#line 1 "verify/geometry/half_plane_intersection_random.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "geometry/half_plane_intersection.hpp"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstddef>
#include <deque>
#include <limits>
#include <numbers>
#include <optional>
#include <random>
#include <utility>
#include <vector>
#line 1 "geometry/linear.hpp"
#line 7 "geometry/linear.hpp"
#line 1 "geometry/point.hpp"
#line 5 "geometry/point.hpp"
#include <concepts>
#line 7 "geometry/point.hpp"
#include <type_traits>
#line 1 "geometry/detail/floating_predicate.hpp"
namespace m1une {
namespace geometry {
namespace predicate_detail {
template <typename T>
constexpr T absolute(T value) {
return value < T(0) ? -value : value;
}
template <typename T>
constexpr T max_value(T first, T second) {
return first < second ? second : first;
}
template <typename T>
constexpr T vector_scale(T x, T y) {
return max_value(absolute(x), absolute(y));
}
template <bool Exact, typename T>
constexpr int scaled_sign(T value, T scale, long double eps) {
if constexpr (Exact) {
return (value > T(0)) - (value < T(0));
} else {
const T tolerance = T(eps) * scale;
return (value > tolerance) - (value < -tolerance);
}
}
template <bool Exact, typename T>
constexpr T determinant_scale(T ax, T ay, T bx, T by) {
if constexpr (Exact) {
return T(0);
} else {
return vector_scale(ax, ay) * vector_scale(bx, by);
}
}
template <bool Exact, typename T>
constexpr int determinant_sign(
T ax,
T ay,
T bx,
T by,
long double eps
) {
const T determinant = ax * by - ay * bx;
return scaled_sign<Exact>(
determinant,
determinant_scale<Exact>(ax, ay, bx, by),
eps
);
}
template <bool Exact, typename T>
constexpr int orientation_sign(
T direction_x,
T direction_y,
T offset_x,
T offset_y,
long double eps
) {
const T determinant =
direction_x * offset_y - direction_y * offset_x;
T scale = T(0);
if constexpr (!Exact) {
const T direction_scale =
vector_scale(direction_x, direction_y);
scale = direction_scale * max_value(
direction_scale,
vector_scale(offset_x, offset_y)
);
}
return scaled_sign<Exact>(determinant, scale, eps);
}
template <bool Exact, typename T>
constexpr int dot_sign(
T ax,
T ay,
T bx,
T by,
long double eps
) {
const T value = ax * bx + ay * by;
T scale = T(0);
if constexpr (!Exact) {
scale = vector_scale(ax, ay) * vector_scale(bx, by);
}
return scaled_sign<Exact>(value, scale, eps);
}
} // namespace predicate_detail
} // namespace geometry
} // namespace m1une
#line 10 "geometry/point.hpp"
namespace m1une {
namespace geometry {
template <typename T>
concept Coordinate = !std::same_as<std::remove_cv_t<T>, bool> &&
(std::is_arithmetic_v<T> ||
(std::copyable<T> && std::totally_ordered<T> && requires(T a, T b) {
T(0);
T(1);
static_cast<long double>(a);
{ +a } -> std::same_as<T>;
{ -a } -> std::same_as<T>;
{ a + b } -> std::same_as<T>;
{ a - b } -> std::same_as<T>;
{ a * b } -> std::same_as<T>;
{ a / b } -> std::same_as<T>;
{ a += b } -> std::same_as<T&>;
{ a -= b } -> std::same_as<T&>;
}));
// Custom coordinate types keep their own exact arithmetic.
template <typename T>
concept ExactCoordinate = Coordinate<T> && !std::floating_point<T>;
template <Coordinate T>
using wide_type = std::conditional_t<std::integral<T>, __int128_t,
std::conditional_t<std::floating_point<T>, long double, T>>;
template <Coordinate T>
struct Point {
T x;
T y;
constexpr Point() : x(0), y(0) {}
constexpr Point(T x_value, T y_value) : x(x_value), y(y_value) {}
template <Coordinate U>
explicit constexpr Point(const Point<U>& other)
: x(static_cast<T>(other.x)), y(static_cast<T>(other.y)) {}
constexpr Point& operator+=(const Point& other) {
x += other.x;
y += other.y;
return *this;
}
constexpr Point& operator-=(const Point& other) {
x -= other.x;
y -= other.y;
return *this;
}
constexpr Point operator+() const {
return *this;
}
constexpr Point operator-() const {
return Point(-x, -y);
}
friend constexpr Point operator+(Point left, const Point& right) {
return left += right;
}
friend constexpr Point operator-(Point left, const Point& right) {
return left -= right;
}
friend constexpr bool operator==(const Point&, const Point&) = default;
friend constexpr bool operator<(const Point& left, const Point& right) {
if (left.x != right.x) return left.x < right.x;
return left.y < right.y;
}
};
template <Coordinate T>
constexpr Point<long double> centroid(const Point<T>& point) {
return Point<long double>(point);
}
template <Coordinate T, typename Scalar>
requires (std::is_arithmetic_v<Scalar> || Coordinate<Scalar>)
constexpr auto operator*(const Point<T>& point, Scalar scalar) {
using Result = std::common_type_t<T, Scalar>;
return Point<Result>(
Result(point.x) * Result(scalar),
Result(point.y) * Result(scalar)
);
}
template <typename Scalar, Coordinate T>
requires (std::is_arithmetic_v<Scalar> || Coordinate<Scalar>)
constexpr auto operator*(Scalar scalar, const Point<T>& point) {
return point * scalar;
}
template <Coordinate T, typename Scalar>
requires (std::is_arithmetic_v<Scalar> || Coordinate<Scalar>)
constexpr auto operator/(const Point<T>& point, Scalar scalar) {
using Result = std::common_type_t<T, Scalar>;
return Point<Result>(
Result(point.x) / Result(scalar),
Result(point.y) / Result(scalar)
);
}
template <Coordinate T>
constexpr wide_type<T> dot(const Point<T>& a, const Point<T>& b) {
using W = wide_type<T>;
return W(a.x) * W(b.x) + W(a.y) * W(b.y);
}
template <Coordinate T>
constexpr wide_type<T> cross(const Point<T>& a, const Point<T>& b) {
using W = wide_type<T>;
return W(a.x) * W(b.y) - W(a.y) * W(b.x);
}
template <Coordinate T>
constexpr wide_type<T> cross(
const Point<T>& origin,
const Point<T>& a,
const Point<T>& b
) {
using W = wide_type<T>;
W ax = W(a.x) - W(origin.x);
W ay = W(a.y) - W(origin.y);
W bx = W(b.x) - W(origin.x);
W by = W(b.y) - W(origin.y);
return ax * by - ay * bx;
}
template <Coordinate T>
constexpr wide_type<T> norm2(const Point<T>& point) {
return dot(point, point);
}
template <Coordinate T>
constexpr wide_type<T> distance2(const Point<T>& a, const Point<T>& b) {
using W = wide_type<T>;
W dx = W(a.x) - W(b.x);
W dy = W(a.y) - W(b.y);
return dx * dx + dy * dy;
}
template <Coordinate T>
long double norm(const Point<T>& point) {
return std::hypot(
static_cast<long double>(point.x),
static_cast<long double>(point.y)
);
}
template <Coordinate T>
long double distance(const Point<T>& a, const Point<T>& b) {
return std::hypot(
static_cast<long double>(a.x) - static_cast<long double>(b.x),
static_cast<long double>(a.y) - static_cast<long double>(b.y)
);
}
template <Coordinate T, typename M, typename N>
requires (std::is_arithmetic_v<M> || Coordinate<M>) &&
(std::is_arithmetic_v<N> || Coordinate<N>)
constexpr Point<long double> internal_division_point(
const Point<T>& a,
const Point<T>& b,
M m,
N n
) {
long double first_ratio = static_cast<long double>(m);
long double second_ratio = static_cast<long double>(n);
long double denominator = first_ratio + second_ratio;
assert(denominator != 0);
Point<long double> first(a);
Point<long double> direction = Point<long double>(b) - first;
return first + direction * (first_ratio / denominator);
}
template <Coordinate T, typename M, typename N>
requires (std::is_arithmetic_v<M> || Coordinate<M>) &&
(std::is_arithmetic_v<N> || Coordinate<N>)
constexpr Point<long double> external_division_point(
const Point<T>& a,
const Point<T>& b,
M m,
N n
) {
long double first_ratio = static_cast<long double>(m);
long double second_ratio = static_cast<long double>(n);
long double denominator = first_ratio - second_ratio;
assert(denominator != 0);
Point<long double> first(a);
Point<long double> direction = Point<long double>(b) - first;
return first + direction * (first_ratio / denominator);
}
template <Coordinate T>
constexpr int sign(wide_type<T> value, long double eps = 1e-12L) {
return predicate_detail::scaled_sign<ExactCoordinate<T>>(
value,
wide_type<T>(1),
eps
);
}
template <Coordinate T>
constexpr int orientation(
const Point<T>& a,
const Point<T>& b,
const Point<T>& c,
long double eps = 1e-12L
) {
using W = wide_type<T>;
const W first_x = W(b.x) - W(a.x);
const W first_y = W(b.y) - W(a.y);
const W second_x = W(c.x) - W(a.x);
const W second_y = W(c.y) - W(a.y);
return predicate_detail::orientation_sign<ExactCoordinate<T>>(
first_x,
first_y,
second_x,
second_y,
eps
);
}
template <Coordinate T>
constexpr bool collinear(
const Point<T>& a,
const Point<T>& b,
const Point<T>& c,
long double eps = 1e-12L
) {
return orientation(a, b, c, eps) == 0;
}
template <Coordinate T>
Point<long double> rotate(const Point<T>& point, long double angle) {
long double cosine = std::cos(angle);
long double sine = std::sin(angle);
return Point<long double>(
static_cast<long double>(point.x) * cosine -
static_cast<long double>(point.y) * sine,
static_cast<long double>(point.x) * sine +
static_cast<long double>(point.y) * cosine
);
}
template <Coordinate T>
Point<long double> normalized(const Point<T>& point) {
long double length = norm(point);
assert(length != 0);
return Point<long double>(
static_cast<long double>(point.x) / length,
static_cast<long double>(point.y) / length
);
}
} // namespace geometry
} // namespace m1une
#line 9 "geometry/linear.hpp"
namespace m1une {
namespace geometry {
