geometry/reflection.hpp

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Last update: 2022-09-11 00:53:50+09:00
Include: #include "geometry/reflection.hpp"
Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B

Depends on

Verified with

test/verify/aoj-cgl-1-b.test.cpp

Code

#include "point.hpp"
#include "line.hpp"
#include "projection.hpp"

namespace geometry {
  // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B
  Point reflection(const Line &l, const Point &p) {
    return p + (projection(l, p) - p) * 2;
  }
}

#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 3 "geometry/line.hpp"

namespace geometry {
  struct Line {
    Point a, b;

    Line() = default;

    Line(const Point &a, const Point &b) : a(a), b(b) {}

    Line(const Real &A, const Real &B, const Real &C) { // Ax+By=C
      if(equals(A, 0)) {
        assert(!equals(B, 0));
        a = Point(0, C / B);
        b = Point(1, C / B);
      } else if(equals(B, 0)) {
        a = Point(C / A, 0);
        b = Point(C / A, 1);
      } else {
        a = Point(0, C / B);
        b = Point(C / A, 0);
      }
    }

    friend ostream &operator<<(ostream &os, Line &l) {
      return os << l.a << " to " << l.b;
    }

    friend istream &operator>>(istream &is, Line &l) {
      return is >> l.a >> l.b;
    }
  };

  using Lines = vector< Line >;
}
#line 2 "geometry/projection.hpp"

#line 5 "geometry/projection.hpp"

namespace geometry {
  // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_A
  Point projection(const Line &l, const Point &p) {
    auto t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
    return l.a + (l.a - l.b) * t;
  }
}
#line 4 "geometry/reflection.hpp"

namespace geometry {
  // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B
  Point reflection(const Line &l, const Point &p) {
    return p + (projection(l, p) - p) * 2;
  }
}