/// <summary>
/// Create a circle from three points which lie along its circumference.
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="p3"></param>
public Circle3D(Point3D p1, Point3D p2, Point3D p3)
{
https: //www.physicsforums.com/threads/equation-of-a-circle-through-3-points-in-3d-space.173847/
Vector3D p1p2 = p2 - p1;
Vector3D p2p3 = p3 - p2;
this.Axis = p1p2.CrossProduct(p2p3).Normalize();
Point3D midPointA = p1 + 0.5 * p1p2;
Point3D midPointB = p2 + 0.5 * p2p3;
Vector3D directionA = p1p2.CrossProduct(this.Axis);
Vector3D directionB = p2p3.CrossProduct(this.Axis);
Ray3D bisectorA = new Ray3D(midPointA, directionA);
Plane bisectorB = new Plane(midPointB, midPointB + directionB.Normalize(), midPointB + this.Axis);
var center = bisectorA.IntersectionWith(bisectorB);
if (center == null)
{
throw new ArgumentException("A circle cannot be created from these points, are they colinear?");
}
this.CenterPoint = (Point3D)center;
this.Radius = this.CenterPoint.DistanceTo(p1);
}
/// <summary>
/// Initializes a new instance of the <see cref="Circle3D"/> struct.
/// Create a circle from three points which lie along its circumference.
/// </summary>
/// <param name="p1">The first point on the circle</param>
/// <param name="p2">The second point on the circle</param>
/// <param name="p3">The third point on the circle</param>
/// <returns>A <see cref="Circle3D"/></returns>
public static Circle3D FromPoints(Point3D p1, Point3D p2, Point3D p3)
{
// https://www.physicsforums.com/threads/equation-of-a-circle-through-3-points-in-3d-space.173847/
//// ReSharper disable InconsistentNaming
var p1p2 = p2 - p1;
var p2p3 = p3 - p2;
//// ReSharper restore InconsistentNaming
var axis = p1p2.CrossProduct(p2p3).Normalize();
var midPointA = p1 + (0.5 * p1p2);
var midPointB = p2 + (0.5 * p2p3);
var directionA = p1p2.CrossProduct(axis);
var directionB = p2p3.CrossProduct(axis);
var bisectorA = new Ray3D(midPointA, directionA);
var bisectorB = Plane.FromPoints(midPointB, midPointB + directionB.Normalize(), midPointB + axis);
var center = bisectorA.IntersectionWith(bisectorB);
if (center == null)
{
throw new ArgumentException("A circle cannot be created from these points, are they collinear?");
}
return(new Circle3D(center.Value, axis, center.Value.DistanceTo(p1)));
}