template <Coordinate T>
struct Line {
Point<T> a;
Point<T> b;
};
template <Coordinate T>
struct Segment {
Point<T> a;
Point<T> b;
};
template <Coordinate T>
struct Ray {
Point<T> origin;
Point<T> through;
};
enum class LinearIntersectionKind {
Empty,
Point,
Segment,
Ray,
Line,
};
struct LinearIntersection {
LinearIntersectionKind kind;
Point<long double> first;
Point<long double> second;
};
struct ClosestPoints {
Point<long double> first;
Point<long double> second;
};
namespace linear_intersection_detail {
inline LinearIntersection make_empty() {
const Point<long double> zero;
return LinearIntersection{
LinearIntersectionKind::Empty,
zero,
zero,
};
}
template <Coordinate T>
LinearIntersection make_point(const Point<T>& point) {
const Point<long double> converted(point);
return LinearIntersection{
LinearIntersectionKind::Point,
converted,
converted,
};
}
template <Coordinate T>
LinearIntersection make_object(
LinearIntersectionKind kind,
const Point<T>& first,
const Point<T>& second
) {
return LinearIntersection{
kind,
Point<long double>(first),
Point<long double>(second),
};
}
} // namespace linear_intersection_detail
template <Coordinate T>
constexpr Point<long double> centroid(const Segment<T>& segment) {
return Point<long double>(
(
static_cast<long double>(segment.a.x) +
static_cast<long double>(segment.b.x)
) / 2,
(
static_cast<long double>(segment.a.y) +
static_cast<long double>(segment.b.y)
) / 2
);
}
template <Coordinate T>
bool on_line(
const Line<T>& line,
const Point<T>& point,
long double eps = 1e-12L
) {
assert(line.a != line.b);
return orientation(line.a, line.b, point, eps) == 0;
}
template <Coordinate T>
bool parallel(const Line<T>& first, const Line<T>& second, long double eps = 1e-12L) {
using W = wide_type<T>;
W first_x = W(first.b.x) - W(first.a.x);
W first_y = W(first.b.y) - W(first.a.y);
W second_x = W(second.b.x) - W(second.a.x);
W second_y = W(second.b.y) - W(second.a.y);
return predicate_detail::determinant_sign<ExactCoordinate<T>>(
first_x,
first_y,
second_x,
second_y,
eps
) == 0;
}
template <Coordinate T>
bool orthogonal(const Line<T>& first, const Line<T>& second, long double eps = 1e-12L) {
using W = wide_type<T>;
W first_x = W(first.b.x) - W(first.a.x);
W first_y = W(first.b.y) - W(first.a.y);
W second_x = W(second.b.x) - W(second.a.x);
W second_y = W(second.b.y) - W(second.a.y);
return predicate_detail::dot_sign<ExactCoordinate<T>>(
first_x,
first_y,
second_x,
second_y,
eps
) == 0;
}
template <Coordinate T>
Point<long double> projection(const Line<T>& line, const Point<T>& point) {
assert(line.a != line.b);
Point<long double> a(line.a);
Point<long double> direction(
static_cast<long double>(line.b.x) - static_cast<long double>(line.a.x),
static_cast<long double>(line.b.y) - static_cast<long double>(line.a.y)
);
Point<long double> offset(
static_cast<long double>(point.x) - a.x,
static_cast<long double>(point.y) - a.y
);
long double ratio = dot(offset, direction) / dot(direction, direction);
return a + direction * ratio;
}
template <Coordinate T>
Point<long double> reflection(const Line<T>& line, const Point<T>& point) {
Point<long double> projected = projection(line, point);
return projected * 2.0L - Point<long double>(point);
}
template <Coordinate T>
bool intersects(
const Line<T>& first,
const Line<T>& second,
long double eps = 1e-12L
) {
return !parallel(first, second, eps) || on_line(first, second.a, eps);
}
template <Coordinate T>
bool on_segment(
const Segment<T>& segment,
const Point<T>& point,
long double eps = 1e-12L
) {
if (orientation(segment.a, segment.b, point, eps) != 0) return false;
using W = wide_type<T>;
const W direction_x = W(segment.b.x) - W(segment.a.x);
const W direction_y = W(segment.b.y) - W(segment.a.y);
if (direction_x == W(0) && direction_y == W(0)) {
if constexpr (ExactCoordinate<T>) {
return point == segment.a;
} else {
return
predicate_detail::absolute(W(point.x) - W(segment.a.x)) <= eps &&
predicate_detail::absolute(W(point.y) - W(segment.a.y)) <= eps;
}
}
const W offset_x = W(point.x) - W(segment.a.x);
const W offset_y = W(point.y) - W(segment.a.y);
const W projection =
offset_x * direction_x + offset_y * direction_y;
const W length_squared =
direction_x * direction_x + direction_y * direction_y;
return
predicate_detail::scaled_sign<ExactCoordinate<T>>(
projection,
length_squared,
eps
) >= 0 &&
predicate_detail::scaled_sign<ExactCoordinate<T>>(
projection - length_squared,
length_squared,
eps
) <= 0;
}
template <Coordinate T>
Point<long double> projection(
const Segment<T>& segment,
const Point<T>& point
) {
const Point<long double> first(segment.a);
const Point<long double> direction =
Point<long double>(segment.b) - first;
const long double length_squared = dot(direction, direction);
if (length_squared == 0) return first;
const long double ratio = std::clamp(
dot(Point<long double>(point) - first, direction) / length_squared,
0.0L,
1.0L
);
return first + direction * ratio;
}
template <Coordinate T>
bool intersects(
const Segment<T>& first,
const Segment<T>& second,
long double eps = 1e-12L
) {
int abc = orientation(first.a, first.b, second.a, eps);
int abd = orientation(first.a, first.b, second.b, eps);
int cda = orientation(second.a, second.b, first.a, eps);
int cdb = orientation(second.a, second.b, first.b, eps);
if (abc == 0 && on_segment(first, second.a, eps)) return true;
if (abd == 0 && on_segment(first, second.b, eps)) return true;
if (cda == 0 && on_segment(second, first.a, eps)) return true;
if (cdb == 0 && on_segment(second, first.b, eps)) return true;
return abc * abd < 0 && cda * cdb < 0;
}
template <Coordinate T>
bool intersects(
const Line<T>& line,
const Segment<T>& segment,
long double eps = 1e-12L
) {
int first_side = orientation(line.a, line.b, segment.a, eps);
int second_side = orientation(line.a, line.b, segment.b, eps);
return first_side == 0 || second_side == 0 || first_side != second_side;
}
template <Coordinate T>
bool intersects(
const Segment<T>& segment,
const Line<T>& line,
long double eps = 1e-12L
) {
return intersects(line, segment, eps);
}
namespace linear_parameter_detail {
template <Coordinate T>
struct Parameters {
wide_type<T> denominator;
wide_type<T> denominator_scale;
wide_type<T> first_numerator;
wide_type<T> second_numerator;
};
template <Coordinate T>
Parameters<T> parameters(
const Point<T>& first_origin,
const Point<T>& first_through,
const Point<T>& second_origin,
const Point<T>& second_through
) {
using W = wide_type<T>;
W first_x = W(first_through.x) - W(first_origin.x);
W first_y = W(first_through.y) - W(first_origin.y);
W second_x = W(second_through.x) - W(second_origin.x);
W second_y = W(second_through.y) - W(second_origin.y);
W offset_x = W(second_origin.x) - W(first_origin.x);
W offset_y = W(second_origin.y) - W(first_origin.y);
return Parameters<T>{
first_x * second_y - first_y * second_x,
predicate_detail::determinant_scale<ExactCoordinate<T>>(
first_x,
first_y,
second_x,
second_y
),
offset_x * second_y - offset_y * second_x,
offset_x * first_y - offset_y * first_x
};
}
template <Coordinate T>
int denominator_sign(const Parameters<T>& values, long double eps) {
return predicate_detail::scaled_sign<ExactCoordinate<T>>(
values.denominator,
values.denominator_scale,
eps
);
}
template <Coordinate T>
bool ratio_nonnegative(
wide_type<T> numerator,
wide_type<T> denominator,
long double eps
) {
const int numerator_sign =
predicate_detail::scaled_sign<ExactCoordinate<T>>(
numerator,
predicate_detail::absolute(denominator),
eps
);
const int denominator_direction =
(denominator > 0) - (denominator < 0);
return
numerator_sign == 0 ||
numerator_sign == denominator_direction;
}
template <Coordinate T>
bool ratio_in_unit_interval(
wide_type<T> numerator,
wide_type<T> denominator,
long double eps
) {
const auto scale = predicate_detail::absolute(denominator);
const int start_sign =
predicate_detail::scaled_sign<ExactCoordinate<T>>(
numerator,
scale,
eps
);
const int finish_sign =
predicate_detail::scaled_sign<ExactCoordinate<T>>(
numerator - denominator,
scale,
eps
);
if (denominator > 0) {
return start_sign >= 0 && finish_sign <= 0;
}
return start_sign <= 0 && finish_sign >= 0;
}
} // namespace linear_parameter_detail
template <Coordinate T>
bool on_ray(
const Ray<T>& ray,
const Point<T>& point,
long double eps = 1e-12L
) {
assert(ray.origin != ray.through);
if (orientation(ray.origin, ray.through, point, eps) != 0) return false;
using W = wide_type<T>;
W direction_x = W(ray.through.x) - W(ray.origin.x);
W direction_y = W(ray.through.y) - W(ray.origin.y);
W offset_x = W(point.x) - W(ray.origin.x);
W offset_y = W(point.y) - W(ray.origin.y);
const W projection =
direction_x * offset_x + direction_y * offset_y;
const W length_squared =
direction_x * direction_x + direction_y * direction_y;
return predicate_detail::scaled_sign<ExactCoordinate<T>>(
projection,
length_squared,
eps
) >= 0;
}
template <Coordinate T>
Point<long double> projection(const Ray<T>& ray, const Point<T>& point) {
assert(ray.origin != ray.through);
Point<long double> origin(ray.origin);
Point<long double> direction =
Point<long double>(ray.through) - origin;
Point<long double> offset = Point<long double>(point) - origin;
long double ratio = dot(offset, direction) / dot(direction, direction);
