axmol/thirdparty/clipper2/clipper.core.h

793 lines
22 KiB
C++

/*******************************************************************************
* Author : Angus Johnson *
* Date : 26 January 2023 *
* Website : http://www.angusj.com *
* Copyright : Angus Johnson 2010-2023 *
* Purpose : Core Clipper Library structures and functions *
* License : http://www.boost.org/LICENSE_1_0.txt *
*******************************************************************************/
#ifndef CLIPPER_CORE_H
#define CLIPPER_CORE_H
#include <cstdlib>
#include <cmath>
#include <vector>
#include <string>
#include <iostream>
#include <algorithm>
#include <climits>
namespace Clipper2Lib
{
#ifdef __cpp_exceptions
class Clipper2Exception : public std::exception {
public:
explicit Clipper2Exception(const char* description) :
m_descr(description) {}
virtual const char* what() const throw() { return m_descr.c_str(); }
private:
std::string m_descr;
};
static const char* precision_error =
"Precision exceeds the permitted range";
static const char* range_error =
"Values exceed permitted range";
#endif
static const double PI = 3.141592653589793238;
static const int64_t MAX_COORD = INT64_MAX >> 2;
static const int64_t MIN_COORD = -MAX_COORD;
static const int64_t INVALID = INT64_MAX;
static const double MAX_DBL = (std::numeric_limits<double>::max)();
static const double MIN_DBL = (std::numeric_limits<double>::min)();
//By far the most widely used filling rules for polygons are EvenOdd
//and NonZero, sometimes called Alternate and Winding respectively.
//https://en.wikipedia.org/wiki/Nonzero-rule
enum class FillRule { EvenOdd, NonZero, Positive, Negative };
// Point ------------------------------------------------------------------------
template <typename T>
struct Point {
T x;
T y;
#ifdef USINGZ
int64_t z;
template <typename T2>
inline void Init(const T2 x_ = 0, const T2 y_ = 0, const int64_t z_ = 0)
{
if constexpr (std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T2>::is_integer)
{
x = static_cast<T>(std::round(x_));
y = static_cast<T>(std::round(y_));
z = z_;
}
else
{
x = static_cast<T>(x_);
y = static_cast<T>(y_);
z = z_;
}
}
explicit Point() : x(0), y(0), z(0) {};
template <typename T2>
Point(const T2 x_, const T2 y_, const int64_t z_ = 0)
{
Init(x_, y_);
z = z_;
}
template <typename T2>
explicit Point<T>(const Point<T2>& p)
{
Init(p.x, p.y, p.z);
}
Point operator * (const double scale) const
{
return Point(x * scale, y * scale, z);
}
friend std::ostream& operator<<(std::ostream& os, const Point& point)
{
os << point.x << "," << point.y << "," << point.z << " ";
return os;
}
#else
template <typename T2>
inline void Init(const T2 x_ = 0, const T2 y_ = 0)
{
if constexpr (std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T2>::is_integer)
{
x = static_cast<T>(std::round(x_));
y = static_cast<T>(std::round(y_));
}
else
{
x = static_cast<T>(x_);
y = static_cast<T>(y_);
}
}
explicit Point() : x(0), y(0) {};
template <typename T2>
Point(const T2 x_, const T2 y_) { Init(x_, y_); }
template <typename T2>
explicit Point<T>(const Point<T2>& p) { Init(p.x, p.y); }
Point operator * (const double scale) const
{
return Point(x * scale, y * scale);
}
friend std::ostream& operator<<(std::ostream& os, const Point& point)
{
os << point.x << "," << point.y << " ";
return os;
}
