geometry/projection.hpp

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

Depends on

• geometry/base.hpp
• geometry/dot.hpp
• geometry/line.hpp
• geometry/segment.hpp

Required by

• geometry/convex-cut.hpp
• geometry/cross-point.hpp
• 幾何ライブラリ (geometry/geometry.hpp)
• geometry/reflection.hpp
• geometry/tangent-to-circle.hpp

Verified with

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

Code

#pragma once

#include "dot.hpp"
#include "line.hpp"
#include "segment.hpp"

namespace geometry {
    // 射影(projection)
    // 直線(線分)lに点pから引いた垂線の足を求める
    inline Point projection(const Line &l, const Point &p) {
        D t = dot(p - l.a, l.a - l.b) / std::norm(l.a - l.b);
        return l.a + (l.a - l.b) * t;
    }

    inline Point projection(const Segment &l, const Point &p) {
        D 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 2 "geometry/projection.hpp"

#line 2 "geometry/dot.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/dot.hpp"

namespace geometry {
    // 内積(dot product) : a・b = |a||b|cosΘ
    inline D dot(const Point &a, const Point &b) {
        return (a.real() * b.real() + a.imag() * b.imag());
    }
} // namespace geometry
#line 2 "geometry/line.hpp"

#line 4 "geometry/line.hpp"

namespace geometry {
    // Line : 直線を表す構造体
    // b - a で直線・線分を表せる
    struct Line {
        Point a, b;
        Line() = default;
        Line(Point a, Point b) : a(a), b(b) {}
        // Ax+By=C
        Line(D A, D B, D C) {
            if(equal(A, 0)) {
                a = Point(0, C / B), b = Point(1, C / B);
            } else if(equal(B, 0)) {
                a = Point(C / A, 0), b = Point(C / A, 1);
            } else if(equal(C, 0)) {
                a = Point(0, C / B), b = Point(1, (C - A) / B);
            } else {
                a = Point(0, C / B), b = Point(C / A, 0);
            }
        }
    };
} // namespace geometry
#line 2 "geometry/segment.hpp"

#line 4 "geometry/segment.hpp"

namespace geometry {
    // Segment : 線分を表す構造体
    // Lineと同じ
    struct Segment : Line {
        Segment() = default;

        Segment(Point a, Point b) : Line(a, b) {}
        D get_dist() { return std::abs(a - b); }
    };
} // namespace geometry
#line 6 "geometry/projection.hpp"

namespace geometry {
    // 射影(projection)
    // 直線(線分)lに点pから引いた垂線の足を求める
    inline Point projection(const Line &l, const Point &p) {
        D t = dot(p - l.a, l.a - l.b) / std::norm(l.a - l.b);
        return l.a + (l.a - l.b) * t;
    }

    inline Point projection(const Segment &l, const Point &p) {
        D 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

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