if (ratio < 0) ratio = 0;
return origin + direction * ratio;
}
template <Coordinate T>
Ray<long double> reflection(const Line<T>& line, const Ray<T>& ray) {
assert(ray.origin != ray.through);
return Ray<long double>{
reflection(line, ray.origin),
reflection(line, ray.through)
};
}
template <Coordinate T>
Ray<long double> reflected_ray(
const Ray<T>& incoming,
const Point<T>& hit,
const Line<T>& mirror,
long double eps = 1e-12L
) {
assert(incoming.origin != incoming.through);
assert(on_line(mirror, hit, eps));
Point<T> translated = hit + (incoming.through - incoming.origin);
return Ray<long double>{
Point<long double>(hit),
reflection(mirror, translated)
};
}
template <Coordinate T>
bool intersects(
const Ray<T>& ray,
const Line<T>& line,
long double eps = 1e-12L
) {
assert(ray.origin != ray.through);
assert(line.a != line.b);
linear_parameter_detail::Parameters<T> values =
linear_parameter_detail::parameters(
ray.origin,
ray.through,
line.a,
line.b
);
if (linear_parameter_detail::denominator_sign(values, eps) == 0) {
return on_line(line, ray.origin, eps);
}
return linear_parameter_detail::ratio_nonnegative<T>(
values.first_numerator,
values.denominator,
eps
);
}
template <Coordinate T>
bool intersects(
const Line<T>& line,
const Ray<T>& ray,
long double eps = 1e-12L
) {
return intersects(ray, line, eps);
}
template <Coordinate T>
bool intersects(
const Ray<T>& ray,
const Segment<T>& segment,
long double eps = 1e-12L
) {
assert(ray.origin != ray.through);
if (segment.a == segment.b) return on_ray(ray, segment.a, eps);
linear_parameter_detail::Parameters<T> values =
linear_parameter_detail::parameters(
ray.origin,
ray.through,
segment.a,
segment.b
);
if (linear_parameter_detail::denominator_sign(values, eps) == 0) {
if (orientation(ray.origin, ray.through, segment.a, eps) != 0) {
return false;
}
return on_ray(ray, segment.a, eps) ||
on_ray(ray, segment.b, eps) ||
on_segment(segment, ray.origin, eps);
}
return linear_parameter_detail::ratio_nonnegative<T>(
values.first_numerator,
values.denominator,
eps
) &&
linear_parameter_detail::ratio_in_unit_interval<T>(
values.second_numerator,
values.denominator,
eps
);
}
template <Coordinate T>
bool intersects(
const Segment<T>& segment,
const Ray<T>& ray,
long double eps = 1e-12L
) {
return intersects(ray, segment, eps);
}
template <Coordinate T>
bool intersects(
const Ray<T>& first,
const Ray<T>& second,
long double eps = 1e-12L
) {
assert(first.origin != first.through);
assert(second.origin != second.through);
linear_parameter_detail::Parameters<T> values =
linear_parameter_detail::parameters(
first.origin,
first.through,
second.origin,
second.through
);
if (linear_parameter_detail::denominator_sign(values, eps) == 0) {
if (orientation(first.origin, first.through, second.origin, eps) != 0) {
return false;
}
return on_ray(first, second.origin, eps) ||
on_ray(second, first.origin, eps);
}
return linear_parameter_detail::ratio_nonnegative<T>(
values.first_numerator,
values.denominator,
eps
) &&
linear_parameter_detail::ratio_nonnegative<T>(
values.second_numerator,
values.denominator,
eps
);
}
namespace linear_intersection_detail {
enum class Domain {
Line,
Segment,
Ray,
};
template <Coordinate T>
struct ParametricObject {
Point<T> origin;
Point<T> through;
Domain domain;
};
template <Coordinate T>
ParametricObject<T> parametric_object(const Line<T>& line) {
assert(line.a != line.b);
return ParametricObject<T>{line.a, line.b, Domain::Line};
}
template <Coordinate T>
ParametricObject<T> parametric_object(const Segment<T>& segment) {
return ParametricObject<T>{segment.a, segment.b, Domain::Segment};
}
template <Coordinate T>
ParametricObject<T> parametric_object(const Ray<T>& ray) {
assert(ray.origin != ray.through);
return ParametricObject<T>{ray.origin, ray.through, Domain::Ray};
}
template <Coordinate T>
bool contains(
const ParametricObject<T>& object,
const Point<T>& point,
long double eps
) {
if (object.domain == Domain::Line) {
return on_line(Line<T>{object.origin, object.through}, point, eps);
}
if (object.domain == Domain::Segment) {
return on_segment(
Segment<T>{object.origin, object.through},
point,
eps
);
}
return on_ray(Ray<T>{object.origin, object.through}, point, eps);
}
template <Coordinate T>
bool accepts_parameter(
Domain domain,
wide_type<T> numerator,
wide_type<T> denominator,
long double eps
) {
if (domain == Domain::Line) return true;
if (domain == Domain::Ray) {
return linear_parameter_detail::ratio_nonnegative<T>(
numerator,
denominator,
eps
);
}
return linear_parameter_detail::ratio_in_unit_interval<T>(
numerator,
denominator,
eps
);
}
template <Coordinate T>
Point<long double> point_at_ratio(
const ParametricObject<T>& object,
wide_type<T> numerator,
wide_type<T> denominator
) {
const long double ratio =
static_cast<long double>(numerator) /
static_cast<long double>(denominator);
const Point<long double> origin(object.origin);
const Point<long double> direction =
Point<long double>(object.through) - origin;
return origin + direction * ratio;
}
template <Coordinate T>
struct AxisProjection {
bool use_x;
bool negate;
wide_type<T> operator()(const Point<T>& point) const {
const wide_type<T> value = use_x
? wide_type<T>(point.x)
: wide_type<T>(point.y);
return negate ? -value : value;
}
};
template <Coordinate T>
AxisProjection<T> axis_projection(const ParametricObject<T>& object) {
using W = wide_type<T>;
const W direction_x = W(object.through.x) - W(object.origin.x);
const W direction_y = W(object.through.y) - W(object.origin.y);
const bool use_x =
predicate_detail::absolute(direction_x) >=
predicate_detail::absolute(direction_y);
const W component = use_x ? direction_x : direction_y;
assert(component != W(0));
return AxisProjection<T>{use_x, component < W(0)};
}
template <Coordinate T>
struct ParameterInterval {
bool has_lower;
bool has_upper;
wide_type<T> lower;
wide_type<T> upper;
};
template <Coordinate T>
ParameterInterval<T> parameter_interval(
const ParametricObject<T>& object,
const AxisProjection<T>& projection
) {
using W = wide_type<T>;
const W origin = projection(object.origin);
const W through = projection(object.through);
if (object.domain == Domain::Line) {
return ParameterInterval<T>{false, false, W(0), W(0)};
}
if (object.domain == Domain::Segment) {
return ParameterInterval<T>{
true,
true,
std::min(origin, through),
std::max(origin, through),
};
}
if (origin < through) {
return ParameterInterval<T>{true, false, origin, W(0)};
}
return ParameterInterval<T>{false, true, W(0), origin};
}
template <Coordinate T>
ParameterInterval<T> intersect_intervals(
ParameterInterval<T> first,
const ParameterInterval<T>& second
) {
if (
second.has_lower &&
(!first.has_lower || first.lower < second.lower)
) {
first.has_lower = true;
first.lower = second.lower;
}
if (
second.has_upper &&
(!first.has_upper || second.upper < first.upper)
) {
first.has_upper = true;
first.upper = second.upper;
}
return first;
}
template <Coordinate T>
Point<long double> point_at_projection(
const ParametricObject<T>& object,
const AxisProjection<T>& projection,
long double target
) {
const long double origin =
static_cast<long double>(projection(object.origin));
const long double through =
static_cast<long double>(projection(object.through));
const long double ratio = (target - origin) / (through - origin);
const Point<long double> point(object.origin);
const Point<long double> direction =
Point<long double>(object.through) - point;
return point + direction * ratio;
}
template <Coordinate T>
LinearIntersection collinear_intersection(
const ParametricObject<T>& first,
const ParametricObject<T>& second,
long double eps
) {
using W = wide_type<T>;
const AxisProjection<T> projection = axis_projection(first);
const ParameterInterval<T> first_interval =
parameter_interval(first, projection);
const ParameterInterval<T> second_interval =
parameter_interval(second, projection);
const ParameterInterval<T> common =
intersect_intervals(first_interval, second_interval);
W scale = predicate_detail::absolute(
projection(first.through) - projection(first.origin)
);
scale = std::max(
scale,
predicate_detail::absolute(
projection(second.through) - projection(second.origin)
)
);
if (common.has_lower && common.has_upper) {
const int order = predicate_detail::scaled_sign<ExactCoordinate<T>>(
common.lower - common.upper,
scale,
eps
);
if (order > 0) return make_empty();
if (order == 0) {
const long double coordinate =
(
static_cast<long double>(common.lower) +
static_cast<long double>(common.upper)
) / 2.0L;
return make_point(
point_at_projection(first, projection, coordinate)
);
}
return make_object(
LinearIntersectionKind::Segment,
point_at_projection(
first,
projection,
static_cast<long double>(common.lower)
),
point_at_projection(
first,
projection,
static_cast<long double>(common.upper)
)
);
}
const Point<long double> direction =
Point<long double>(first.through) -
Point<long double>(first.origin);
if (common.has_lower) {
const Point<long double> origin = point_at_projection(
first,
projection,
static_cast<long double>(common.lower)
);
return make_object(
LinearIntersectionKind::Ray,
origin,
origin + direction
);
}
if (common.has_upper) {
const Point<long double> origin = point_at_projection(
first,
projection,