#endif
friend bool operator==(const Point& a, const Point& b)
{
return a.x == b.x && a.y == b.y;
}
friend bool operator!=(const Point& a, const Point& b)
{
return !(a == b);
}
inline Point<T> operator-() const
{
return Point<T>(-x, -y);
}
inline Point operator+(const Point& b) const
{
return Point(x + b.x, y + b.y);
}
inline Point operator-(const Point& b) const
{
return Point(x - b.x, y - b.y);
}
inline void Negate() { x = -x; y = -y; }
};
//nb: using 'using' here (instead of typedef) as they can be used in templates
using Point64 = Point<int64_t>;
using PointD = Point<double>;
template <typename T>
using Path = std::vector<Point<T>>;
template <typename T>
using Paths = std::vector<Path<T>>;
using Path64 = Path<int64_t>;
using PathD = Path<double>;
using Paths64 = std::vector< Path64>;
using PathsD = std::vector< PathD>;
// Rect ------------------------------------------------------------------------
template <typename T>
struct Rect;
using Rect64 = Rect<int64_t>;
using RectD = Rect<double>;
template <typename T>
struct Rect {
T left;
T top;
T right;
T bottom;
Rect() :
left(0),
top(0),
right(0),
bottom(0) {}
Rect(T l, T t, T r, T b) :
left(l),
top(t),
right(r),
bottom(b) {}
T Width() const { return right - left; }
T Height() const { return bottom - top; }
void Width(T width) { right = left + width; }
void Height(T height) { bottom = top + height; }
Point<T> MidPoint() const
{
return Point<T>((left + right) / 2, (top + bottom) / 2);
}
Path<T> AsPath() const
{
Path<T> result;
result.reserve(4);
result.push_back(Point<T>(left, top));
result.push_back(Point<T>(right, top));
result.push_back(Point<T>(right, bottom));
result.push_back(Point<T>(left, bottom));
return result;
}
bool Contains(const Point<T>& pt) const
{
return pt.x > left && pt.x < right&& pt.y > top && pt.y < bottom;
}
bool Contains(const Rect<T>& rec) const
{
return rec.left >= left && rec.right <= right &&
rec.top >= top && rec.bottom <= bottom;
}
void Scale(double scale) {
left *= scale;
top *= scale;
right *= scale;
bottom *= scale;
}
bool IsEmpty() const { return bottom <= top || right <= left; };
bool Intersects(const Rect<T>& rec) const
{
return ((std::max)(left, rec.left) < (std::min)(right, rec.right)) &&
((std::max)(top, rec.top) < (std::min)(bottom, rec.bottom));
};
friend std::ostream& operator<<(std::ostream& os, const Rect<T>& rect) {
os << "("
<< rect.left << "," << rect.top << "," << rect.right << "," << rect.bottom
<< ")";
return os;
}
};
template <typename T1, typename T2>
inline Rect<T1> ScaleRect(const Rect<T2>& rect, double scale)
{
Rect<T1> result;
if constexpr (std::numeric_limits<T1>::is_integer &&
!std::numeric_limits<T2>::is_integer)
{
result.left = static_cast<T1>(std::round(rect.left * scale));
result.top = static_cast<T1>(std::round(rect.top * scale));
result.right = static_cast<T1>(std::round(rect.right * scale));
result.bottom = static_cast<T1>(std::round(rect.bottom * scale));
}
else
{
result.left = rect.left * scale;
result.top = rect.top * scale;
result.right = rect.right * scale;
result.bottom = rect.bottom * scale;
}
return result;
}
static const Rect64 MaxInvalidRect64 = Rect64(
INT64_MAX, INT64_MAX, INT64_MIN, INT64_MIN);
static const RectD MaxInvalidRectD = RectD(
MAX_DBL, MAX_DBL, MIN_DBL, MIN_DBL);
inline Rect64 Bounds(const Path64& path)
