ P1 P2 P3 = let c=c P1 P2 P3 in (c,d c P1)
Line 15 ⟶ 395:
{{out}}
<pre>
Centre = (18.97851566, 16.2654108), radius =
</pre>
Line 59 ⟶ 439:
Check radius as the distance between the centre and the first point:
14.70862397833418</pre>
=={{header|jq}}==
'''Adapted from [[#Julia|Julia]]'''
'''Works with jq, the C implementation of jq'''
'''Works with gojq, the Go implementation of jq'''
<syntaxhighlight lang="jq">
# Emit {x,y,r} corresponding to the circle through the three points
# specified as [x,y] pairs.
def findcircle($p1; $p2; $p3):
def assertEq($p; $q): if ($p - $q)|length < 1e-12 then . else "assertion failed: \($p) != \($q)" | error end;
def ss($a; $b) : ($a|.*.) + ($b|.*.);
$p1 as [$a,$b]
| $p2 as [$c,$d]
| $p3 as [$e,$f]
| ($a - $e) as $ae
| ($d - $b) as $db
| ($b - $f) as $bf
| ($e - $c) as $ec
| ($c - $a) as $ca
| ($f - $d) as $fd
| ss($a; $b) as $a2b2
| ss($c; $d) as $c2d2
| ss($e; $f) as $e2f2
| {x: (0.5 * ($a2b2 * $fd + $c2d2 * $bf + $e2f2 * $db) / ($a * $fd + $c * $bf + $e * $db)),
y: (0.5 * ($a2b2 * $ec + $c2d2 * $ae + $e2f2 * $ca) / ($b * $ec + $d * $ae + $f * $ca)) }
# any one of these should do / be nearly identical:
| [ss(.x-$a; .y-$b), ss(.x-$c; .y-$d), ss(.x-$e; .y-$f)] as $r123
| assertEq( $r123|max; $r123|min )
| .r = (($r123 | add) / 3 | sqrt) ;
findcircle( [22.83, 2.07]; [14.39, 30.24]; [33.65, 17.31])
| "Centre = \([.x, .y]), radius = \(.r)"
</syntaxhighlight>
{{output}}
<pre>
Centre = [18.978515660148815,16.26541079771587], radius = 14.708623978334177
</pre>
=={{header|Julia}}==
{{trans|Phix}}{{trans|F#}}
<syntaxhighlight lang="julia">function findcircle(p1, p2, p3)
a, b = p1
c, d = p2
e, f = p3
a2b2 = a * a + b * b
ae = a - e
db = d - b
c2d2 = c * c + d * d
bf = b - f
ec = e - c
e2f2 = e * e + f * f
ca = c - a
fd = f - d
cx = 0.5 * (a2b2 * fd + c2d2 * bf + e2f2 * db) / (a * fd + c * bf + e * db)
cy = 0.5 * (a2b2 * ec + c2d2 * ae + e2f2 * ca) / (b * ec + d * ae + f * ca)
# any one of these should do / be nearly identical:
r123 = [(cx-a)^2 + (cy-b)^2, (cx-c)^2 + (cy-d)^2, (cx-e)^2 + (cy-f)^2]
@assert maximum(r123) - minimum(r123) < 1e-12
r = sqrt(sum(r123) / length(r123))
return (cx, cy), r
end
ctr, r = findcircle((22.83, 2.07), (14.39, 30.24), (33.65, 17.31))
println("Centre = $ctr, radius = $r")
</syntaxhighlight>{{out}}
<pre>Centre = (18.978515660148815, 16.26541079771587), radius = 14.708623978334177</pre>
=={{header|Kotlin}}==
<syntaxhighlight lang="kotlin">
import kotlin.math.sqrt
data class Point(val x: Double, val y: Double)
fun findCircle(p1: Point, p2: Point, p3: Point): Pair<Point, Double> {
fun sq(x: Double) = x * x
val centreX =
0.5 * (
(sq(p1.x) + sq(p1.y)) * (p3.y - p2.y) +
(sq(p2.x) + sq(p2.y)) * (p1.y - p3.y) +
(sq(p3.x) + sq(p3.y)) * (p2.y - p1.y)
) / (
p1.x * (p3.y - p2.y) +
p2.x * (p1.y - p3.y) +
p3.x * (p2.y - p1.y)
)
val centreY =
0.5 * (
(sq(p1.x) + sq(p1.y)) * (p3.x - p2.x) +
(sq(p2.x) + sq(p2.y)) * (p1.x - p3.x) +
(sq(p3.x) + sq(p3.y)) * (p2.x - p1.x)
) / (
p1.y * (p3.x - p2.x) +
p2.y * (p1.x - p3.x) +
p3.y * (p2.x - p1.x)
)
val centre = Point(centreX, centreY)
val radius = sqrt(sq(centreX - p1.x) + sq(centreY - p1.y))
return Pair(centre, radius)
}
fun main() {
findCircle(Point(22.83,2.07), Point(14.39,30.24), Point(33.65,17.31))
.let { (c, r) ->
println("Centre = $c")
println("Radius = $r")
}
}
</syntaxhighlight>
{{out}}
<pre>
Centre = Point(x=18.978515660148815, y=16.26541079771587)
Radius = 14.70862397833418
</pre>
=={{header|Phix}}==
Line 67 ⟶ 569:
function circle(sequence p1, p2, p3)
atom {a,b} = p1, {c,d} = p2, {e,f} = p3,
a2b2 = a*a+b*b, ae = a-e, db = d-b,
c2d2 = c*c+d*d, bf = b-f, ec = e-c,
e2f2 = e*e+f*f, ca = c-a, fd = f-d,
cx = 0.5*(a2b2*fd+c2d2*bf+e2f2*db)/(a*fd+c*bf+e*db),
cy = 0.5*(a2b2*ec+c2d2*ae+e2f2*ca)/(b*ec+d*ae+f*ca)
-- any one of these should do / be nearly identical:
sequence r123 = {power(cx-a,2)+power(cy-b,2),
power(cx-c,2)+power(cy-d,2),
power(cx-e,2)+power(cy-f,2)}
assert((max(r123)-min(r123))<1e-12)
atom r = sqrt(average(r123))
return {{cx,cy},r}
end function
Line 88 ⟶ 589:
<pre>
Centre = 18.97851566, 16.2654108, radius = 14.708624
</pre>
=={{header|Raku}}==
Don't bother defining all the intermediate variables.
