using System;

using System.Collections.Generic;

public class Program

{

    public static Random random;

    public static void Main()

    {

        random = new Random();

        var Vertices = new List<string>();

        var Faces = new List<string>();

        var p = new Vector2(551, -17);

        var p1 = new Vector3(561.5292, 214.9312, -19.92188);

        var p2 = new Vector3(537.413, 215.8389, -10.5);

        var p3 = new Vector3(550.4863, 214.7789, -21.1875);

        if (GetBarycentricCoordinate(p1, p2, p3, p))

        {

            var v4 = new Vector4(p.X, GetDeterminant(p1, p2, p3, p), p.Y, random.NextDouble() * 2 * Math.PI - Math.PI);

            Console.WriteLine(v4.X.ToString("F3") + " " + v4.Y.ToString("F3") + " " + v4.Z.ToString("F3") + " " + v4.W.ToString("F3"));

        }

    }

    public static bool GetBarycentricCoordinate(Vector3 p1, Vector3 p2, Vector3 p3, Vector2 p)

    {

        double lambda1 = ((p2.Z - p3.Z)*(p.X - p3.X) + (p3.X - p2.X)*(p.Y - p3.Z)) /

            ((p2.Z - p3.Z)*(p1.X - p3.X) + (p3.X - p2.X)*(p1.Z - p3.Z));

        double lambda2 = ((p3.Z - p1.Z)*(p.X - p3.X) + (p1.X - p3.X)*(p.Y - p3.Z)) /

            ((p2.Z - p3.Z)*(p1.X - p3.X) + (p3.X - p2.X)*(p1.Z - p3.Z));

        double lambda3 = 1 - lambda1 - lambda2;

        if (lambda1 > 0 && lambda2 > 0 && lambda3 > 0)

            return true;

        else

            return false;

    }

    public static double GetDeterminant(Vector3 p1, Vector3 p2, Vector3 p3, Vector2 p)

    {

        double aei = (p.X - p1.X)*(p2.Y - p1.Y)*(p3.Z - p1.Z);

        double fg = (p2.Z - p1.Z)*(p3.X - p1.X);

        double cdh = (p.Y - p1.Z)*(p2.X - p1.X)*(p3.Y - p1.Y);

        double ceg = (p.Y - p1.Z)*(p2.Y - p1.Y)*(p3.X - p1.X);

        double di = (p2.X - p1.X)*(p3.Z - p1.Z);

        double afh = (p.X - p1.X)*(p2.Z - p1.Z)*(p3.Y - p1.Y);

        return (double)((aei + cdh - ceg - afh) / (di - fg)) + p1.Y;

    }

}

​

public class Vector2

{

    public Vector2(double x, double y)

    {

        X = x;

        Y = y;

    }

    public double X { get; set; }

    public double Y { get; set; }

}

​

public class Vector3

{

    public Vector3(double x, double y, double z)

    {

        X = x;

        Y = y;

        Z = z;

    }

    public double X { get; set; }

    public double Y { get; set; }

    public double Z { get; set; }

}

​

public class Vector4

{

    public Vector4(double x, double y, double z, double w)

    {

        X = x;

        Y = y;

        Z = z;

        W = w;

    }

    public double X { get; set; }

    public double Y { get; set; }

    public double Z { get; set; }

    public double W { get; set; }

}