{
Rect64 rec = MaxInvalidRect64;
for (const Point64& pt : path)
{
if (pt.x < rec.left) rec.left = pt.x;
if (pt.x > rec.right) rec.right = pt.x;
if (pt.y < rec.top) rec.top = pt.y;
if (pt.y > rec.bottom) rec.bottom = pt.y;
}
if (rec.IsEmpty()) return Rect64();
return rec;
}
inline Rect64 Bounds(const Paths64& paths)
{
Rect64 rec = MaxInvalidRect64;
for (const Path64& path : paths)
for (const Point64& pt : path)
{
if (pt.x < rec.left) rec.left = pt.x;
if (pt.x > rec.right) rec.right = pt.x;
if (pt.y < rec.top) rec.top = pt.y;
if (pt.y > rec.bottom) rec.bottom = pt.y;
}
if (rec.IsEmpty()) return Rect64();
return rec;
}
inline RectD Bounds(const PathD& path)
{
RectD rec = MaxInvalidRectD;
for (const PointD& pt : path)
{
if (pt.x < rec.left) rec.left = pt.x;
if (pt.x > rec.right) rec.right = pt.x;
if (pt.y < rec.top) rec.top = pt.y;
if (pt.y > rec.bottom) rec.bottom = pt.y;
}
if (rec.IsEmpty()) return RectD();
return rec;
}
inline RectD Bounds(const PathsD& paths)
{
RectD rec = MaxInvalidRectD;
for (const PathD& path : paths)
for (const PointD& pt : path)
{
if (pt.x < rec.left) rec.left = pt.x;
if (pt.x > rec.right) rec.right = pt.x;
if (pt.y < rec.top) rec.top = pt.y;
if (pt.y > rec.bottom) rec.bottom = pt.y;
}
if (rec.IsEmpty()) return RectD();
return rec;
}
template <typename T>
std::ostream& operator << (std::ostream& outstream, const Path<T>& path)
{
if (!path.empty())
{
auto pt = path.cbegin(), last = path.cend() - 1;
while (pt != last)
outstream << *pt++ << ", ";
outstream << *last << std::endl;
}
return outstream;
}
template <typename T>
std::ostream& operator << (std::ostream& outstream, const Paths<T>& paths)
{
for (auto p : paths)
outstream << p;
return outstream;
}
template <typename T1, typename T2>
inline Path<T1> ScalePath(const Path<T2>& path, double scale_x, double scale_y)
{
Path<T1> result;
result.reserve(path.size());
#ifdef USINGZ
std::transform(path.begin(), path.end(), back_inserter(result),
[scale_x, scale_y](const auto& pt)
{ return Point<T1>(pt.x * scale_x, pt.y * scale_y, pt.z); });
#else
std::transform(path.begin(), path.end(), back_inserter(result),
[scale_x, scale_y](const auto& pt)
{ return Point<T1>(pt.x * scale_x, pt.y * scale_y); });
#endif
return result;
}
template <typename T1, typename T2>
inline Path<T1> ScalePath(const Path<T2>& path, double scale)
{
return ScalePath<T1, T2>(path, scale, scale);
}
template <typename T1, typename T2>
inline Paths<T1> ScalePaths(const Paths<T2>& paths, double scale_x, double scale_y)
{
Paths<T1> result;
if constexpr (std::numeric_limits<T1>::is_integer &&
!std::numeric_limits<T2>::is_integer)
{
RectD r = Bounds(paths);
const double max_coord_d = static_cast<double>(MAX_COORD);
const double min_coord_d = static_cast<double>(MIN_COORD);
if ((r.left * scale_x) < min_coord_d ||
(r.right * scale_x) > max_coord_d ||
(r.top * scale_y) < min_coord_d ||
(r.bottom * scale_y) > max_coord_d)
#ifdef __cpp_exceptions
throw Clipper2Exception(range_error);
#else
return result;
#endif
}
result.reserve(paths.size());
std::transform(paths.begin(), paths.end(), back_inserter(result),
[scale_x, scale_y](const auto& path)
{ return ScalePath<T1, T2>(path, scale_x, scale_y); });
return result;
}
template <typename T1, typename T2>
inline Paths<T1> ScalePaths(const Paths<T2>& paths, double scale)
