geometry/angle.hpp

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• Last update: 2022-09-11 00:53:50+09:00
• Include: #include "geometry/angle.hpp"

Depends on

• geometry/base.hpp
• geometry/point.hpp

Code

#include "point.hpp"

namespace geometry {
  Real radian_to_degree(const Real &theta) {
    return theta * 180.0 / PI;
  }

  Real degree_to_radian(const Real &deg) {
    return deg * PI / 180.0;
  }

  // smaller angle of the a-b-c
  Real get_smaller_angle(const Point &a, const Point &b, const Point &c) {
    const Point v(a - b), w(c - b);
    auto alpha = atan2(imag(v), real(v));
    auto beta = atan2(imag(w), real(w));
    if(alpha > beta) swap(alpha, beta);
    Real theta = (beta - alpha);
    return min(theta, 2 * PI - theta);
  }
}

#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;
  }
}
#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 >;
}
#line 2 "geometry/angle.hpp"

namespace geometry {
  Real radian_to_degree(const Real &theta) {
    return theta * 180.0 / PI;
  }

  Real degree_to_radian(const Real &deg) {
    return deg * PI / 180.0;
  }

  // smaller angle of the a-b-c
  Real get_smaller_angle(const Point &a, const Point &b, const Point &c) {
    const Point v(a - b), w(c - b);
    auto alpha = atan2(imag(v), real(v));
    auto beta = atan2(imag(w), real(w));
    if(alpha > beta) swap(alpha, beta);
    Real theta = (beta - alpha);
    return min(theta, 2 * PI - theta);
  }
}

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