/// <summary>
/// Calculates the closest Coordinate to a line created by two other Coordinates. The resulting Coordinate is not garunteed
/// to fall between the two endpoint Coordinates.
/// </summary>
/// <param name="endpoint1">A Coordinate on the line.</param>
/// <param name="endpoint2">Another Coordinate on the line.</param>
/// <returns>The closest Coordinate on the line to this Coordinate.</returns>
public Coordinate ClosestPoint(Coordinate endpoint1, Coordinate endpoint2)
{
double R = 3956;
Point3D ep1cart = new Point3D(
R * Math.Cos(DegToRad(endpoint1.latitude)) * Math.Cos(DegToRad(endpoint1.longitude)),
R * Math.Cos(DegToRad(endpoint1.latitude)) * Math.Sin(DegToRad(endpoint1.longitude)),
R * Math.Sin(DegToRad(endpoint1.latitude)));
Point3D ep2cart = new Point3D(
R * Math.Cos(DegToRad(endpoint2.latitude)) * Math.Cos(DegToRad(endpoint2.longitude)),
R * Math.Cos(DegToRad(endpoint2.latitude)) * Math.Sin(DegToRad(endpoint2.longitude)),
R * Math.Sin(DegToRad(endpoint2.latitude)));
Point3D ptcart = new Point3D(
R * Math.Cos(DegToRad(this.latitude)) * Math.Cos(DegToRad(this.longitude)),
R * Math.Cos(DegToRad(this.latitude)) * Math.Sin(DegToRad(this.longitude)),
R * Math.Sin(DegToRad(this.latitude)));
Point3D origin = new Point3D(0, 0, 0);
double d = ((ptcart - ep1cart).CrossProduct(ptcart - ep2cart)).Magnitude() / (ep2cart - ep1cart).Magnitude();
double hypotenuse = ptcart.DistanceTo(ep1cart);
double theta = Math.Asin(d/hypotenuse);
double adjacent = d / Math.Tan(theta);
Point3D closestcart = ep1cart.MoveTowards(ep2cart, adjacent);
Point3D surfacecart = origin.MoveTowards(closestcart, R);
return new Coordinate(
(int)(RadToDeg(Math.Asin(surfacecart.Z / R)) * 1E6),
(int)(RadToDeg(Math.Atan2(surfacecart.Y, surfacecart.X)) * 1E6));
}
/// <summary>
/// Calculates the Euclidian distance between this point and another point.
/// </summary>
/// <param name="p">The point to measure the distance to.</param>
/// <returns>The distance between this point and point p.</returns>
public double DistanceTo(Point3D p)
{
return Math.Sqrt(Math.Pow(p.X - this.X, 2) + Math.Pow(p.Y - this.Y, 2) + Math.Pow(p.Z - this.Z, 2));
}
/// <summary>
/// Calculate the result of moving this point a given distance towards another point.
/// </summary>
/// <param name="p">The point to move towards.</param>
/// <param name="distance">The distance to move. It is possible to move past either endpoint.</param>
/// <returns>A point representing the result of moving this point towards the other.</returns>
public Point3D MoveTowards(Point3D p, double distance)
{
Point3D directionVector = p - this;
directionVector = directionVector / directionVector.Magnitude();
return (directionVector * distance) + this;
}
/// <summary>
/// Calculates the cross product of two points as vectors positioned on the origin.
/// </summary>
/// <param name="p">The point to cross with.</param>
/// <returns>The cross product of the points.</returns>
public Point3D CrossProduct(Point3D p)
{
return new Point3D(
this.Y * p.Z - this.Z * p.Y,
this.Z * p.X - this.X * p.Z,
this.X * p.Y - this.Y * p.X);
}