{
return ScalePaths<T1, T2>(paths, scale, scale);
}
template <typename T1, typename T2>
inline Path<T1> TransformPath(const Path<T2>& path)
{
Path<T1> result;
result.reserve(path.size());
std::transform(path.cbegin(), path.cend(), std::back_inserter(result),
[](const Point<T2>& pt) {return Point<T1>(pt); });
return result;
}
template <typename T1, typename T2>
inline Paths<T1> TransformPaths(const Paths<T2>& paths)
{
Paths<T1> result;
std::transform(paths.cbegin(), paths.cend(), std::back_inserter(result),
[](const Path<T2>& path) {return TransformPath<T1, T2>(path); });
return result;
}
inline PathD Path64ToPathD(const Path64& path)
{
return TransformPath<double, int64_t>(path);
}
inline PathsD Paths64ToPathsD(const Paths64& paths)
{
return TransformPaths<double, int64_t>(paths);
}
inline Path64 PathDToPath64(const PathD& path)
{
return TransformPath<int64_t, double>(path);
}
inline Paths64 PathsDToPaths64(const PathsD& paths)
{
return TransformPaths<int64_t, double>(paths);
}
template<typename T>
inline double Sqr(T val)
{
return static_cast<double>(val) * static_cast<double>(val);
}
template<typename T>
inline bool NearEqual(const Point<T>& p1,
const Point<T>& p2, double max_dist_sqrd)
{
return Sqr(p1.x - p2.x) + Sqr(p1.y - p2.y) < max_dist_sqrd;
}
template<typename T>
inline Path<T> StripNearEqual(const Path<T>& path,
double max_dist_sqrd, bool is_closed_path)
{
if (path.size() == 0) return Path<T>();
Path<T> result;
result.reserve(path.size());
typename Path<T>::const_iterator path_iter = path.cbegin();
Point<T> first_pt = *path_iter++, last_pt = first_pt;
result.push_back(first_pt);
for (; path_iter != path.cend(); ++path_iter)
{
if (!NearEqual(*path_iter, last_pt, max_dist_sqrd))
{
last_pt = *path_iter;
result.push_back(last_pt);
}
}
if (!is_closed_path) return result;
while (result.size() > 1 &&
NearEqual(result.back(), first_pt, max_dist_sqrd)) result.pop_back();
return result;
}
template<typename T>
inline Paths<T> StripNearEqual(const Paths<T>& paths,
double max_dist_sqrd, bool is_closed_path)
{
Paths<T> result;
result.reserve(paths.size());
for (typename Paths<T>::const_iterator paths_citer = paths.cbegin();
paths_citer != paths.cend(); ++paths_citer)
{
result.push_back(StripNearEqual(*paths_citer, max_dist_sqrd, is_closed_path));
}
return result;
}
template<typename T>
inline Path<T> StripDuplicates(const Path<T>& path, bool is_closed_path)
{
if (path.size() == 0) return Path<T>();
Path<T> result;
result.reserve(path.size());
typename Path<T>::const_iterator path_iter = path.cbegin();
Point<T> first_pt = *path_iter++, last_pt = first_pt;
result.push_back(first_pt);
for (; path_iter != path.cend(); ++path_iter)
{
if (*path_iter != last_pt)
{
last_pt = *path_iter;
result.push_back(last_pt);
}
}
if (!is_closed_path) return result;
while (result.size() > 1 && result.back() == first_pt) result.pop_back();
return result;
}
template<typename T>
inline Paths<T> StripDuplicates(const Paths<T>& paths, bool is_closed_path)
{
Paths<T> result;
result.reserve(paths.size());
for (typename Paths<T>::const_iterator paths_citer = paths.cbegin();
paths_citer != paths.cend(); ++paths_citer)
{
result.push_back(StripDuplicates(*paths_citer, is_closed_path));
}
return result;
}
// Miscellaneous ------------------------------------------------------------
