add geom/line.cpp

Author: snuke

README.md

@@ -46,4 +46,5 @@ AtCoder解説放送ライブラリ集
 |:--|:--|:--|
 |基本|[geom.cpp](geom.cpp)|幾何のベース＋目次|
 |Vector|[geom/vector.cpp](geom/vector.cpp)|ベクトル（点を扱う際にも使う）|
+|Line|[geom/line.cpp](geom/line.cpp)|直線・線分|
 |Circle|[geom/circle.cpp](geom/circle.cpp)|円|

geom.cpp

@@ -3,4 +3,5 @@ const double eps = 1e-9;
 bool equal(double a, double b) { return abs(a-b) < eps;}
 
 [geom/vector]
+[geom/line]
 [geom/circle]

geom/line.cpp

@@ -0,0 +1,23 @@
+struct Line {
+  V s, t;
+  Line(V s=V(0,0), V t=V(0,0)):s(s),t(t){}
+  V dir() const { return t-s;}
+  V normalize() const { return dir().normalize();}
+  double norm() const { return dir().norm();}
+  /* +1: s-t,s-p : ccw
+   * -1: s-t,s-p : cw
+   * +2: t-s-p
+   * -2: s-t-p
+   *  0: s-p-t */
+  int ccw(const V& p) const {
+    if (dir().cross(p-s) > eps) return +1;
+    if (dir().cross(p-s) < -eps) return -1;
+    if (dir().dot(p-s) < -eps) return +2;
+    if (dir().norm()+eps < (p-s).norm()) return -2;
+    return 0;
+  }
+  bool touch(const Line& l) const {
+    int a = ccw(l.s)*ccw(l.t), b = l.ccw(s)*l.ccw(t);
+    return !a || !b || (a == -1 && b == -1);
+  }
+};

geom/vector.cpp

@@ -15,6 +15,7 @@ struct V {
   double cross(const V& v) const { return x*v.y - v.x*y;}
   double norm2() const { return x*x + y*y;}
   double norm() const { return sqrt(norm2());}
+  V normalize() const { return *this/norm();}
   V rotate90() const { return V(y, -x);}
   int ort() const { // orthant
     if (abs(x) < eps && abs(y) < eps) return 0;