If two points intersect

src/Tour.cpp

@@ -116,46 +116,69 @@ void Tour::insertNearest(Point p) {
     nearest->next = newNode;
 }
 
-Node *findbestNodeTSP(Node *const start, Point &point) {
+enum class Orientation { COLLINEAR, CLOCKWISE, COUNTER_CLOCKWISE };
-    auto calcHeuristic = [&point](Node *const insertAt) -> double {
-        double distanceWithNewPoint = insertAt->point.distanceTo(point) +
-                                      point.distanceTo(insertAt->next->point);
-        double originalDistance = insertAt->point.distanceTo(insertAt->next->point);
 
-        return distanceWithNewPoint - originalDistance;
+// I'm not going to pretend that I came up with this on my own.
-    };
+// The description for the algorithms is found both in the
+// linear algebra course, and on this wiki
+// https://en.wikipedia.org/w/index.php?title=Line-line_intersection&oldid=1229564037
 
-    double optimalH = Q_INFINITY;
+// Calculate the calcOrientation of the triplet (p, q, r)
-    Node *optimalNode;
+inline Orientation calcOrientation(const Point &p, const Point &q, const Point &r) {
+    int val = (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);
 
-    Node *node = start;
+    if (val == 0)
-    do {
+        return Orientation::COLLINEAR;
-        double h = calcHeuristic(node);
+    return (val > 0) ? Orientation::CLOCKWISE : Orientation::COUNTER_CLOCKWISE;
-        if (h < optimalH) {
+}
-            optimalH = h;
+// True if q lies on the segment p-r
-            optimalNode = node;
+inline bool isOnSegment(const Point &p, const Point &q, const Point &r) {
-        }
+    return (q.x <= std::max(p.x, r.x) && q.x >= std::min(p.x, r.x) &&
-        node = node->next;
+            q.y <= std::max(p.y, r.y) && q.y >= std::min(p.y, r.y));
-    } while (node != start);
+}
+// Check if the two line segments p1q1 and p2q2 intersect
+bool doesPointsIntersect(const Point &p1, const Point &q1, const Point &p2,
+                     const Point &q2) {
+    Orientation o1 = calcOrientation(p1, q1, p2);
+    Orientation o2 = calcOrientation(p1, q1, q2);
+    Orientation o3 = calcOrientation(p2, q2, p1);
+    Orientation o4 = calcOrientation(p2, q2, q1);
 
-    return optimalNode;
+    // General case: line segments intersect if they have different orientations
+    if (o1 != o2 && o3 != o4)
+        return true;
+
+    // Special cases
+    // p1, q1, p2 are collinear and p2 lies on segment p1q1
+    if (o1 == Orientation::COLLINEAR && isOnSegment(p1, p2, q1))
+        return true;
+    // p1, q1, q2 are collinear and q2 lies on segment p1q1
+    if (o2 == Orientation::COLLINEAR && isOnSegment(p1, q2, q1))
+        return true;
+    // p2, q2, p1 are collinear and p1 lies on segment p2q2
+    if (o3 == Orientation::COLLINEAR && isOnSegment(p2, p1, q2))
+        return true;
+    // p2, q2, q1 are collinear and q1 lies on segment p2q2
+    if (o4 == Orientation::COLLINEAR && isOnSegment(p2, q1, q2))
+        return true;
+
+    return false;
 }
 
-void Tour::insertOptimalHeuristic(Point p) {
+bool Tour::pointsCross(Point &p1, Point &p2) {
-    if (m_startNode == nullptr) {
+    if (m_startNode == nullptr || m_startNode->next == m_startNode)
-        m_startNode = new Node(p);
+        return false;
-        m_startNode->next = m_startNode; // Make it cirkular
+    Node *n1 = m_startNode, *n2 = m_startNode->next;
-        return;
+    do {
-    }
+        Point &q1 = n1->point, &q2 = n2->point;
-    if (m_startNode->next == nullptr) {
+        if (doesPointsIntersect(p1, p2, q1, q2))
-        auto newNode = new Node(p, m_startNode);
+            return true;
-        m_startNode->next = newNode;
-        return;
-    }
 
-    Node *bestNode = findbestNodeTSP(m_startNode, p);
+        n1 = n2;
-    auto *newNode = new Node(p, bestNode->next);
+        n2 = n2->next;
-    bestNode->next = newNode;
+    } while (n1 != m_startNode);
+
+    return false;
 }
 
 void Tour::insertSmallest(Point p) {

src/Tour.h

@@ -24,10 +24,11 @@ public:
     double distance() const;
     void insertNearest(Point p);
     void insertSmallest(Point p);
-    void insertOptimalHeuristic(Point p);
 
 private:
     Node* m_startNode;
+
+    bool pointsCross(Point &p1, Point &p2);
 };
 
 #endif // TOUR_H

src/tsp.cpp

@@ -49,7 +49,7 @@ int main(int argc, char *argv[]) {
     auto timeStart = std::chrono::high_resolution_clock::now();
     while (input >> x >> y) {
         Point p(x, y);
-        tour.insertOptimalHeuristic(p);
+        tour.insertNearest(p);
         //uncomment the 4 lines below to animate
         //tour.draw(scene);
         //std::chrono::milliseconds dura(50);