Project Euler p102 - finding origin

Problem description:
-----------------------------------------------------
Three distinct points are plotted at random on a Cartesian plane, for which -1000 ≤ x, y ≤ 1000, such that a triangle is formed.

Consider the following two triangles:

A(-340,495), B(-153,-910), C(835,-947)

X(-175,41), Y(-421,-714), Z(574,-645)

It can be verified that triangle ABC contains the origin, whereas triangle XYZ does not.

Using triangles.txt (right click and 'Save Link/Target As...'), a 27K text file containing the co-ordinates of one thousand "random" triangles, find the number of triangles for which the interior contains the origin.

NOTE: The first two examples in the file represent the triangles in the example given above.
-----------------------------------------------------

I`ve exploited the idea that for origin to be in the triangle interior, triangle lines segments should cross x and y axis 2 times: x+ / x- and y+ / y-.
Basically it is enough to check does triangle cross y+ and y- axis parts, but I didn`t know that and checked both axis. This worked too :-)

Solution ( C# as always):

---

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;

namespace ConsoleApplication1
{
    class Program
    {
        static int[][] ReadTriangleCoordinates(string file)
        {
            int[][] res;
            StreamReader sr = new StreamReader(file);
            res = Array.ConvertAll(sr.ReadToEnd().TrimEnd().Split("\n".ToCharArray()), 
                  s => {return Array.ConvertAll(s.Split(",".ToCharArray()),
                                         n => { return int.Parse(n); }) ;});
            sr.Close();
            return res;
        }

        static void CrossesAxisAt(int x1, 
                                  int y1, 
                                  int x2, 
                                  int y2, 
                                  out double? xAt, 
                                  out double? yAt)
        {
            int dx = x2 - x1;
            int dy = y2 - y1;
            int xmin = Math.Min(x1, x2);
            int ymin = Math.Min(y1, y2);
            int xmax = Math.Max(x1, x2);
            int ymax = Math.Max(y1, y2);
            double? xcross;
            double? ycross;
            double a;
            double b;

            if (dx == 0)
            {
                xcross = x1;
                ycross = null;
            }
            else if (dy == 0)
            {
                xcross = null;
                ycross = y1;
            }
            else
            {
                a = (double)dy / (double)dx;
                b = y1 - (a * x1);
                xcross = -(b / a);
                ycross = b;
            }

            if (xcross != null)
            {
                if (xcross < xmin || xcross > xmax 
                                  || ymin > 0 || ymax < 0)
                    xcross = null;
            }

            if (ycross != null)
            {
                if (ycross < ymin || ycross > ymax 
                                  || xmin > 0 || xmax < 0)
                    ycross = null;
            }

            xAt = xcross;
            yAt = ycross;
        }

        static bool ContainsOrigin(int[] abc)
        {
            double? xc1, xc2, xc3;
            double? yc1, yc2, yc3;
            int xposc = 0, xnegc = 0, yposc = 0, ynegc = 0;
            bool res;

            CrossesAxisAt(abc[0], abc[1], abc[4], abc[5], out xc1, out yc1);
            CrossesAxisAt(abc[0], abc[1], abc[2], abc[3], out xc2, out yc2);
            CrossesAxisAt(abc[2], abc[3], abc[4], abc[5], out xc3, out yc3);

            xposc = ((xc1 > 0) ? 1 : 0) + ((xc2 > 0) ? 1 : 0) + ((xc3 > 0) ? 1 : 0);
            xnegc = ((xc1 < 0) ? 1 : 0) + ((xc2 < 0) ? 1 : 0) + ((xc3 < 0) ? 1 : 0);
            yposc = ((yc1 > 0) ? 1 : 0) + ((yc2 > 0) ? 1 : 0) + ((yc3 > 0) ? 1 : 0);
            ynegc = ((yc1 < 0) ? 1 : 0) + ((yc2 < 0) ? 1 : 0) + ((yc3 < 0) ? 1 : 0);

            if (xposc > 0 && xnegc > 0 && yposc > 0 && ynegc > 0)
                res = true;
            else
                res = false;

            return res;
        }

        static int TrianglesWithOrigin(string file)
        {
            int[][] tr = ReadTriangleCoordinates(file);
            int trcount = 0;

            for (int i = 0; i < tr.Length; i++)
            {
                if (ContainsOrigin(tr[i]))
                    trcount++;
            }

            return trcount;
        }

        static void Main(string[] args)
        {
            Console.WriteLine(TrianglesWithOrigin("C:\\ProjectEuler\\triangles.txt"));
            Console.ReadLine();
        }
    }
}

---