/// <summary>
/// http://www.had2know.com/academics/equation-plane-through-3-points.html
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="p3"></param>
public Plane(Point3D p1, Point3D p2, Point3D p3)
{
if (p1 == p2 || p1 == p3 || p2 == p3)
{
throw new ArgumentException("Must use three different points");
}
Vector3D v1 = new Vector3D(p2.X - p1.X, p2.Y - p1.Y, p2.Z - p1.Z);
Vector3D v2 = new Vector3D(p3.X - p1.X, p3.Y - p1.Y, p3.Z - p1.Z);
Vector3D cross = v1.CrossProduct(v2);
if (cross.Length <= float.Epsilon)
{
throw new ArgumentException("The 3 points should not be on the same line");
}
this.RootPoint = p1;
this.Normal = cross.Normalize();
this.D = -this.RootPoint.ToVector3D().DotProduct(this.Normal);
}
/// <summary>
/// Initializes a new instance of the <see cref="Plane"/> struct.
/// Creates a plane that contains the three given points.
/// </summary>
/// <param name="p1">The first point on the plane.</param>
/// <param name="p2">The second point on the plane.</param>
/// <param name="p3">The third point on the plane.</param>
/// <returns>The plane containing the three points.</returns>
public static Plane FromPoints(Point3D p1, Point3D p2, Point3D p3)
{
// http://www.had2know.com/academics/equation-plane-through-3-points.html
if (p1 == p2 || p1 == p3 || p2 == p3)
{
throw new ArgumentException("Must use three different points");
}
var v1 = new Vector3D(p2.X - p1.X, p2.Y - p1.Y, p2.Z - p1.Z);
var v2 = new Vector3D(p3.X - p1.X, p3.Y - p1.Y, p3.Z - p1.Z);
var cross = v1.CrossProduct(v2);
if (cross.Length <= float.Epsilon)
{
throw new ArgumentException("The 3 points should not be on the same line");
}
return(new Plane(cross.Normalize(), p1));
}
