using System;

using System.Drawing;

namespace Geometry

{

/// <summary>

/// Geometric solutions for circles

/// </summary>

public class CircleGeometry

{

private CircleGeometry()

{

}

/// <summary>

/// Find the centre and radius of a circle through 3 points

/// </summary>

/// <param name="pt1">First point</param>

/// <param name="pt2">Second point</param>

/// <param name="pt3">Third point</param>

/// <param name="ptCentre">Centre point result</param>

/// <param name="nRadius">Radius result</param>

/// <returns>Status value</returns>

public static int Circle3P(Point pt1, Point pt2, Point pt3,

ref Point ptCentre, ref int nRadius)

//*****************************************************************

// Find the centre and radius of a circle passing through 3 points

// Return 0 : success, 1 : two or more points are co-incident or co-linear,

// 2 : solution out of range

{

double x1, y1, x2, y2, x3, y3, xc, yc, fRadius, Div;

// Check points are distinct

if((pt1 == pt2) || (pt1 == pt3) || (pt2 == pt3)) return 1;

// Convert points to real for accuracy

x1 = pt1.X; y1 = pt1.Y;

x2 = pt2.X; y2 = pt2.Y;

x3 = pt3.X; y3 = pt3.Y;

// Calculate x-coordinate of centre

Div = 2.0 * ((x1 - x2)*(y2 - y3)-(x2 - x3)*(y1 - y2));

if(Div == 0.0) return 1;

xc = ((y2 - y3) *( x1*x1 - x2*x2 + y1*y1 - y2*y2) -

(y1 - y2) * (x2*x2 - x3*x3 + y2*y2 - y3*y3)) / Div;

// Calculate y-coordinate

if(y1 != y2) yc = ((2.0 * xc * (x2-x1)) + (x1*x1 - x2*x2 + y1*y1 - y2*y2))/

(2.0 * (y1-y2));

else yc = ((2.0 * xc * (x3-x1)) + (x1*x1 - x3*x3 + y1*y1 - y3*y3))/

(2.0 * (y1-y3));

// Derive radius

fRadius = Math.Sqrt((xc - x1) * (xc - x1) + (yc - y1) * (yc - y1));

// Convert results to integers

if(Math.Abs(xc) > (double)Int32.MaxValue) return 2;

if(Math.Abs(yc) > (double)Int32.MaxValue) return 2;

if(Math.Abs(fRadius) > (double)Int32.MaxValue) return 2;

ptCentre.X = (int)Math.Round(xc);

ptCentre.Y = (int)Math.Round(yc);

nRadius = (int)Math.Round(fRadius);

// Return success

return 0;

}

}

}