geometry/is-point-on-segment.hpp

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• Last update: 2026-08-30 15:33:14+09:00
• Include: #include "geometry/is-point-on-segment.hpp"

Depends on

• geometry/base.hpp

Required by

• 幾何ライブラリ (geometry/geometry.hpp)

Verified with

• test/mytest/geometry/geometry.test.cpp

Code

#pragma once

#include "base.hpp"

namespace geometry {
    // 点cが"線分"ab上にあるか
    inline bool isPointOnSegment(const Point &a, const Point &b, const Point &c) {
        // |a-c| + |c-b| <= |a-b| なら線分上
        return (std::abs(a - c) + std::abs(c - b) < std::abs(a - b) + EPS);
    }
} // namespace geometry

#line 2 "geometry/is-point-on-segment.hpp"

#line 2 "geometry/base.hpp"

#include <cmath>
#include <complex>

namespace geometry {
    // Point : 複素数型を位置ベクトルとして扱う
    // 実軸(real)をx軸、挙軸(imag)をy軸として見る
    using D = long double;
    using Point = std::complex<D>;
    const D EPS = 1e-7;
    const D PI = std::acos(D(-1));

    inline bool equal(const D &a, const D &b) { return std::fabs(a - b) < EPS; }
} // namespace geometry
#line 4 "geometry/is-point-on-segment.hpp"

namespace geometry {
    // 点cが"線分"ab上にあるか
    inline bool isPointOnSegment(const Point &a, const Point &b, const Point &c) {
        // |a-c| + |c-b| <= |a-b| なら線分上
        return (std::abs(a - c) + std::abs(c - b) < std::abs(a - b) + EPS);
    }
} // namespace geometry

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