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:heavy_check_mark: Src/GeometryR2/CircumscribedCircle.hpp

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#pragma once

#include "./Circle.hpp"
#include "./Segment.hpp"
#include "./Bisector/PerpendicularBisector.hpp"
#include "./CrossPoint/LineAndLine.hpp"
#include "./Distance/PointAndPoint.hpp"

#include <optional>

namespace zawa {

namespace geometryR2 {

std::optional<Circle> CircumscribedCircle(const Point& p0, const Point& p1, const Point& p2) {
    if (Zero(Cross(p1 - p0, p2 - p0))) return std::nullopt;
    const Point c = CrossPoint(
           PerpendicularBisector(Segment{p0, p1}),
           PerpendicularBisector(Segment{p0, p2})
           );
    const Real r = Distance(p0, c);
    return Circle{c, r};
}

} // namespace geometryR2

} // namespace zawa
#line 2 "Src/GeometryR2/CircumscribedCircle.hpp"

#line 2 "Src/GeometryR2/Circle.hpp"

#line 2 "Src/Template/TypeAlias.hpp"

#include <cstdint>
#include <cstddef>

namespace zawa {

using i16 = std::int16_t;
using i32 = std::int32_t;
using i64 = std::int64_t;
using i128 = __int128_t;

using u8 = std::uint8_t;
using u16 = std::uint16_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;

using usize = std::size_t;

} // namespace zawa
#line 2 "Src/GeometryR2/Real.hpp"

#line 4 "Src/GeometryR2/Real.hpp"

#include <cmath>
#include <cassert>

namespace zawa {

namespace geometryR2 {

using Real = long double;

namespace internal {

Real EPS{1e-12};
constexpr i32 negative{-1};
constexpr i32 zero{};
constexpr i32 positive{1};

} // namespace internal

Real& Eps() {
    return internal::EPS;
}

i32 Sign(Real value) {
    if (value < -Eps()) return internal::negative;
    if (value > Eps()) return internal::positive;
    return internal::zero;
}

bool Zero(Real value) {
    return Sign(value) == internal::zero;
}

bool Positive(Real value) {
    return Sign(value) == internal::positive;
}

bool Negative(Real value) {
    return Sign(value) == internal::negative;
}

bool Equal(Real a, Real b) {
    return Zero(a - b);
}

bool Smaller(Real a, Real b) {
    return Negative(a - b);
}

bool Bigger(Real a, Real b) {
    return Positive(a - b);
}

Real Square(Real value) {
    return (Zero(value) ? value : value * value);
}

Real Sqrt(Real value) {
    assert(!Negative(value));
    return (Zero(value) ? value : sqrtl(value));
}

Real Abs(Real value) {
    return (Negative(value) ? -value : value);
}

} // namespace geometryR2
 
} // namespace zawa
#line 2 "Src/GeometryR2/Point.hpp"

#line 2 "Src/GeometryR2/Angle.hpp"

#line 4 "Src/GeometryR2/Angle.hpp"

#line 6 "Src/GeometryR2/Angle.hpp"

namespace zawa {

namespace geometryR2 {

constexpr Real PI{acosl(-1)};
constexpr Real TAU{static_cast<Real>(2) * PI};

constexpr Real ArcToRadian(Real arc) {
    return (arc * PI) / static_cast<Real>(180);
}

constexpr Real RadianToArc(Real radian) {
    return (radian * static_cast<Real>(180)) / PI;
}

} // namespace geometryR2

} // namespace zawa
#line 5 "Src/GeometryR2/Point.hpp"

#line 7 "Src/GeometryR2/Point.hpp"
#include <iostream>
#line 9 "Src/GeometryR2/Point.hpp"

namespace zawa {

namespace geometryR2 {

class Point {
private:
    Real x_{}, y_{};
public:
    /* constructor */
    Point() = default;
    Point(Real x, Real y) : x_{x}, y_{y} {}

    /* getter, setter */
    Real x() const {
        return x_;
    }
    Real& x() {
        return x_;
    }
    Real y() const {
        return y_;
    }
    Real& y() {
        return y_;
    }

