Task: Determine if two triangles overlap
C: #include <errno.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>

typedef struct {
    double x, y;
} Point;

double det2D(const Point * const p1, const Point * const p2, const Point * const p3) {
    return p1->x * (p2->y - p3->y)
        + p2->x * (p3->y - p1->y)
        + p3->x * (p1->y - p2->y);
}

void checkTriWinding(Point * p1, Point * p2, Point * p3, bool allowReversed) {
    double detTri = det2D(p1, p2, p3);
    if (detTri < 0.0) {
        if (allowReversed) {
            double t = p3->x;
            p3->x = p2->x;
            p2->x = t;

            t = p3->y;
            p3->y = p2->y;
            p2->y = t;
        } else {
            errno = 1;
        }
    }
}

bool boundaryCollideChk(const Point *p1, const Point *p2, const Point *p3, double eps) {
    return det2D(p1, p2, p3) < eps;
}

bool boundaryDoesntCollideChk(const Point *p1, const Point *p2, const Point *p3, double eps) {
    return det2D(p1, p2, p3) <= eps;
}

bool triTri2D(Point t1[], Point t2[], double eps, bool allowReversed, bool onBoundary) {
    bool(*chkEdge)(Point*, Point*, Point*, double);
    int i;

    
    checkTriWinding(&t1[0], &t1[1], &t1[2], allowReversed);
    if (errno != 0) {
        return false;
    }
    checkTriWinding(&t2[0], &t2[1], &t2[2], allowReversed);
    if (errno != 0) {
        return false;
    }

    if (onBoundary) {
        
        chkEdge = boundaryCollideChk;
    } else {
        
        chkEdge = boundaryDoesntCollideChk;
    }

    
    for (i = 0; i < 3; ++i) {
        int j = (i + 1) % 3;

        
        
        if (chkEdge(&t1[i], &t1[j], &t2[0], eps) &&
            chkEdge(&t1[i], &t1[j], &t2[1], eps) &&
            chkEdge(&t1[i], &t1[j], &t2[2], eps)) {
            return false;
        }
    }

    
    for (i = 0; i < 3; i++) {
        int j = (i + 1) % 3;

        
        
        if (chkEdge(&t2[i], &t2[j], &t1[0], eps) &&
            chkEdge(&t2[i], &t2[j], &t1[1], eps) &&
            chkEdge(&t2[i], &t2[j], &t1[2], eps))
            return false;
    }

    
    return true;
}

int main() {
    {
        Point t1[] = { {0, 0}, {5, 0}, {0, 5} };
        Point t2[] = { {0, 0}, {5, 0}, {0, 6} };
        printf("%d,true\n", triTri2D(t1, t2, 0.0, false, true));
    }

    {
        Point t1[] = { {0, 0}, {0, 5}, {5, 0} };
        Point t2[] = { {0, 0}, {0, 5}, {5, 0} };
        printf("%d,true\n", triTri2D(t1, t2, 0.0, true, true));
    }

    {
        Point t1[] = { {0, 0}, {5, 0}, {0, 5} };
        Point t2[] = { {-10, 0}, {-5, 0}, {-1, 6} };
        printf("%d,false\n", triTri2D(t1, t2, 0.0, false, true));
    }

    {
        Point t1[] = { {0, 0}, {5, 0}, {2.5, 5} };
        Point t2[] = { {0, 4}, {2.5, -1}, {5, 4} };
        printf("%d,true\n", triTri2D(t1, t2, 0.0, false, true));
    }

    {
        Point t1[] = { {0, 0}, {1, 1}, {0, 2} };
        Point t2[] = { {2, 1}, {3, 0}, {3, 2} };
        printf("%d,false\n", triTri2D(t1, t2, 0.0, false, true));
    }

    {
        Point t1[] = { {0, 0}, {1, 1}, {0, 2} };
        Point t2[] = { {2, 1}, {3, -2}, {3, 4} };
        printf("%d,false\n", triTri2D(t1, t2, 0.0, false, true));
    }

    
    {
        Point t1[] = { {0, 0}, {1, 0}, {0, 1} };
        Point t2[] = { {1, 0}, {2, 0}, {1, 1} };
        printf("%d,true\n", triTri2D(t1, t2, 0.0, false, true));
    }

    
    {
        Point t1[] = { {0, 0}, {1, 0}, {0, 1} };
        Point t2[] = { {1, 0}, {2, 0}, {1, 1} };
        printf("%d,false\n", triTri2D(t1, t2, 0.0, false, false));
    }

    return EXIT_SUCCESS;
}

C#: using System;
using System.Collections.Generic;

namespace TriangleOverlap {
    class Triangle {
        public Tuple<double, double> P1 { get; set; }
        public Tuple<double, double> P2 { get; set; }
        public Tuple<double, double> P3 { get; set; }

        public Triangle(Tuple<double, double> p1, Tuple<double, double> p2, Tuple<double, double> p3) {
            P1 = p1;
            P2 = p2;
            P3 = p3;
        }

        public double Det2D() {
            return P1.Item1 * (P2.Item2 - P3.Item2)
                 + P2.Item1 * (P3.Item2 - P1.Item2)
                 + P3.Item1 * (P3.Item1 - P2.Item2);
        }

        public void CheckTriWinding(bool allowReversed) {
            var detTri = Det2D();
            if (detTri < 0.0) {
                if (allowReversed) {
                    var a = P3;
                    P3 = P2;
                    P2 = a;
                } else {
                    throw new Exception("Triangle has wrong winding direction");
                }
            }
        }

