geometry/is_convex_polygon.hpp

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• Last update: 2024-04-27 01:27:28+09:00
• Include: #include "geometry/is_convex_polygon.hpp"
• Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_B

Depends on

• geometry/base.hpp
• geometry/ccw.hpp
• geometry/point.hpp
• geometry/polygon.hpp

Verified with

• test/verify/aoj-cgl-3-b.test.cpp

Code

#include "ccw.hpp"
#include "point.hpp"
#include "polygon.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_B
bool is_convex_polygon(const Polygon &p) {
  int n = (int)p.size();
  for (int i = 0; i < n; i++) {
    if (ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]) == CLOCKWISE)
      return false;
  }
  return true;
}
}  // namespace geometry

#line 2 "geometry/base.hpp"

namespace geometry {
using Real = double;
const Real EPS = 1e-8;
const Real PI = acos(static_cast<Real>(-1));

enum { OUT, ON, IN };

inline int sign(const Real &r) { return r <= -EPS ? -1 : r >= EPS ? 1 : 0; }

inline bool equals(const Real &a, const Real &b) { return sign(a - b) == 0; }
}  // namespace geometry
#line 3 "geometry/point.hpp"

namespace geometry {
using Point = complex<Real>;

istream &operator>>(istream &is, Point &p) {
  Real a, b;
  is >> a >> b;
  p = Point(a, b);
  return is;
}

ostream &operator<<(ostream &os, const Point &p) {
  return os << real(p) << " " << imag(p);
}

Point operator*(const Point &p, const Real &d) {
  return Point(real(p) * d, imag(p) * d);
}

// rotate point p counterclockwise by theta rad
Point rotate(Real theta, const Point &p) {
  return Point(cos(theta) * real(p) - sin(theta) * imag(p),
               sin(theta) * real(p) + cos(theta) * imag(p));
}

Real cross(const Point &a, const Point &b) {
  return real(a) * imag(b) - imag(a) * real(b);
}

Real dot(const Point &a, const Point &b) {
  return real(a) * real(b) + imag(a) * imag(b);
}

bool compare_x(const Point &a, const Point &b) {
  return equals(real(a), real(b)) ? imag(a) < imag(b) : real(a) < real(b);
}

bool compare_y(const Point &a, const Point &b) {
  return equals(imag(a), imag(b)) ? real(a) < real(b) : imag(a) < imag(b);
}

using Points = vector<Point>;
}  // namespace geometry
#line 3 "geometry/ccw.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C
constexpr int COUNTER_CLOCKWISE = +1;
constexpr int CLOCKWISE = -1;
constexpr int ONLINE_BACK = +2;   // c-a-b
constexpr int ONLINE_FRONT = -2;  // a-b-c
constexpr int ON_SEGMENT = 0;     // a-c-b
int ccw(const Point &a, Point b, Point c) {
  b = b - a, c = c - a;
  if (sign(cross(b, c)) == +1) return COUNTER_CLOCKWISE;
  if (sign(cross(b, c)) == -1) return CLOCKWISE;
  if (sign(dot(b, c)) == -1) return ONLINE_BACK;
  if (norm(b) < norm(c)) return ONLINE_FRONT;
  return ON_SEGMENT;
}
}  // namespace geometry
#line 2 "geometry/polygon.hpp"

#line 4 "geometry/polygon.hpp"

namespace geometry {
using Polygon = vector<Point>;
using Polygons = vector<Polygon>;
}  // namespace geometry
#line 4 "geometry/is_convex_polygon.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_B
bool is_convex_polygon(const Polygon &p) {
  int n = (int)p.size();
  for (int i = 0; i < n; i++) {
    if (ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]) == CLOCKWISE)
      return false;
  }
  return true;
}
}  // namespace geometry

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