static_cast<long double>(common.upper)
);
return make_object(
LinearIntersectionKind::Ray,
origin,
origin - direction
);
}
return make_object(
LinearIntersectionKind::Line,
first.origin,
first.through
);
}
template <Coordinate T>
LinearIntersection intersect(
const ParametricObject<T>& first,
const ParametricObject<T>& second,
long double eps
) {
const bool first_degenerate = first.origin == first.through;
const bool second_degenerate = second.origin == second.through;
if (first_degenerate) {
assert(first.domain == Domain::Segment);
if (contains(second, first.origin, eps)) {
return make_point(first.origin);
}
return make_empty();
}
if (second_degenerate) {
assert(second.domain == Domain::Segment);
if (contains(first, second.origin, eps)) {
return make_point(second.origin);
}
return make_empty();
}
const linear_parameter_detail::Parameters<T> values =
linear_parameter_detail::parameters(
first.origin,
first.through,
second.origin,
second.through
);
if (linear_parameter_detail::denominator_sign(values, eps) != 0) {
if (
!accepts_parameter<T>(
first.domain,
values.first_numerator,
values.denominator,
eps
) ||
!accepts_parameter<T>(
second.domain,
values.second_numerator,
values.denominator,
eps
)
) {
return make_empty();
}
return make_point(
point_at_ratio(
first,
values.first_numerator,
values.denominator
)
);
}
if (
orientation(
first.origin,
first.through,
second.origin,
eps
) != 0
) {
return make_empty();
}
return collinear_intersection(first, second, eps);
}
} // namespace linear_intersection_detail
template <Coordinate T>
LinearIntersection linear_intersection(
const Line<T>& first,
const Line<T>& second,
long double eps = 1e-12L
) {
return linear_intersection_detail::intersect(
linear_intersection_detail::parametric_object(first),
linear_intersection_detail::parametric_object(second),
eps
);
}
template <Coordinate T>
LinearIntersection linear_intersection(
const Line<T>& line,
const Segment<T>& segment,
long double eps = 1e-12L
) {
return linear_intersection_detail::intersect(
linear_intersection_detail::parametric_object(line),
linear_intersection_detail::parametric_object(segment),
eps
);
}
template <Coordinate T>
LinearIntersection linear_intersection(
const Segment<T>& segment,
const Line<T>& line,
long double eps = 1e-12L
) {
return linear_intersection_detail::intersect(
linear_intersection_detail::parametric_object(segment),
linear_intersection_detail::parametric_object(line),
eps
);
}
template <Coordinate T>
LinearIntersection linear_intersection(
const Segment<T>& first,
const Segment<T>& second,
long double eps = 1e-12L
) {
return linear_intersection_detail::intersect(
linear_intersection_detail::parametric_object(first),
linear_intersection_detail::parametric_object(second),
eps
);
}
template <Coordinate T>
LinearIntersection linear_intersection(
const Ray<T>& ray,
const Line<T>& line,
long double eps = 1e-12L
) {
return linear_intersection_detail::intersect(
linear_intersection_detail::parametric_object(ray),
linear_intersection_detail::parametric_object(line),
eps
);
}
template <Coordinate T>
LinearIntersection linear_intersection(
const Line<T>& line,
const Ray<T>& ray,
long double eps = 1e-12L
) {
return linear_intersection_detail::intersect(
linear_intersection_detail::parametric_object(line),
linear_intersection_detail::parametric_object(ray),
eps
);
}
template <Coordinate T>
LinearIntersection linear_intersection(
const Ray<T>& ray,
const Segment<T>& segment,
long double eps = 1e-12L
) {
return linear_intersection_detail::intersect(
linear_intersection_detail::parametric_object(ray),
linear_intersection_detail::parametric_object(segment),
eps
);
}
template <Coordinate T>
LinearIntersection linear_intersection(
const Segment<T>& segment,
const Ray<T>& ray,
long double eps = 1e-12L
) {
return linear_intersection_detail::intersect(
linear_intersection_detail::parametric_object(segment),
linear_intersection_detail::parametric_object(ray),
eps
);
}
template <Coordinate T>
LinearIntersection linear_intersection(
const Ray<T>& first,
const Ray<T>& second,
long double eps = 1e-12L
) {
return linear_intersection_detail::intersect(
linear_intersection_detail::parametric_object(first),
linear_intersection_detail::parametric_object(second),
eps
);
}
namespace closest_points_detail {
inline ClosestPoints reversed(const ClosestPoints& result) {
return ClosestPoints{result.second, result.first};
}
inline bool point_less(
const Point<long double>& first,
const Point<long double>& second
) {
if (first.x != second.x) return first.x < second.x;
return first.y < second.y;
}
inline ClosestPoints common_point(const LinearIntersection& intersection) {
assert(intersection.kind != LinearIntersectionKind::Empty);
Point<long double> point = intersection.first;
if (intersection.kind == LinearIntersectionKind::Segment) {
if (point_less(intersection.second, point)) {
point = intersection.second;
}
} else if (intersection.kind == LinearIntersectionKind::Line) {
const Line<long double> line{
intersection.first,
intersection.second
};
point = projection(line, Point<long double>(0, 0));
}
return ClosestPoints{point, point};
}
inline long double separation2(const ClosestPoints& result) {
return distance2(result.first, result.second);
}
inline bool canonical_less(
const ClosestPoints& first,
const ClosestPoints& second
) {
Point<long double> first_start = first.first;
Point<long double> first_finish = first.second;
if (point_less(first_finish, first_start)) {
std::swap(first_start, first_finish);
}
Point<long double> second_start = second.first;
Point<long double> second_finish = second.second;
if (point_less(second_finish, second_start)) {
std::swap(second_start, second_finish);
}
if (point_less(first_start, second_start)) return true;
if (point_less(second_start, first_start)) return false;
return point_less(first_finish, second_finish);
}
inline void consider(ClosestPoints& best, const ClosestPoints& candidate) {
const long double best_distance = separation2(best);
const long double candidate_distance = separation2(candidate);
if (
candidate_distance < best_distance ||
(
candidate_distance == best_distance &&
canonical_less(candidate, best)
)
) {
best = candidate;
}
}
} // namespace closest_points_detail
template <Coordinate T>
ClosestPoints closest_points(
const Point<T>& first,
const Point<T>& second
) {
return ClosestPoints{
Point<long double>(first),
Point<long double>(second),
};
}
template <Coordinate T>
ClosestPoints closest_points(
const Line<T>& line,
const Point<T>& point
) {
return ClosestPoints{
projection(line, point),
Point<long double>(point),
};
}
template <Coordinate T>
ClosestPoints closest_points(
const Point<T>& point,
const Line<T>& line
) {
return closest_points_detail::reversed(closest_points(line, point));
}
template <Coordinate T>
ClosestPoints closest_points(
const Segment<T>& segment,
const Point<T>& point
) {
return ClosestPoints{
projection(segment, point),
Point<long double>(point),
};
}
template <Coordinate T>
ClosestPoints closest_points(
const Point<T>& point,
const Segment<T>& segment
) {
return closest_points_detail::reversed(closest_points(segment, point));
}
template <Coordinate T>
ClosestPoints closest_points(
const Ray<T>& ray,
const Point<T>& point
) {
return ClosestPoints{
projection(ray, point),
Point<long double>(point),
};
}
template <Coordinate T>
ClosestPoints closest_points(
const Point<T>& point,
const Ray<T>& ray
) {
return closest_points_detail::reversed(closest_points(ray, point));
}
template <Coordinate T>
ClosestPoints closest_points(
const Line<T>& first,
const Line<T>& second,
long double eps = 1e-12L
) {
const LinearIntersection intersection =
linear_intersection(first, second, eps);
if (intersection.kind != LinearIntersectionKind::Empty) {
return closest_points_detail::common_point(intersection);
}
ClosestPoints result = closest_points(first, second.a);
closest_points_detail::consider(
result,
closest_points(first.a, second)
);
return result;
}
template <Coordinate T>
ClosestPoints closest_points(
const Line<T>& line,
const Segment<T>& segment,
long double eps = 1e-12L
) {
const LinearIntersection intersection =
linear_intersection(line, segment, eps);
if (intersection.kind != LinearIntersectionKind::Empty) {
return closest_points_detail::common_point(intersection);
}
ClosestPoints result = closest_points(line, segment.a);
closest_points_detail::consider(
result,
closest_points(line, segment.b)
);
return result;
}
template <Coordinate T>
ClosestPoints closest_points(
const Segment<T>& segment,
const Line<T>& line,
long double eps = 1e-12L
) {
return closest_points_detail::reversed(
closest_points(line, segment, eps)
);
}
template <Coordinate T>
ClosestPoints closest_points(
const Segment<T>& first,
const Segment<T>& second,
long double eps = 1e-12L
) {
const LinearIntersection intersection =
linear_intersection(first, second, eps);
if (intersection.kind != LinearIntersectionKind::Empty) {
return closest_points_detail::common_point(intersection);
}
ClosestPoints result = closest_points(first, second.a);
closest_points_detail::consider(
result,
closest_points(first, second.b)
);
closest_points_detail::consider(
result,
closest_points(first.a, second)
);
closest_points_detail::consider(
result,
closest_points(first.b, second)
);