    /* operator */
    Point& operator+=(const Point& rhs) {
        x_ += rhs.x();
        y_ += rhs.y();
        return *this;
    }
    friend Point operator+(const Point& lhs, const Point& rhs) {
        return Point{lhs} += rhs;
    }
    Point operator+() const {
        return *this;
    }
    Point& operator-=(const Point& rhs) {
        x_ -= rhs.x();
        y_ -= rhs.y();
        return *this;
    }
    friend Point operator-(const Point& lhs, const Point& rhs) {
        return Point{lhs} -= rhs;
    }
    Point operator-() const {
        return Point{} - *this;
    }
    Point& operator*=(Real k) {
        x_ *= k;
        y_ *= k;
        return *this;
    }
    friend Point operator*(Real k, const Point& p) {
        return Point{p} *= k;
    }
    friend Point operator*(const Point& p, Real k) {
        return Point{p} *= k;
    }
    Point& operator/=(Real k) {
        assert(!Zero(k));
        x_ /= k;
        y_ /= k;
        return *this;
    }
    friend Point operator/(Real k, const Point& p) {
        return Point{p} /= k;
    }
    friend Point operator/(const Point& p, Real k) {
        return Point{p} /= k;
    }
    friend bool operator==(const Point& lhs, const Point& rhs) {
        return Equal(lhs.x(), rhs.x()) and Equal(lhs.y(), rhs.y());
    }
    friend bool operator!=(const Point& lhs, const Point& rhs) {
        return !Equal(lhs.x(), rhs.x()) or !Equal(lhs.y(), rhs.y());
    }
    friend bool operator<(const Point& lhs, const Point& rhs) {
        return Smaller(lhs.x(), rhs.x()) or 
            (Equal(lhs.x(), rhs.x()) and Smaller(lhs.y(), rhs.y()));
    }
    friend bool operator<=(const Point& lhs, const Point& rhs) {
        return Smaller(lhs.x(), rhs.x()) or 
            (Equal(lhs.x(), rhs.x()) and (Smaller(lhs.y(), rhs.y()) or Equal(lhs.y(), rhs.y())));
    }
    friend bool operator>(const Point& lhs, const Point& rhs) {
        return Bigger(lhs.x(), rhs.x()) or
            (Equal(lhs.x(), rhs.x()) and Bigger(lhs.y(), rhs.y()));
    }
    friend bool operator>=(const Point& lhs, const Point& rhs) {
        return Bigger(lhs.x(), rhs.x()) or
            (Equal(lhs.x(), rhs.x()) and (Bigger(lhs.y(), rhs.y()) or Equal(lhs.y(), rhs.y())));
    }
    friend std::istream& operator>>(std::istream& is, Point& p) {
        is >> p.x_ >> p.y_;
        return is;
    }
    friend std::ostream& operator<<(std::ostream& os, const Point& p) {
        os << '(' << p.x_ << ',' << p.y_ << ')';
        return os;
    }
    
    /* member function */
    Real normSquare() const {
        return Square(x_) + Square(y_);
    }
    Real norm() const {
        return Sqrt(normSquare());
    }
    void normalize() {
        assert((*this) != Point{});
        (*this) /= norm(); 
    }
    Point normalized() const {
        Point res{*this};
        res.normalize();
        return res;
    }
    Point rotated(Real radian) const {
        return Point{
            x_ * cosl(radian) - y_ * sinl(radian),
            x_ * sinl(radian) + y_ * cosl(radian)
        };
    }
    void rotate(Real radian) {
        *this = rotated(radian); 
    }
    Point rotatedByArc(Real arc) const {
        return rotated(ArcToRadian(arc));
    }
    void rotateByArc(Real arc) {
        *this = rotatedByArc(arc);
    }
    Real argument() const {
        return (Negative(y_) ? TAU : static_cast<Real>(0)) + atan2l(y_, x_);
    }
    Real argumentByArc() const {
        return RadianToArc(argument());
    }

    /* friend function */
    friend Real Dot(const Point& lhs, const Point& rhs) {
        return lhs.x() * rhs.x() + lhs.y() * rhs.y();
    }
    friend Real Cross(const Point& lhs, const Point& rhs) {
        return lhs.x() * rhs.y() - lhs.y() * rhs.x();
    }
    friend Real Argument(const Point& lhs, const Point& rhs) {
        return rhs.argument() - lhs.argument();
    }
    friend bool ArgComp(const Point& lhs, const Point& rhs) {
        return Smaller(lhs.argument(), rhs.argument());
    }
};

using Vector = Point;

} // namespace geometryR2

} // namespace zawa
#line 2 "Src/GeometryR2/Distance/PointAndPoint.hpp"

#line 4 "Src/GeometryR2/Distance/PointAndPoint.hpp"

namespace zawa {

namespace geometryR2 {

Real Distance(const Point& p0, const Point& p1) {
    return Point{p1 - p0}.norm();
}

