triangles.cs

using System;
using System.Collections.Generic;
using System.Linq;

namespace KataTriangles
{
    class Program
    {       
        static void Main(string[] args)
        {
            var triangles = new List<List<(double x, double y)>> {
                new List<(double x, double y)> { (0,0),(0,10),(5,10) },
                new List<(double x, double y)> { (0,0),(0,10),(6,10) },
                new List<(double x, double y)> { (1,9),(2,6),(3,9) },
                new List<(double x, double y)> { (1,0),(1,5),(8,0) },
                new List<(double x, double y)> { (14,0),(16,5),(18,0) },
                new List<(double x, double y)> { (-3,0),(0,0),(0,5) },
                new List<(double x, double y)> { (-3,-4),(-1,1),(1,-6) },
            };

            IsTrue(() => TriangleCompare(triangles[0], triangles[0]) == Intersect.Enclosed).Show();
            IsTrue(() => TriangleCompare(triangles[0], triangles[1]) == Intersect.Enclosed).Show();
            IsTrue(() => TriangleCompare(triangles[2], triangles[0]) == Intersect.Enclosed).Show();
            IsTrue(() => TriangleCompare(triangles[1], triangles[0]) == Intersect.Enclosing).Show();
            IsTrue(() => TriangleCompare(triangles[0], triangles[3]) == Intersect.Overlapping).Show();
            IsTrue(() => TriangleCompare(triangles[3], triangles[0]) == Intersect.Overlapping).Show();
            IsTrue(() => TriangleCompare(triangles[5], triangles[6]) == Intersect.Overlapping).Show();
            IsTrue(() => TriangleCompare(triangles[0], triangles[5]) == Intersect.Overlapping).Show();
            IsTrue(() => TriangleCompare(triangles[0], triangles[4]) == Intersect.Separated).Show();
        }

        static Intersect TriangleCompare(List<(double x, double y)> t1, List<(double x, double y)> t2)
        {
            if (t1.All(t => PointInside(t, t2[0], t2[1], t2[2])))
                return Intersect.Enclosed;
                
            if (t2.All(t => PointInside(t, t1[0], t1[1], t1[2])))
                return Intersect.Enclosing;
                
            if (t1.Any(t => PointInside(t, t2[0], t2[1], t2[2])) ||
                t2.Any(t => PointInside(t, t1[0], t1[1], t1[2])))
                return Intersect.Overlapping;
                    
            return Intersect.Separated;
        }

        static double sign((double x, double y) p1, 
                           (double x, double y) p2, 
                           (double x, double y) p3)
        {
            return (p1.x - p3.x) * (p2.y - p3.y) - (p2.x - p3.x) * (p1.y - p3.y);
        }

        static bool PointInside((double x, double y) pt, 
            (double x, double y) v1, 
            (double x, double y) v2, 
            (double x, double y) v3)
        {
            double d1, d2, d3;
            bool has_neg, has_pos;

            d1 = sign(pt, v1, v2);
            d2 = sign(pt, v2, v3);
            d3 = sign(pt, v3, v1);

            has_neg = (d1 < 0) || (d2 < 0) || (d3 < 0);
            has_pos = (d1 > 0) || (d2 > 0) || (d3 > 0);

            return !(has_neg && has_pos);
        }

        static bool IsTrue(Func<bool> predicate) {
            return predicate();
        }
    }

    enum Intersect
    {
        Enclosed,
        Enclosing,
        Overlapping,
        Separated
    }

    static class Ext
    {
        public static void Show(this object o)
        {
            Console.WriteLine(o.ToString());
        }

    }
}