return result;
}
template <Coordinate T>
ClosestPoints closest_points(
const Line<T>& line,
const Ray<T>& ray,
long double eps = 1e-12L
) {
const LinearIntersection intersection =
linear_intersection(line, ray, eps);
if (intersection.kind != LinearIntersectionKind::Empty) {
return closest_points_detail::common_point(intersection);
}
return closest_points(line, ray.origin);
}
template <Coordinate T>
ClosestPoints closest_points(
const Ray<T>& ray,
const Line<T>& line,
long double eps = 1e-12L
) {
return closest_points_detail::reversed(closest_points(line, ray, eps));
}
template <Coordinate T>
ClosestPoints closest_points(
const Ray<T>& ray,
const Segment<T>& segment,
long double eps = 1e-12L
) {
const LinearIntersection intersection =
linear_intersection(ray, segment, eps);
if (intersection.kind != LinearIntersectionKind::Empty) {
return closest_points_detail::common_point(intersection);
}
ClosestPoints result = closest_points(ray, segment.a);
closest_points_detail::consider(
result,
closest_points(ray, segment.b)
);
closest_points_detail::consider(
result,
closest_points(ray.origin, segment)
);
return result;
}
template <Coordinate T>
ClosestPoints closest_points(
const Segment<T>& segment,
const Ray<T>& ray,
long double eps = 1e-12L
) {
return closest_points_detail::reversed(
closest_points(ray, segment, eps)
);
}
template <Coordinate T>
ClosestPoints closest_points(
const Ray<T>& first,
const Ray<T>& second,
long double eps = 1e-12L
) {
const LinearIntersection intersection =
linear_intersection(first, second, eps);
if (intersection.kind != LinearIntersectionKind::Empty) {
return closest_points_detail::common_point(intersection);
}
ClosestPoints result = closest_points(first, second.origin);
closest_points_detail::consider(
result,
closest_points(first.origin, second)
);
return result;
}
template <Coordinate T>
long double distance(const Line<T>& line, const Point<T>& point) {
const ClosestPoints result = closest_points(line, point);
return geometry::distance(result.first, result.second);
}
template <Coordinate T>
long double distance(const Point<T>& point, const Line<T>& line) {
return distance(line, point);
}
template <Coordinate T>
long double distance(const Segment<T>& segment, const Point<T>& point) {
const ClosestPoints result = closest_points(segment, point);
return geometry::distance(result.first, result.second);
}
template <Coordinate T>
long double distance(const Point<T>& point, const Segment<T>& segment) {
return distance(segment, point);
}
template <Coordinate T>
long double distance(const Ray<T>& ray, const Point<T>& point) {
const ClosestPoints result = closest_points(ray, point);
return geometry::distance(result.first, result.second);
}
template <Coordinate T>
long double distance(const Point<T>& point, const Ray<T>& ray) {
return distance(ray, point);
}
template <Coordinate T>
long double distance(const Line<T>& first, const Line<T>& second) {
const ClosestPoints result = closest_points(first, second);
return geometry::distance(result.first, result.second);
}
template <Coordinate T>
long double distance(const Line<T>& line, const Segment<T>& segment) {
const ClosestPoints result = closest_points(line, segment);
return geometry::distance(result.first, result.second);
}
template <Coordinate T>
long double distance(const Segment<T>& segment, const Line<T>& line) {
return distance(line, segment);
}
template <Coordinate T>
long double distance(const Segment<T>& first, const Segment<T>& second) {
const ClosestPoints result = closest_points(first, second);
return geometry::distance(result.first, result.second);
}
template <Coordinate T>
long double distance(const Line<T>& line, const Ray<T>& ray) {
const ClosestPoints result = closest_points(line, ray);
return geometry::distance(result.first, result.second);
}
template <Coordinate T>
long double distance(const Ray<T>& ray, const Line<T>& line) {
return distance(line, ray);
}
template <Coordinate T>
long double distance(const Ray<T>& ray, const Segment<T>& segment) {
const ClosestPoints result = closest_points(ray, segment);
return geometry::distance(result.first, result.second);
}
template <Coordinate T>
long double distance(const Segment<T>& segment, const Ray<T>& ray) {
return distance(ray, segment);
}
template <Coordinate T>
long double distance(const Ray<T>& first, const Ray<T>& second) {
const ClosestPoints result = closest_points(first, second);
return geometry::distance(result.first, result.second);
}
} // namespace geometry
} // namespace m1une
#line 17 "geometry/half_plane_intersection.hpp"
namespace m1une {
namespace geometry {
enum class HalfPlaneIntersectionStatus {
Empty,
Unbounded,
Degenerate,
Bounded,
};
struct HalfPlaneIntersectionResult {
HalfPlaneIntersectionStatus status;
std::vector<Point<long double>> polygon;
};
namespace half_plane_intersection_detail {
struct HalfPlane {
Point<long double> point;
Point<long double> direction;
long double angle;
HalfPlane(
const Point<long double>& point_value,
const Point<long double>& direction_value
) : point(point_value), direction(direction_value) {
angle = std::atan2(direction.y, direction.x);
if (angle < 0) angle += 2 * std::numbers::pi_v<long double>;
}
};
inline bool direction_less(const HalfPlane& first, const HalfPlane& second) {
return first.angle < second.angle;
}
inline bool parallel(
const HalfPlane& first,
const HalfPlane& second,
long double eps
) {
return std::fabs(cross(first.direction, second.direction)) <= eps;
}
inline bool same_direction(
const HalfPlane& first,
const HalfPlane& second,
long double eps
) {
return parallel(first, second, eps) &&
dot(first.direction, second.direction) > 0;
}
inline bool outside(
const HalfPlane& half_plane,
const Point<long double>& point,
long double eps
) {
return cross(half_plane.direction, point - half_plane.point) < -eps;
}
inline bool more_restrictive(
const HalfPlane& candidate,
const HalfPlane& current,
long double eps
) {
return cross(
current.direction,
candidate.point - current.point
) > eps;
}
inline std::optional<Point<long double>> intersection(
const HalfPlane& first,
const HalfPlane& second,
long double eps
) {
long double denominator = cross(first.direction, second.direction);
if (std::fabs(denominator) <= eps) return std::nullopt;
long double ratio = cross(
second.point - first.point,
second.direction
) / denominator;
return first.point + first.direction * ratio;
}
inline void merge_same_direction(
std::vector<HalfPlane>& half_planes,
const HalfPlane& half_plane,
long double eps
) {
if (
half_planes.empty() ||
!same_direction(half_planes.back(), half_plane, eps)
) {
half_planes.push_back(half_plane);
return;
}
if (more_restrictive(half_plane, half_planes.back(), eps)) {
half_planes.back() = half_plane;
}
}
inline void merge_cyclic_ends(
std::vector<HalfPlane>& half_planes,
long double eps
) {
if (
half_planes.size() < 2 ||
!same_direction(half_planes.front(), half_planes.back(), eps)
) {
return;
}
if (more_restrictive(half_planes.back(), half_planes.front(), eps)) {
half_planes.front() = half_planes.back();
}
half_planes.pop_back();
}
inline bool has_feasible_point(
std::vector<HalfPlane> half_planes,
long double eps
) {
std::mt19937_64 generator(0x6a09e667f3bcc909ULL);
std::shuffle(half_planes.begin(), half_planes.end(), generator);
Point<long double> feasible(0, 0);
for (std::size_t index = 0; index < half_planes.size(); ++index) {
const HalfPlane& current = half_planes[index];
if (!outside(current, feasible, eps)) continue;
Point<long double> normal(
-current.direction.y,
current.direction.x
);
Point<long double> base = normal * dot(normal, current.point);
long double lower = -std::numeric_limits<long double>::infinity();
long double upper = std::numeric_limits<long double>::infinity();
for (std::size_t previous_index = 0;
previous_index < index;
++previous_index) {
const HalfPlane& previous = half_planes[previous_index];
long double coefficient = cross(
previous.direction,
current.direction
);
long double constant = cross(
previous.direction,
base - previous.point
);
if (std::fabs(coefficient) <= eps) {
if (constant < -eps) return false;
continue;
}
long double bound = (-eps - constant) / coefficient;
if (coefficient > 0) {
lower = std::max(lower, bound);
} else {
upper = std::min(upper, bound);
}
if (lower > upper) return false;
}
long double parameter = 0;
if (parameter < lower) parameter = lower;
if (parameter > upper) parameter = upper;
feasible = base + current.direction * parameter;
}
return true;
}
inline bool has_bounded_recession_cone(
const std::vector<HalfPlane>& half_planes,
long double eps
) {
if (half_planes.empty()) return false;
constexpr long double pi = std::numbers::pi_v<long double>;
long double maximum_gap =
half_planes.front().angle + 2 * pi - half_planes.back().angle;
for (std::size_t index = 1; index < half_planes.size(); ++index) {
maximum_gap = std::max(
maximum_gap,
half_planes[index].angle - half_planes[index - 1].angle
);
}
return maximum_gap < pi - eps;
}
} // namespace half_plane_intersection_detail
// Each directed line keeps its closed left half-plane. Returns the vertices of
// a bounded intersection with positive area in counterclockwise order. Empty,
// unbounded, and bounded zero-area intersections have distinct statuses.