Real DistanceSquare(const Point& p0, const Point& p1) {
    return Point{p1 - p0}.normSquare();
}

} // namespace geometryR2

} // namespace zawa
#line 7 "Src/GeometryR2/Circle.hpp"

#line 9 "Src/GeometryR2/Circle.hpp"
#include <utility>

namespace zawa {

namespace geometryR2 {

class Circle {
private:
    Point center_{};
    Real radius_{};
public:
    /* constructor */
    Circle() = default;
    Circle(const Point& center, Real radius) : center_{center}, radius_{radius} {
        assert(!Negative(radius));
    }
    Circle(Real x, Real y, Real r) : center_{x, y}, radius_{r} {
        assert(!Negative(r));
    }

    /* getter setter */
    const Point& center() const {
        return center_;
    }
    Point& center() {
        return center_;
    }
    Real radius() const {
        return radius_;
    }
    Real& radius() {
        return radius_;
    }

    /* operator */
    friend bool operator==(const Circle& lhs, const Circle& rhs) {
        return lhs.center() == rhs.center() and Equal(lhs.radius(), rhs.radius());
    }
    friend bool operator!=(const Circle& lhs, const Circle& rhs) {
        return lhs.center() != rhs.center() or !Equal(lhs.radius(), rhs.radius());
    }

    /* friend function */
    friend u32 NumberCommonTangent(const Circle& c0, const Circle& c1) {
        Real dist{DistanceSquare(c0.center(), c1.center())};
        Real down{Square(Abs(c0.radius() - c1.radius()))};
        if (Smaller(dist, down)) return 0;
        if (Equal(dist, down)) return 1;
        Real up{Square(c0.radius() + c1.radius())};
        if (Smaller(dist, up)) return 2;
        if (Equal(dist, up)) return 3;
        return 4;
    }
};

} // namespace geometryR2

} // namespace zawa
#line 2 "Src/GeometryR2/Segment.hpp"

#line 2 "Src/GeometryR2/Relation.hpp"

#line 5 "Src/GeometryR2/Relation.hpp"

namespace zawa {

namespace geometryR2 {

enum RELATION {
    // p0 -> p1 -> p2の順で直線上に並んでいる
    ONLINE_FRONT = -2,
    // (p1 - p0) -> (p2 - p0)が時計回りになっている
    CLOCKWISE,
    // p0 -> p2 -> p1の順で直線上に並んでいる
    ON_SEGMENT,
    // (p1 - p0) -> (p2 - p0)が反時計回りになっている
    COUNTER_CLOCKWISE,
    // p2 -> p0 -> p1、またはp1 -> p0 -> p2の順で直線上に並んでいる
    ONLINE_BACK
};

RELATION Relation(const Point& p0, const Point& p1, const Point& p2) {
    Point a{p1 - p0}, b{p2 - p0};
    if (Positive(Cross(a, b))) return COUNTER_CLOCKWISE;
    if (Negative(Cross(a, b))) return CLOCKWISE;
    if (Negative(Dot(a, b))) return ONLINE_BACK;
    if (Smaller(a.normSquare(), b.normSquare())) return ONLINE_FRONT;
    return ON_SEGMENT;
};

} // namespace geometryR2

} // namespace zawa
#line 6 "Src/GeometryR2/Segment.hpp"

#include <algorithm>
#line 9 "Src/GeometryR2/Segment.hpp"

namespace zawa {

namespace geometryR2 {

class Segment {
private:
    Point p0_{}, p1_{};
public:
    /* constructor */
    Segment() = default;
    Segment(const Point& p0, const Point& p1) : p0_{p0}, p1_{p1} {}
    Segment(Real x0, Real y0, Real x1, Real y1) : p0_{x0, y0}, p1_{x1, y1} {}

    /* getter setter */
    const Point& p0() const {
        return p0_;
    }
    Point& p0() {
        return p0_;
    }
    const Point& p1() const {
        return p1_;
    }
    Point& p1() {
        return p1_;
    }

    /* member function */
    bool valid() const {
        return p0_ != p1_;
    }
    bool straddle(const Segment& s) const {
        return Relation(p0_, p1_, s.p0()) * Relation(p0_, p1_, s.p1()) <= 0;
    }
    Real length() const {
        assert(valid());
        return Distance(p0_, p1_);
    }
    Point midpoint() const {
        assert(valid());
        return p0_ + Vector{p1_ - p0_} / static_cast<Real>(2);
    }
};

