PowerShell code to get a circle from three points on an arc.

GetCircleFromPoints.ps1

class Point {
    [double]$X;
    [double]$Y;

    Point([double]$x, [double]$y) {
        $this.X = $x;
        $this.Y = $y;
    }

    [Point]Add([double]$xDelta, [double]$yDelta) {
        return [Point]::new($this.X + $xDelta, $this.Y + $yDelta);
    }

    [string]ToString() {
        return "($($this.X),$($this.Y))";
    }
}


class Circle {
    [string]$Name; 
    [Point]$Origin;
    [double]$Radius;

    Circle([double]$x, [double]$y, [double]$r) {
        $this.Origin = [Point]::new($x, $y);
        $this.Radius = $r;
    }

    [Point]GetPoint([double]$angle) {
        $cosDelta = [Math]::Cos($angle) * $this.Radius;
        $sinDelta = [Math]::Sin($angle) * $this.Radius;

        return $this.Origin.Add($cosDelta, $sinDelta);
    }
}
function GetCircleFromPoints(
    [Point]$Point1,
    [Point]$Point2,
    [Point]$Point3) {

        function Square([double]$x) { [double][Math]::Pow($x, 2.0) };

        $rhsTop = ((Square $Point1.X) - (Square $Point2.X) + (Square $Point1.Y) - (Square $Point2.Y))/2.0;
        $rhsBottom = ((Square $Point2.X) - (Square $Point3.X) + (Square $Point2.Y) - (Square $Point3.Y))/2.0;

        $topLeft = $Point1.X - $Point2.X;
        $topRight = $Point1.Y - $Point2.Y;
        $bottomLeft = $Point2.X - $Point3.X;
        $bottomRight = $Point2.Y - $Point3.Y;

        $originXCoeff = ($topLeft * $bottomRight) - ($bottomLeft * $topRight);
        $originXCoeffValue = ($bottomRight * $rhsTop) - ($topRight * $rhsBottom);
        $originX = $originXCoeffValue / $originXCoeff;

        $originY = ((($Point1.X - $Point2.X) * $originX) - $rhsTop)/(-1 * ($Point1.Y - $Point2.Y));
        $radius = [Math]::Sqrt((Square ($Point1.X - $originX)) + (Square ($Point1.Y - $originY)));

        return [Circle]::new($originX, $originY, $radius);
}

# test code:

$circ = [Circle]::new(20.0, 10.0, 8);
$circ.Name = 'Original';

$point1 = $circ.GetPoint([Math]::PI * 0.1);
$point2 = $circ.GetPoint([Math]::PI * 0.25);
$point3 = $circ.GetPoint([Math]::PI * 0.35);

$circFromPoints = GetCircleFromPoints $point1 $point2 $point3;
$circFromPoints.Name = 'Derived';

$circ, $circFromPoints | Format-Table;

<#

Name     Origin            Radius
----     ------            ------
Original (20,10)                8
Derived  (20,10) 7.99999999999994

#>

Here is the same function in python:

from math import sqrt
def GetCircleFromPoints(Point1,Point2,Point3):

        rhsTop = ((Point1.x**2) - (Point2.x**2) + (Point1.y**2) - (Point2.y**2)) / 2.0
        rhsBottom = ((Point2.x**2) - (Point3.x**2) + (Point2.y**2) - (Point3.y**2)) / 2.0
        topLeft = Point1.x - Point2.x
        topRight = Point1.y - Point2.y
        bottomLeft = Point2.x - Point3.x
        bottomRight = Point2.y - Point3.y

        originXCoeff = (topLeft * bottomRight) - (bottomLeft * topRight)
        originXCoeffValue = (bottomRight * rhsTop) - (topRight * rhsBottom)
        originX = originXCoeffValue / originXCoeff

        originY = (((Point1.x - Point2.x) * originX) - rhsTop) / (-1 * (Point1.y - Point2.y))
        radius = sqrt(((Point1.x - originX)**2) + ((Point1.y - originY)**2))

        return originX, originY, radius

from shapely.geometry import Point
assert GetCircleFromPoints(Point((0,0)), Point((1,1)),Point((2,0))) == (1.0, 0.0, 1.0)

Nice concise python code @rajanski.

It's the reason I'm looking into xonsh.