template <Coordinate T>
HalfPlaneIntersectionResult half_plane_intersection(
const std::vector<Line<T>>& half_planes,
long double eps = 1e-12L
) {
using half_plane_intersection_detail::HalfPlane;
namespace detail = half_plane_intersection_detail;
assert(eps >= 0);
std::vector<HalfPlane> sorted;
sorted.reserve(half_planes.size());
for (const Line<T>& line : half_planes) {
assert(line.a != line.b);
Point<long double> point(line.a);
Point<long double> direction = Point<long double>(line.b) - point;
long double length = norm(direction);
direction = direction / length;
sorted.push_back(HalfPlane{point, direction});
}
if (!detail::has_feasible_point(sorted, eps)) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Empty,
{},
};
}
std::sort(sorted.begin(), sorted.end(), detail::direction_less);
if (!detail::has_bounded_recession_cone(sorted, eps)) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Unbounded,
{},
};
}
if (sorted.size() < 3) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Degenerate,
{},
};
}
std::vector<HalfPlane> unique;
unique.reserve(sorted.size());
for (const HalfPlane& half_plane : sorted) {
detail::merge_same_direction(unique, half_plane, eps);
}
detail::merge_cyclic_ends(unique, eps);
if (unique.size() < 3) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Degenerate,
{},
};
}
std::deque<HalfPlane> deque;
for (const HalfPlane& half_plane : unique) {
while (deque.size() >= 2) {
auto point = detail::intersection(
deque[deque.size() - 2],
deque.back(),
eps
);
if (!point.has_value()) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Degenerate,
{},
};
}
if (!detail::outside(half_plane, *point, eps)) break;
deque.pop_back();
}
while (deque.size() >= 2) {
auto point = detail::intersection(deque[0], deque[1], eps);
if (!point.has_value()) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Degenerate,
{},
};
}
if (!detail::outside(half_plane, *point, eps)) break;
deque.pop_front();
}
deque.push_back(half_plane);
}
while (deque.size() >= 3) {
auto point = detail::intersection(
deque[deque.size() - 2],
deque.back(),
eps
);
if (!point.has_value()) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Degenerate,
{},
};
}
if (!detail::outside(deque.front(), *point, eps)) break;
deque.pop_back();
}
while (deque.size() >= 3) {
auto point = detail::intersection(deque[0], deque[1], eps);
if (!point.has_value()) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Degenerate,
{},
};
}
if (!detail::outside(deque.back(), *point, eps)) break;
deque.pop_front();
}
if (deque.size() < 3) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Degenerate,
{},
};
}
std::vector<Point<long double>> polygon;
polygon.reserve(deque.size());
for (std::size_t index = 0; index < deque.size(); ++index) {
auto point = detail::intersection(
deque[index],
deque[(index + 1) % deque.size()],
eps
);
if (!point.has_value()) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Degenerate,
{},
};
}
if (
polygon.empty() ||
distance(polygon.back(), *point) > eps
) {
polygon.push_back(*point);
}
}
if (
polygon.size() >= 2 &&
distance(polygon.front(), polygon.back()) <= eps
) {
polygon.pop_back();
}
if (polygon.size() < 3) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Degenerate,
{},
};
}
long double signed_area2 = 0;
Point<long double> origin = polygon.front();
for (std::size_t index = 1; index + 1 < polygon.size(); ++index) {
signed_area2 += cross(
polygon[index] - origin,
polygon[index + 1] - origin
);
}
if (signed_area2 <= eps) {
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Degenerate,
{},
};
}
auto first = std::min_element(polygon.begin(), polygon.end());
std::rotate(polygon.begin(), first, polygon.end());
return HalfPlaneIntersectionResult{
HalfPlaneIntersectionStatus::Bounded,
std::move(polygon),
};
}
} // namespace geometry
} // namespace m1une
#line 4 "verify/geometry/half_plane_intersection_random.test.cpp"
#line 9 "verify/geometry/half_plane_intersection_random.test.cpp"
#include <cstdint>
#line 1 "utilities/fast_io.hpp"
#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#line 9 "utilities/fast_io.hpp"
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"
namespace m1une {
namespace utilities {
struct FastOutput;
namespace internal {
// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;
// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};
template <class T>
struct is_range<T, std::void_t<
decltype(std::begin(std::declval<T&>())),
decltype(std::end(std::declval<T&>()))
>> : std::true_type {};
template <class T>
inline constexpr bool is_range_v = is_range<T>::value;
template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));
template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;
template <class T, class = void>
struct range_stored_value {
using type = range_value_t<T>;
};
template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};
template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;
// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};
template <class T, std::size_t N>
struct is_char_array<T[N]>
: std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};
template <class T>
struct is_string_like
: std::bool_constant<
std::is_same_v<std::decay_t<T>, std::string>
|| std::is_same_v<std::decay_t<T>, const char*>
|| std::is_same_v<std::decay_t<T>, char*>
|| is_char_array<std::remove_reference_t<T>>::value
> {};
template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;
// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};
template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
: std::true_type {};
template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;
template <class T, class = void>
struct has_static_mod_raw : std::false_type {};
template <class T>
struct has_static_mod_raw<
T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
: std::true_type {};
template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;
// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
std::is_integral_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>
|| std::is_same_v<std::remove_cv_t<T>, __uint128_t>;
template <class T>
inline constexpr bool is_signed_v =
std::is_signed_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>;
template <class T>
struct make_unsigned {
using type = std::make_unsigned_t<T>;
};
template <>
struct make_unsigned<__int128_t> {
using type = __uint128_t;
};
template <>
struct make_unsigned<__uint128_t> {
using type = __uint128_t;
};
template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;
} // namespace internal
struct FastInput {
static constexpr int buffer_size = 1 << 20;
private:
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _length;
int _file_descriptor;
bool _streaming;
bool refill() {
_position = 0;
if (_streaming) {
ssize_t length;
do {
length = ::read(_file_descriptor, _buffer, buffer_size);
} while (length < 0 && errno == EINTR);
if (length <= 0) {
_length = 0;
return false;
}
_length = int(length);
} else {
_length = int(std::fread(_buffer, 1, buffer_size, _stream));
}
return _length != 0;
}
template <class T>
bool read_integer_from_stream(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-') {
negative = true;
c = read_char_raw();
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
result = negative ? result * 10 - (c - '0')
: result * 10 + (c - '0');
c = read_char_raw();
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + T(c - '0');
c = read_char_raw();
}
value = negative ? T(0) - result : result;
}
return true;
}
bool prepare_number() {
if (_length - _position >= 64) return true;
const int remaining = _length - _position;
if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
_position = 0;
_length = remaining + added;
if (_length < buffer_size) _buffer[_length] = '\0';
return _length != 0;
}
public:
explicit FastInput(std::FILE* stream = stdin)
: _stream(stream),
_position(0),
_length(0),
_file_descriptor(::fileno(stream)),
_streaming([&] {
struct stat status;
return _file_descriptor >= 0
&& ::fstat(_file_descriptor, &status) == 0
&& !S_ISREG(status.st_mode);
}()) {}
FastInput(const FastInput&) = delete;
FastInput& operator=(const FastInput&) = delete;
int read_char_raw() {
if (_position == _length && !refill()) return EOF;
return _buffer[_position++];
}
bool skip_spaces() {
int c = read_char_raw();
while (c != EOF && c <= ' ') c = read_char_raw();
if (c == EOF) return false;
--_position;
return true;
}
bool read(char& value) {
if (!skip_spaces()) return false;
value = char(read_char_raw());
return true;
}
bool read(std::string& value) {
if (!skip_spaces()) return false;
value.clear();
while (true) {
const int begin = _position;
while (_position < _length &&
static_cast<unsigned char>(_buffer[_position]) > ' ') {
++_position;
}
value.append(_buffer + begin, _position - begin);
if (_position < _length) {
++_position;
return true;
}
if (!refill()) return true;
}
}
bool read(bool& value) {
int x;
if (!read(x)) return false;
value = x != 0;
return true;
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>,
bool
>
read(T& value) {
if (_streaming) return read_integer_from_stream(value);
if (!prepare_number()) return false;
int c = static_cast<unsigned char>(_buffer[_position++]);
while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);
bool negative = false;
if (c == '-') {
negative = true;
c = static_cast<unsigned char>(_buffer[_position++]);
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
const int first = c - '0';