} // namespace geometryR2

} // namespace zawa
#line 2 "Src/GeometryR2/Bisector/PerpendicularBisector.hpp"

#line 2 "Src/GeometryR2/Line.hpp"

#line 5 "Src/GeometryR2/Line.hpp"

#line 7 "Src/GeometryR2/Line.hpp"

namespace zawa {

namespace geometryR2 {

class Line {
private:
    Point p0_{}, p1_{};
public:
    /* constructor */
    Line() = default;
    Line(const Point& p0, const Point& p1) : p0_{p0}, p1_{p1} {}
    // y = ax + b 
    Line(Real a, Real b) : p0_{static_cast<Real>(0), b}, p1_{static_cast<Real>(1), a + b} {}

    /* getter, setter */
    const Point& p0() const {
        return p0_;
    }
    Point& p0() {
        return p0_;
    }
    const Point& p1() const {
        return p1_;
    }
    Point& p1() {
        return p1_;
    }

    /* operator */
    friend bool operator==(const Line& l0, const Line& l1) {
        return Zero(Cross(l0.p1() - l0.p0(), l1.p1() - l1.p0())) and Zero(Cross(l0.p1() - l0.p0(), l1.p1() - l0.p0()));
    }
    friend bool operator!=(const Line& l0, const Line& l1) {
        return !Zero(Cross(l0.p1() - l0.p0(), l1.p1() - l1.p0())) or !Zero(Cross(l0.p1() - l0.p0(), l1.p1() - l0.p0()));
    }

    /* member function */
    bool valid() const {
        return p0_ != p1_;
    }
    Vector slope() const {
        assert(valid());
        return Vector{p1() - p0()}.normalized();
    }
};

} // namespace geometryR2

} // namespace zawa
#line 6 "Src/GeometryR2/Bisector/PerpendicularBisector.hpp"

#line 8 "Src/GeometryR2/Bisector/PerpendicularBisector.hpp"

namespace zawa {

namespace geometryR2 {

Line PerpendicularBisector(const Segment& s) {
    assert(s.valid());
    Point midpoint{s.midpoint()}; 
    Vector vertical{Vector{s.p1() - s.p0()}.rotatedByArc(90)};
    return Line{midpoint, midpoint + vertical};
}

} // namespace geometryR2

} // namespace zawa
#line 2 "Src/GeometryR2/CrossPoint/LineAndLine.hpp"

#line 2 "Src/GeometryR2/Intersect/LineAndLine.hpp"

#line 4 "Src/GeometryR2/Intersect/LineAndLine.hpp"

#line 6 "Src/GeometryR2/Intersect/LineAndLine.hpp"

namespace zawa {

namespace geometryR2 {

bool Intersect(const Line& l0, const Line& l1) {
    assert(l0.valid());
    assert(l1.valid());
    if (!Zero(Cross(l0.p1() - l0.p0(), l1.p1() - l1.p0()))) {
        return true;
    }
    else if (!Zero(Cross(l0.p1() - l0.p0(), l1.p0() - l0.p0()))) {
        return false;
    }
    else {
        return true;
    }
}

} // namespace geometryR2

} // namespace 
#line 6 "Src/GeometryR2/CrossPoint/LineAndLine.hpp"

#line 8 "Src/GeometryR2/CrossPoint/LineAndLine.hpp"

namespace zawa {

namespace geometryR2 {

Point CrossPoint(const Line& l0, const Line& l1) {
    assert(l0.valid());
    assert(l1.valid());
    assert(Intersect(l0, l1));
    assert(l0 != l1);
    return l0.p0() + (l0.p1() - l0.p0()) * 
        (Cross(l1.p0() - l0.p0(), l1.p1() - l1.p0()) / Cross(l0.p1() - l0.p0(), l1.p1() - l1.p0()));
}

} // namespace geometryR2

} // namespace zawa
#line 8 "Src/GeometryR2/CircumscribedCircle.hpp"

#include <optional>

namespace zawa {

namespace geometryR2 {

std::optional<Circle> CircumscribedCircle(const Point& p0, const Point& p1, const Point& p2) {
    if (Zero(Cross(p1 - p0, p2 - p0))) return std::nullopt;
    const Point c = CrossPoint(
           PerpendicularBisector(Segment{p0, p1}),
           PerpendicularBisector(Segment{p0, p2})
           );
    const Real r = Distance(p0, c);
    return Circle{c, r};
}

} // namespace geometryR2

} // namespace zawa
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