<syntaxhighlight lang="raku" line>sub circle( (\𝒳ᵢ, \𝒴ᵢ), (\𝒳ⱼ, \𝒴ⱼ), (\𝒳ₖ, \𝒴ₖ) ) {
:center(
my $𝒞ₓ = ((𝒳ᵢ² + 𝒴ᵢ²) × (𝒴ₖ - 𝒴ⱼ) + (𝒳ⱼ² + 𝒴ⱼ²) × (𝒴ᵢ - 𝒴ₖ) + (𝒳ₖ² + 𝒴ₖ²) × (𝒴ⱼ - 𝒴ᵢ)) /
(𝒳ᵢ × (𝒴ₖ - 𝒴ⱼ) + 𝒳ⱼ × (𝒴ᵢ - 𝒴ₖ) + 𝒳ₖ × (𝒴ⱼ - 𝒴ᵢ)) / 2,
my $𝒞ᵧ = ((𝒳ᵢ² + 𝒴ᵢ²) × (𝒳ₖ - 𝒳ⱼ) + (𝒳ⱼ² + 𝒴ⱼ²) × (𝒳ᵢ - 𝒳ₖ) + (𝒳ₖ² + 𝒴ₖ²) × (𝒳ⱼ - 𝒳ᵢ)) /
(𝒴ᵢ × (𝒳ₖ - 𝒳ⱼ) + 𝒴ⱼ × (𝒳ᵢ - 𝒳ₖ) + 𝒴ₖ × (𝒳ⱼ - 𝒳ᵢ)) / 2
),
radius => (($𝒞ₓ - 𝒳ᵢ)² + ($𝒞ᵧ - 𝒴ᵢ)²).sqrt
}
say circle (22.83,2.07), (14.39,30.24), (33.65,17.31);</syntaxhighlight>
{{out}}
<pre>(center => (18.97851566 16.2654108) radius => 14.70862397833418)</pre>
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=={{header|Swift}}==
<syntaxhighlight lang="swift">
import Foundation
import Matrix
extension Matrix where Element: SignedNumeric {
func minor(row: Int, column: Int) -> Element {
var submatrix = self
_ = submatrix.remove(rowAt: row - 1)
_ = submatrix.remove(columnAt: column - 1)
return submatrix.determinant as Element
}
}
enum MatrixErrors: Error {
case notEnoughPoints, tooManyPoints, pointsOnALine, miscError
}
func circleFrom3Points(points: (Double,Double)... ) throws -> (Double,Double,Double){
var pointArray: [[Double]] = [[0,0,0,0]]
for p in points {
pointArray.append([pow(p.0, 2) + pow(p.1, 2), p.0, p.1, 1])
}
guard pointArray.count > 3 else { throw MatrixErrors.notEnoughPoints }
guard pointArray.count < 5 else { throw MatrixErrors.tooManyPoints }
var matrix = Matrix(elements:pointArray)
var m11 = matrix.minor(row: 1, column: 1)
guard m11 != 0 else { throw MatrixErrors.pointsOnALine }
var m12 = matrix.minor(row: 1, column: 2)
var m13 = matrix.minor(row: 1, column: 3)
let x = 0.5 * m12 / m11
let y = -0.5 * m13 / m11
let r = (pow(x - pointArray[1][1],2) + pow(y - pointArray[1][2],2)).squareRoot()
return (x,y,r)
}
do {
let (x,y,r) = try circleFrom3Points(points: (22.83,2.07), (14.39,30.24), (33.65,17.31))
print("x:\(x), y:\(y), r: \(r)")
} catch {
debugPrint(error)
exit(1)
}
</syntaxhighlight>
<pre>
x:18.978515660148812, y:16.265410797715873, r: 14.708623978334185
</pre>
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