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = negative ? result * 100 - (first * 10 + second)
: result * 100 + (first * 10 + second);
++_position;
} else {
result = negative ? result * 10 - first : result * 10 + first;
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
const unsigned first = unsigned(c - '0');
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = result * 100 + T(first * 10 + unsigned(second));
++_position;
} else {
result = result * 10 + T(first);
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = negative ? T(0) - result : result;
}
if (_position > _length) _position = _length;
return true;
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>, bool>
read(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-' || c == '+') {
negative = c == '-';
c = read_char_raw();
}
long double result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + (c - '0');
c = read_char_raw();
}
if (c == '.') {
long double place = 0.1L;
c = read_char_raw();
while ('0' <= c && c <= '9') {
result += (c - '0') * place;
place *= 0.1L;
c = read_char_raw();
}
}
if (c == 'e' || c == 'E') {
c = read_char_raw();
bool exponent_negative = false;
if (c == '-' || c == '+') {
exponent_negative = c == '-';
c = read_char_raw();
}
int exponent = 0;
while ('0' <= c && c <= '9') {
exponent = exponent * 10 + (c - '0');
c = read_char_raw();
}
long double scale = 1;
long double power = 10;
while (exponent > 0) {
if (exponent & 1) scale *= power;
power *= power;
exponent >>= 1;
}
result = exponent_negative ? result / scale : result * scale;
}
value = static_cast<T>(negative ? -result : result);
return true;
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>,
bool
>
read(T& value) {
long long x;
if (!read(x)) return false;
if constexpr (internal::has_static_mod_raw_v<T>) {
if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
value = T::raw(uint32_t(x));
} else {
value = T(x);
}
} else {
value = T(x);
}
return true;
}
template <class First, class Second>
bool read(std::pair<First, Second>& value) {
if (!read(value.first)) return false;
return read(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>,
bool
>
read(Range& range) {
using StoredValue = internal::range_stored_value_t<Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
for (auto&& value : range) {
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
bool x;
if (!read(x)) return false;
value = x;
} else {
if (!read(value)) return false;
}
}
return true;
}
template <class First, class Second, class... Rest>
bool read(First& first, Second& second, Rest&... rest) {
if (!read(first)) return false;
return read(second, rest...);
}
template <class T>
FastInput& operator>>(T& value) {
if (!read(value)) std::abort();
return *this;
}
};
struct FastOutput {
static constexpr int buffer_size = 1 << 20;
private:
inline static const auto digit_quads = [] {
std::array<char, 40000> result{};
for (int i = 0; i < 10000; i++) {
int value = i;
for (int j = 3; j >= 0; j--) {
result[4 * i + j] = char('0' + value % 10);
value /= 10;
}
}
return result;
}();
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _precision;
std::chars_format _float_format;
char _range_separator;
std::string* _capture = nullptr;
template <class T>
std::string format_cell(const T& value) {
std::string result;
struct CaptureGuard {
std::string*& target;
std::string* previous;
~CaptureGuard() { target = previous; }
} guard{_capture, _capture};
_capture = &result;
write(value);
return result;
}
template <class Matrix>
void write_aligned_matrix(const Matrix& matrix) {
std::vector<std::vector<std::string>> rows;
std::vector<std::size_t> widths;
for (const auto& row : matrix) {
auto& cells = rows.emplace_back();
std::size_t column = 0;
for (const auto& value : row) {
cells.push_back(format_cell(value));
if (column == widths.size()) widths.push_back(0);
widths[column] = std::max(widths[column], cells.back().size());
++column;
}
}
bool first = true;
for (const auto& row : rows) {
if (!first) write_char('\n');
first = false;
for (std::size_t column = 0; column < row.size(); ++column) {
if (column != 0) write_char(_range_separator);
for (std::size_t padding = row[column].size();
padding < widths[column]; ++padding) {
write_char(' ');
}
write(row[column]);
}
}
}
public:
explicit FastOutput(std::FILE* stream = stdout)
: _stream(stream),
_position(0),
_precision(6),
_float_format(std::chars_format::general),
_range_separator(' ') {
if (_stream == stdout
&& internal::standard_output_instance == nullptr) {
internal::standard_output_instance = this;
}
}
FastOutput(const FastOutput&) = delete;
FastOutput& operator=(const FastOutput&) = delete;
~FastOutput() {
flush();
if (internal::standard_output_instance == this) {
internal::standard_output_instance = nullptr;
}
}
void flush() {
if (_position != 0) {
std::fwrite(_buffer, 1, _position, _stream);
_position = 0;
}
std::fflush(_stream);
}
void write_char(char c) {
if (_capture != nullptr) {
_capture->push_back(c);
return;
}
if (_position == buffer_size) flush();
_buffer[_position++] = c;
}
void write(const char* s) {
while (*s != '\0') write_char(*s++);
}
void write(const std::string& s) {
if (_capture != nullptr) {
_capture->append(s);
return;
}
std::size_t position = 0;
while (position < s.size()) {
if (_position == buffer_size) flush();
const std::size_t copied =
std::min<std::size_t>(buffer_size - _position, s.size() - position);
std::memcpy(_buffer + _position, s.data() + position, copied);
_position += int(copied);
position += copied;
}
}
void write(char c) {
write_char(c);
}
void write(bool value) {
write_char(value ? '1' : '0');
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>>
write(T value) {
char digits[128];
auto [end, error] = std::to_chars(
digits,
digits + sizeof(digits),
value,
_float_format,
_precision
);
if (error != std::errc()) std::abort();
for (const char* pointer = digits; pointer != end; pointer++) {
write_char(*pointer);
}
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>
>
write(T value) {
using Raw = std::remove_cv_t<T>;
using Unsigned = internal::make_unsigned_t<Raw>;
Unsigned magnitude;
if constexpr (internal::is_signed_v<Raw>) {
if (value < 0) {
write_char('-');
magnitude = Unsigned(0) - Unsigned(value);
} else {
magnitude = Unsigned(value);
}
} else {
magnitude = value;
}
if (magnitude == 0) {
write_char('0');
return;
}
unsigned chunks[16];
int count = 0;
while (magnitude >= 10000) {
const Unsigned quotient = magnitude / 10000;
chunks[count++] = unsigned(magnitude - quotient * 10000);
magnitude = quotient;
}
if (_capture == nullptr && _position > buffer_size - 64) flush();
char captured[64];
char* const begin = _capture != nullptr ? captured : _buffer + _position;
char* destination = begin;
const unsigned leading = unsigned(magnitude);
const char* first = digit_quads.data() + 4 * leading;
int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
for (; skip < 4; skip++) *destination++ = first[skip];
while (count--) {
const char* digits = digit_quads.data() + 4 * chunks[count];
std::memcpy(destination, digits, 4);
destination += 4;
}
if (_capture != nullptr) {
_capture->append(begin, destination - begin);
} else {
_position += int(destination - begin);
}
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>
>
write(const T& value) {
write(value.val());
}
template <class First, class Second>
void write(const std::pair<First, Second>& value) {
write(value.first);
write_char(' ');
write(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>
>
write(const Range& range) {
using StoredValue = internal::range_stored_value_t<const Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
bool first = true;
for (const auto& value : range) {
if (!first) write_char(nested ? '\n' : _range_separator);
first = false;
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
write(static_cast<bool>(value));
} else {
write(value);
}
}
}
template <class First, class... Rest>
void print(const First& first, const Rest&... rest) {
write(first);
((write_char(' '), write(rest)), ...);
}
void println() {
write_char('\n');
}
void set_precision(int precision) {
_precision = precision;
}
void set_fixed(int precision = 6) {
_float_format = std::chars_format::fixed;
_precision = precision;
}
void set_general(int precision = 6) {
_float_format = std::chars_format::general;
_precision = precision;
}
void set_range_separator(char separator) {
_range_separator = separator;
}
template <class Matrix>
void write_aligned(const Matrix& matrix) {
using Row = internal::range_stored_value_t<const Matrix>;
using Cell = internal::range_stored_value_t<const Row>;
static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
"write_aligned requires a two-dimensional range");
static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
"write_aligned requires scalar cells");
write_aligned_matrix(matrix);
}
template <class Matrix>
void println_aligned(const Matrix& matrix) {
write_aligned(matrix);
write_char('\n');
}
template <class... Args>
void println(const Args&... args) {
print(args...);
write_char('\n');
}
template <class T>
FastOutput& operator<<(const T& value) {
write(value);
return *this;
}
};
} // namespace utilities
} // namespace m1une
#line 13 "verify/geometry/half_plane_intersection_random.test.cpp"
namespace {
using m1une::geometry::Line;
using m1une::geometry::Point;
using PointType = Point<long double>;
std::vector<PointType> clip(
const std::vector<PointType>& polygon,
