static void ClosestPlane()
{
//Collect data from user
Console.Write("Enter the x coordinate of the ship (km): ");
float x = Convert.ToSingle(Console.ReadLine());
Console.Write("Enter the y coordinate of the ship (km): ");
float y = Convert.ToSingle(Console.ReadLine());
Console.Write("Enter the z coordinate of the ship (km): ");
float z = Convert.ToSingle(Console.ReadLine());
Vector3D ship = new Vector3D(x, y, z); //km
Console.WriteLine("First planar point:");
Console.Write("Enter the x coordinate (km): ");
x = Convert.ToSingle(Console.ReadLine());
Console.Write("Enter the y coordinate (km): ");
y = Convert.ToSingle(Console.ReadLine());
Console.Write("Enter the z coordinate (km): ");
z = Convert.ToSingle(Console.ReadLine());
Vector3D point1 = new Vector3D(x, y, z); //km
Console.WriteLine("Second planar point:");
Console.Write("Enter the x coordinate (km): ");
x = Convert.ToSingle(Console.ReadLine());
Console.Write("Enter the y coordinate (km): ");
y = Convert.ToSingle(Console.ReadLine());
Console.Write("Enter the z coordinate (km): ");
z = Convert.ToSingle(Console.ReadLine());
Vector3D point2 = new Vector3D(x, y, z); //km
Console.WriteLine("Third planar point:");
Console.Write("Enter the x coordinate (km): ");
x = Convert.ToSingle(Console.ReadLine());
Console.Write("Enter the y coordinate (km): ");
y = Convert.ToSingle(Console.ReadLine());
Console.Write("Enter the z coordinate (km): ");
z = Convert.ToSingle(Console.ReadLine());
Vector3D point3 = new Vector3D(x, y, z); //km
if (point1 == point2 || point2 == point3 || point3 == point1) //check if points are the same
{
Console.WriteLine("Error: Redundant points entered.");
}
else
{
//The mathening
Vector3D point1To2 = point2 - point1; //km, one vector within the plane
Vector3D point1To3 = point3 - point1; //km, another vector within the plane
if ((!point1To2) == (!point1To3) || (!point1To2) == -1 * (!point1To3)) //check if points are on a single line
{
Console.WriteLine("Error: Collinear points entered.");
}
else
{
Vector3D normal = !(point1To2 % point1To3); //the planar normal, normalized to remove units
Vector3D closestPoint = ship.ClosestPointPlane(point1, normal); //km, the closest point on the plane
//Output
Console.WriteLine("Closest Point is: " + closestPoint + " km");
Console.WriteLine("Distance of closest approach is: {0:N2} km", (closestPoint - ship).GetMagnitude());
}
}
}