        public bool BoundaryCollideChk(double eps) {
            return Det2D() < eps;
        }

        public bool BoundaryDoesntCollideChk(double eps) {
            return Det2D() <= eps;
        }

        public override string ToString() {
            return string.Format("Triangle: {0}, {1}, {2}", P1, P2, P3);
        }
    }

    class Program {
        static bool BoundaryCollideChk(Triangle t, double eps) {
            return t.BoundaryCollideChk(eps);
        }

        static bool BoundaryDoesntCollideChk(Triangle t, double eps) {
            return t.BoundaryDoesntCollideChk(eps);
        }

        static bool TriTri2D(Triangle t1, Triangle t2, double eps = 0.0, bool allowReversed = false, bool onBoundary = true) {
            
            t1.CheckTriWinding(allowReversed);
            t2.CheckTriWinding(allowReversed);
            
            var chkEdge = onBoundary
                ? (Func<Triangle, double, bool>)BoundaryCollideChk
                : BoundaryDoesntCollideChk;
            List<Tuple<double, double>> lp1 = new List<Tuple<double, double>>() { t1.P1, t1.P2, t1.P3 };
            List<Tuple<double, double>> lp2 = new List<Tuple<double, double>>() { t2.P1, t2.P2, t2.P3 };

            
            for (int i = 0; i < 3; i++) {
                var j = (i + 1) % 3;
                
                
                if (chkEdge(new Triangle(lp1[i], lp1[j], lp2[0]), eps) &&
                    chkEdge(new Triangle(lp1[i], lp1[j], lp2[1]), eps) &&
                    chkEdge(new Triangle(lp1[i], lp1[j], lp2[2]), eps)) {
                    return false;
                }
            }

            
            for (int i = 0; i < 3; i++) {
                var j = (i + 1) % 3;
                
                
                if (chkEdge(new Triangle(lp2[i], lp2[j], lp1[0]), eps) &&
                    chkEdge(new Triangle(lp2[i], lp2[j], lp1[1]), eps) &&
                    chkEdge(new Triangle(lp2[i], lp2[j], lp1[2]), eps)) {
                    return false;
                }
            }

            
            return true;
        }

        static void Overlap(Triangle t1, Triangle t2, double eps = 0.0, bool allowReversed = false, bool onBoundary = true) {
            if (TriTri2D(t1, t2, eps, allowReversed, onBoundary)) {
                Console.WriteLine("overlap");
            } else {
                Console.WriteLine("do not overlap");
            }
        }

        static void Main(string[] args) {
            var t1 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(5.0, 0.0), new Tuple<double, double>(0.0, 5.0));
            var t2 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(5.0, 0.0), new Tuple<double, double>(0.0, 6.0));
            Console.WriteLine("{0} and\n{1}", t1, t2);
            Overlap(t1, t2);
            Console.WriteLine();

            
            t1 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(0.0, 5.0), new Tuple<double, double>(5.0, 0.0));
            t2 = t1;
            Console.WriteLine("{0} and\n{1}", t1, t2);
            Overlap(t1, t2, 0.0, true);
            Console.WriteLine();

            t1 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(5.0, 0.0), new Tuple<double, double>(0.0, 5.0));
            t2 = new Triangle(new Tuple<double, double>(-10.0, 0.0), new Tuple<double, double>(-5.0, 0.0), new Tuple<double, double>(-1.0, 6.0));
            Console.WriteLine("{0} and\n{1}", t1, t2);
            Overlap(t1, t2);
            Console.WriteLine();

            t1.P3 = new Tuple<double, double>(2.5, 5.0);
            t2 = new Triangle(new Tuple<double, double>(0.0, 4.0), new Tuple<double, double>(2.5, -1.0), new Tuple<double, double>(5.0, 4.0));
            Console.WriteLine("{0} and\n{1}", t1, t2);
            Overlap(t1, t2);
            Console.WriteLine();

            t1 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(1.0, 1.0), new Tuple<double, double>(0.0, 2.0));
            t2 = new Triangle(new Tuple<double, double>(2.0, 1.0), new Tuple<double, double>(3.0, 0.0), new Tuple<double, double>(3.0, 2.0));
            Console.WriteLine("{0} and\n{1}", t1, t2);
            Overlap(t1, t2);
            Console.WriteLine();

            t2 = new Triangle(new Tuple<double, double>(2.0, 1.0), new Tuple<double, double>(3.0, -2.0), new Tuple<double, double>(3.0, 4.0));
            Console.WriteLine("{0} and\n{1}", t1, t2);
            Overlap(t1, t2);
            Console.WriteLine();

            t1 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(1.0, 0.0), new Tuple<double, double>(0.0, 1.0));
            t2 = new Triangle(new Tuple<double, double>(1.0, 0.0), new Tuple<double, double>(2.0, 0.0), new Tuple<double, double>(1.0, 1.1));
            Console.WriteLine("{0} and\n{1}", t1, t2);
            Console.WriteLine("which have only a single corner in contact, if boundary points collide");
            Overlap(t1, t2);
            Console.WriteLine();

            Console.WriteLine("{0} and\n{1}", t1, t2);
            Console.WriteLine("which have only a single corner in contact, if boundary points do not collide");
            Overlap(t1, t2, 0.0, false, false);
        }
    }
}