teamnote history merge

2025spring/source/Geometry/namespace_geometry.cpp

@@ -0,0 +1,109 @@
+template <typename T> 
+class Point {
+public:
+    T x, y;
+    Point() : x(0), y(0) {};
+    Point(T _x, T _y) : x(_x), y(_y) {};
+
+    Point operator+(Point p2){
+        return Point(x + p2.x, y + p2.y);
+    }
+    Point operator-(Point p2){
+        return Point(x - p2.x, y - p2.y);
+    }
+    T operator*(Point p2){
+        return x * p2.x + y * p2.y;
+    }
+    T operator/(Point p2) {
+        return x * p2.y - p2.x * y;
+    }
+    T operator==(Point p2) {
+        return (x == p2.x) && (y == p2.y);
+    }
+    T sqdist() {
+        return x*x + y*y;
+    }
+    bool operator<(Point p2) {
+        if(y == p2.y)
+            return x < p2.x;
+        return y < p2.y;
+    }
+
+};  
+
+namespace geometry {
+    template <typename T> 
+    ll ccw(Point<T> center, Point<T> p2, Point<T> p3) {
+        ll res = (p2 - center) / (p3 - center);
+        return (res > 0) - (res < 0);
+    }
+
+    template <typename T> 
+    double theta(Point<T> center, Point<T> p2, Point<T> p3) {
+        return acos(p2 * p3 / sqrt(p2.sqdist() * p3.sqdist()));
+    }
+
+    template <typename T> 
+    function<bool(Point<T> &, Point<T> &, Point<T>)> cmp_point = [](Point<T> &l, Point<T> &r, Point<T> O = {(T)0, (T)0}) -> bool {
+        return (l < O) != (r < O) ? l < r : l/r > 0;
+    };
+
+    template <typename T> 
+    T sq_dist(Point<T> &p1, Point<T> &p2) {
+        return (p2.x - p1.x)*(p2.x - p1.x) + (p2.y - p1.y)*(p2.y - p1.y);
+    }
+
+    template <typename T>
+    double dist(Point<T> &p1, Point<T> &p2) {
+        return sqrt((double)sq_dist(p1, p2));
+    }
+
+    template <typename T>
+    double line_point_dist(pair<Point<T>, Point<T>> &l, Point<T> p)
+    {
+        Point<T> p1 = p - l.first, p2 = l.second - l.first;
+        return abs(p1 / p2)/(dist(l.first, l.second));
+    }
+
+    template <typename T>
+    double line_min_dist(pair<Point<T>, Point<T>> &l1, pair<Point<T>, Point<T>> &l2) {
+        double ans = INFINITY;
+        ans = min({ans, dist(l1.first, l2.first), dist(l1.first, l2.second), dist(l1.second, l2.first), dist(l1.second, l2.second)});
+
+        if((l1.second - l1.first)*(l2.first - l1.first) > 0 && (l1.first - l1.second)*(l2.first - l1.second) > 0)
+            ans = min({ans, line_point_dist<double>(l1, l2.first)});
+        if((l1.second - l1.first)*(l2.second - l1.first) > 0 && (l1.first - l1.second)*(l2.second - l1.second) > 0)
+            ans = min({ans, line_point_dist<double>(l1, l2.second)});
+        swap(l1, l2);
+        if((l1.second - l1.first)*(l2.first - l1.first) > 0 && (l1.first - l1.second)*(l2.first - l1.second) > 0)
+            ans = min({ans, line_point_dist<double>(l1, l2.first)});
+        if((l1.second - l1.first)*(l2.second - l1.first) > 0 && (l1.first - l1.second)*(l2.second - l1.second) > 0)
+            ans = min({ans, line_point_dist<double>(l1, l2.second)});
+        swap(l1, l2);
+        return ans;
+    }
+
+    template <typename T> 
+    vector<T> convex_hull(vector<Point<T>> &pts) {
+        assert(pts.size() >= 2);
+        vector<Point<T>> res;
+
+        swap(pts[0], *min_element(pts.begin(), pts.end()));
+        sort(pts.begin()+1, pts.end(), [&pts](Point<T> &a, Point<T> &b){
+            ll cw = ccw(pts[0], a, b);
+            if(cw) return cw > 0;
+            return sq_dist(pts[0], a) < sq_dist(pts[0], b);
+        });
+        auto itr = pts.begin();
+        res.push_back(*(itr++)); res.push_back(*(itr++));
+
+        while(itr != pts.end())
+        {
+            while(res.size() >= 2 && ccw(res[res.size()-2], res[res.size()-1], *itr) <= 0)
+                res.pop_back();
+            res.push_back(*(itr++));
+        }
+        return res;
+    }
+}
+using namespace geometry;