geometry/reflection.hpp

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• Last update: 2026-08-10 07:05:08+00:00
• Include: #include "geometry/reflection.hpp"
• Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B

Depends on

• geometry/base.hpp
• geometry/line.hpp
• geometry/point.hpp
• geometry/projection.hpp

Verified with

• test/verify/aoj-cgl-1-b.test.cpp

Code

#pragma once

#include "line.hpp"
#include "point.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;
}
}  // namespace geometry

#line 2 "geometry/reflection.hpp"

#line 2 "geometry/line.hpp"

#include <cassert>
#include <iostream>
#include <vector>

#line 2 "geometry/point.hpp"

#include <cmath>
#include <complex>
#line 7 "geometry/point.hpp"

#line 2 "geometry/base.hpp"

#line 4 "geometry/base.hpp"

namespace geometry {
using Real = double;
const Real EPS = 1e-8;
const Real PI = std::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 9 "geometry/point.hpp"

namespace geometry {
using Point = std::complex<Real>;

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

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

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

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

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

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

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

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

using Points = std::vector<Point>;
}  // namespace geometry
#line 8 "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 if (equals(C, 0)) {
      a = Point(0, C / B);
      b = Point(1, (C - A) / B);
    } else {
      a = Point(0, C / B);
      b = Point(C / A, 0);
    }
  }

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

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

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

#line 4 "geometry/projection.hpp"

#line 7 "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) / std::norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}
}  // namespace geometry
#line 6 "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;
}
}  // namespace geometry

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