const Line<long double>& half_plane
) {
std::vector<PointType> result;
PointType direction = half_plane.b - half_plane.a;
for (std::size_t index = 0; index < polygon.size(); ++index) {
PointType first = polygon[index];
PointType second = polygon[(index + 1) % polygon.size()];
long double first_side = cross(direction, first - half_plane.a);
long double second_side = cross(direction, second - half_plane.a);
bool first_inside = first_side >= -1e-12L;
bool second_inside = second_side >= -1e-12L;
if (first_inside) result.push_back(first);
if (first_inside != second_inside) {
long double ratio = first_side / (first_side - second_side);
result.push_back(first + (second - first) * ratio);
}
}
return result;
}
long double area(const std::vector<PointType>& polygon) {
long double result = 0;
for (std::size_t index = 0; index < polygon.size(); ++index) {
result += cross(
polygon[index],
polygon[(index + 1) % polygon.size()]
);
}
return std::fabs(result) / 2;
}
void add_bounding_square(std::vector<Line<long double>>& half_planes) {
PointType lower_left(-50, -50);
PointType lower_right(50, -50);
PointType upper_right(50, 50);
PointType upper_left(-50, 50);
half_planes.push_back(Line<long double>{lower_left, lower_right});
half_planes.push_back(Line<long double>{lower_right, upper_right});
half_planes.push_back(Line<long double>{upper_right, upper_left});
half_planes.push_back(Line<long double>{upper_left, lower_left});
}
void test_special_cases() {
using IntegerPoint = Point<long long>;
std::vector<Line<long long>> integer_square;
integer_square.push_back(Line<long long>{IntegerPoint(0, 0), IntegerPoint(2, 0)});
integer_square.push_back(Line<long long>{IntegerPoint(2, 0), IntegerPoint(2, 2)});
integer_square.push_back(Line<long long>{IntegerPoint(2, 2), IntegerPoint(0, 2)});
integer_square.push_back(Line<long long>{IntegerPoint(0, 2), IntegerPoint(0, 0)});
auto integer_polygon =
m1une::geometry::half_plane_intersection(integer_square);
assert(
integer_polygon.status ==
m1une::geometry::HalfPlaneIntersectionStatus::Bounded
);
assert(integer_polygon.polygon.size() == 4);
assert(std::fabs(area(integer_polygon.polygon) - 4) <= 1e-12L);
std::vector<Line<long double>> square;
add_bounding_square(square);
square.push_back(Line<long double>{PointType(-4, -5), PointType(4, -5)});
square.push_back(Line<long double>{PointType(-4, -3), PointType(4, -3)});
auto square_result = m1une::geometry::half_plane_intersection(square);
assert(
square_result.status ==
m1une::geometry::HalfPlaneIntersectionStatus::Bounded
);
assert(square_result.polygon.size() == 4);
assert(std::fabs(area(square_result.polygon) - 5300) <= 1e-8L);
std::vector<Line<long double>> impossible;
impossible.push_back(Line<long double>{PointType(1, 1), PointType(1, 0)});
impossible.push_back(Line<long double>{PointType(0, 0), PointType(0, 1)});
impossible.push_back(Line<long double>{PointType(0, 0), PointType(1, 0)});
impossible.push_back(Line<long double>{PointType(1, 1), PointType(0, 1)});
assert(
m1une::geometry::half_plane_intersection(impossible).status ==
m1une::geometry::HalfPlaneIntersectionStatus::Empty
);
std::vector<Line<long double>> triangularly_impossible;
triangularly_impossible.push_back(
Line<long double>{PointType(0, 0), PointType(0, -1)}
);
triangularly_impossible.push_back(
Line<long double>{PointType(0, 0), PointType(1, 0)}
);
triangularly_impossible.push_back(
Line<long double>{PointType(0, -1), PointType(-1, 0)}
);
assert(
m1une::geometry::half_plane_intersection(
triangularly_impossible
).status == m1une::geometry::HalfPlaneIntersectionStatus::Empty
);
std::vector<Line<long double>> unbounded;
unbounded.push_back(Line<long double>{PointType(0, 0), PointType(1, 0)});
unbounded.push_back(Line<long double>{PointType(0, 0), PointType(0, -1)});
unbounded.push_back(Line<long double>{PointType(0, 1), PointType(1, 0)});
assert(
m1une::geometry::half_plane_intersection(unbounded).status ==
m1une::geometry::HalfPlaneIntersectionStatus::Unbounded
);
std::vector<Line<long double>> segment;
segment.push_back(Line<long double>{PointType(0, 0), PointType(0, -1)});
segment.push_back(Line<long double>{PointType(0, 1), PointType(0, 2)});
segment.push_back(Line<long double>{PointType(0, 0), PointType(1, 0)});
segment.push_back(Line<long double>{PointType(1, 1), PointType(0, 1)});
assert(
m1une::geometry::half_plane_intersection(segment).status ==
m1une::geometry::HalfPlaneIntersectionStatus::Degenerate
);
std::vector<Line<long double>> no_constraints;
assert(
m1une::geometry::half_plane_intersection(no_constraints).status ==
m1une::geometry::HalfPlaneIntersectionStatus::Unbounded
);
}
void test_randomized() {
std::uint64_t state = 0x5f3759dfULL;
auto random = [&state]() {
state ^= state << 7;
state ^= state >> 9;
return state;
};
for (int trial = 0; trial < 3000; ++trial) {
std::vector<Line<long double>> half_planes;
add_bounding_square(half_planes);
int count = 1 + int(random() % 30);
for (int index = 0; index < count; ++index) {
long long dx;
long long dy;
do {
dx = static_cast<long long>(random() % 21) - 10;
dy = static_cast<long long>(random() % 21) - 10;
} while (dx == 0 && dy == 0);
long long offset = 1 + static_cast<long long>(random() % 8);
PointType first(dy * offset, -dx * offset);
PointType second(first.x + dx, first.y + dy);
half_planes.push_back(Line<long double>{first, second});
}
std::vector<PointType> expected;
expected.emplace_back(-50, -50);
expected.emplace_back(50, -50);
expected.emplace_back(50, 50);
expected.emplace_back(-50, 50);
for (const auto& half_plane : half_planes) {
expected = clip(expected, half_plane);
}
std::shuffle(
half_planes.begin(),
half_planes.end(),
std::mt19937_64(random())
);
auto actual = m1une::geometry::half_plane_intersection(half_planes);
assert(
actual.status ==
m1une::geometry::HalfPlaneIntersectionStatus::Bounded
);
long double expected_area = area(expected);
long double actual_area = area(actual.polygon);
assert(
std::fabs(expected_area - actual_area) <=
1e-8L * std::max(1.0L, expected_area)
);
for (const PointType& point : actual.polygon) {
for (const auto& half_plane : half_planes) {
assert(cross(
half_plane.b - half_plane.a,
point - half_plane.a
) >= -1e-8L);
}
}
}
for (int trial = 0; trial < 3000; ++trial) {
std::vector<Line<long double>> half_planes;
add_bounding_square(half_planes);
int count = 1 + int(random() % 20);
for (int index = 0; index < count; ++index) {
long long dx;
long long dy;
do {
dx = static_cast<long long>(random() % 21) - 10;
dy = static_cast<long long>(random() % 21) - 10;
} while (dx == 0 && dy == 0);
PointType first(
static_cast<long long>(random() % 121) - 60,
static_cast<long long>(random() % 121) - 60
);
PointType second(first.x + dx, first.y + dy);
half_planes.push_back(Line<long double>{first, second});
}
std::vector<PointType> expected;
expected.emplace_back(-50, -50);
expected.emplace_back(50, -50);
expected.emplace_back(50, 50);
expected.emplace_back(-50, 50);
for (const auto& half_plane : half_planes) {
expected = clip(expected, half_plane);
}
std::shuffle(
half_planes.begin(),
half_planes.end(),
std::mt19937_64(random())
);
auto actual = m1une::geometry::half_plane_intersection(half_planes);
long double expected_area = area(expected);
if (expected_area <= 1e-10L) {
assert(
actual.status ==
m1une::geometry::HalfPlaneIntersectionStatus::Empty ||
actual.status ==
m1une::geometry::HalfPlaneIntersectionStatus::Degenerate
);
} else {
assert(
actual.status ==
m1une::geometry::HalfPlaneIntersectionStatus::Bounded
);
assert(
std::fabs(expected_area - area(actual.polygon)) <=
1e-8L * std::max(1.0L, expected_area)
);
}
}
constexpr long double box_size = 100000;
for (int trial = 0; trial < 3000; ++trial) {
std::vector<Line<long double>> half_planes;
int count = 1 + int(random() % 20);
for (int index = 0; index < count; ++index) {
long long dx;
long long dy;
do {
dx = static_cast<long long>(random() % 21) - 10;
dy = static_cast<long long>(random() % 21) - 10;
} while (dx == 0 && dy == 0);
PointType first(
static_cast<long long>(random() % 21) - 10,
static_cast<long long>(random() % 21) - 10
);
PointType second(first.x + dx, first.y + dy);
half_planes.push_back(Line<long double>{first, second});
}
std::vector<PointType> clipped;
clipped.emplace_back(-box_size, -box_size);
clipped.emplace_back(box_size, -box_size);
clipped.emplace_back(box_size, box_size);
clipped.emplace_back(-box_size, box_size);
for (const auto& half_plane : half_planes) {
clipped = clip(clipped, half_plane);
}
auto actual = m1une::geometry::half_plane_intersection(half_planes);
if (area(clipped) <= 1e-10L) {
assert(
actual.status ==
m1une::geometry::HalfPlaneIntersectionStatus::Empty ||
actual.status ==
m1une::geometry::HalfPlaneIntersectionStatus::Degenerate
);
continue;
}
bool touches_box = false;
for (const PointType& point : clipped) {
if (
std::fabs(point.x) >= box_size - 1e-7L ||
std::fabs(point.y) >= box_size - 1e-7L
) {
touches_box = true;
}
}
auto expected_status = touches_box
? m1une::geometry::HalfPlaneIntersectionStatus::Unbounded
: m1une::geometry::HalfPlaneIntersectionStatus::Bounded;
assert(actual.status == expected_status);
}
}
} // namespace
int main() {
m1une::utilities::FastInput fast_input;
m1une::utilities::FastOutput fast_output;
test_special_cases();
test_randomized();
long long a;
long long b;
fast_input >> a >> b;
fast_output << a + b << '\n';
}
verify/geometry/half_plane_intersection_random.test.cpp