If two points intersect

src/Tour.cpp

@@ -116,6 +116,71 @@ void Tour::insertNearest(Point p) {
     nearest->next = newNode;
 }
 
+enum class Orientation { COLLINEAR, CLOCKWISE, COUNTER_CLOCKWISE };
+
+// 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
+
+// Calculate the calcOrientation of the triplet (p, q, r)
+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);
+
+    if (val == 0)
+        return Orientation::COLLINEAR;
+    return (val > 0) ? Orientation::CLOCKWISE : Orientation::COUNTER_CLOCKWISE;
+}
+// True if q lies on the segment p-r
+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) &&
+            q.y <= std::max(p.y, r.y) && q.y >= std::min(p.y, r.y));
+}
+// 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);
+
+    // 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;
+}
+
+bool Tour::pointsCross(Point &p1, Point &p2) {
+    if (m_startNode == nullptr || m_startNode->next == m_startNode)
+        return false;
+    Node *n1 = m_startNode, *n2 = m_startNode->next;
+    do {
+        Point &q1 = n1->point, &q2 = n2->point;
+        if (doesPointsIntersect(p1, p2, q1, q2))
+            return true;
+
+        n1 = n2;
+        n2 = n2->next;
+    } while (n1 != m_startNode);
+
+    return false;
+}
+
 void Tour::insertSmallest(Point p) {
     if (m_startNode == nullptr) {
         m_startNode = new Node(p);

src/Tour.h

@@ -27,6 +27,8 @@ public:
 
 private:
     Node* m_startNode;
+
+    bool pointsCross(Point &p1, Point &p2);
 };
 
 #endif // TOUR_H