inline void CheckPrecision(int& precision)
{
if (precision >= -8 && precision <= 8) return;
#ifdef __cpp_exceptions
throw Clipper2Exception(precision_error);
#else
precision = precision > 8 ? 8 : -8;
#endif
}
template <typename T>
inline double CrossProduct(const Point<T>& pt1, const Point<T>& pt2, const Point<T>& pt3) {
return (static_cast<double>(pt2.x - pt1.x) * static_cast<double>(pt3.y -
pt2.y) - static_cast<double>(pt2.y - pt1.y) * static_cast<double>(pt3.x - pt2.x));
}
template <typename T>
inline double CrossProduct(const Point<T>& vec1, const Point<T>& vec2)
{
return static_cast<double>(vec1.y * vec2.x) - static_cast<double>(vec2.y * vec1.x);
}
template <typename T>
inline double DotProduct(const Point<T>& pt1, const Point<T>& pt2, const Point<T>& pt3) {
return (static_cast<double>(pt2.x - pt1.x) * static_cast<double>(pt3.x - pt2.x) +
static_cast<double>(pt2.y - pt1.y) * static_cast<double>(pt3.y - pt2.y));
}
template <typename T>
inline double DotProduct(const Point<T>& vec1, const Point<T>& vec2)
{
return static_cast<double>(vec1.x * vec2.x) + static_cast<double>(vec1.y * vec2.y);
}
template <typename T>
inline double DistanceSqr(const Point<T> pt1, const Point<T> pt2)
{
return Sqr(pt1.x - pt2.x) + Sqr(pt1.y - pt2.y);
}
template <typename T>
inline double DistanceFromLineSqrd(const Point<T>& pt, const Point<T>& ln1, const Point<T>& ln2)
{
//perpendicular distance of point (x³,y³) = (Ax³ + By³ + C)/Sqrt(A² + B²)
//see http://en.wikipedia.org/wiki/Perpendicular_distance
double A = static_cast<double>(ln1.y - ln2.y);
double B = static_cast<double>(ln2.x - ln1.x);
double C = A * ln1.x + B * ln1.y;
C = A * pt.x + B * pt.y - C;
return (C * C) / (A * A + B * B);
}
template <typename T>
inline double Area(const Path<T>& path)
{
size_t cnt = path.size();
if (cnt < 3) return 0.0;
double a = 0.0;
typename Path<T>::const_iterator it1, it2 = path.cend() - 1, stop = it2;
if (!(cnt & 1)) ++stop;
for (it1 = path.cbegin(); it1 != stop;)
{
a += static_cast<double>(it2->y + it1->y) * (it2->x - it1->x);
it2 = it1 + 1;
a += static_cast<double>(it1->y + it2->y) * (it1->x - it2->x);
it1 += 2;
}
if (cnt & 1)
a += static_cast<double>(it2->y + it1->y) * (it2->x - it1->x);
return a * 0.5;
}
template <typename T>
inline double Area(const Paths<T>& paths)
{
double a = 0.0;
for (typename Paths<T>::const_iterator paths_iter = paths.cbegin();
paths_iter != paths.cend(); ++paths_iter)
{
a += Area<T>(*paths_iter);
}
return a;
}
template <typename T>
inline bool IsPositive(const Path<T>& poly)
{
// A curve has positive orientation [and area] if a region 'R'
// is on the left when traveling around the outside of 'R'.
//https://mathworld.wolfram.com/CurveOrientation.html
//nb: This statement is premised on using Cartesian coordinates
return Area<T>(poly) >= 0;
}
static const double max_coord = static_cast<double>(MAX_COORD);
static const double min_coord = static_cast<double>(MIN_COORD);
inline int64_t CheckCastInt64(double val)
{
if ((val >= max_coord) || (val <= min_coord)) return INVALID;
else return static_cast<int64_t>(val);
}
inline bool GetIntersectPoint(const Point64& ln1a, const Point64& ln1b,
const Point64& ln2a, const Point64& ln2b, Point64& ip)
{
// https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
double dx1 = static_cast<double>(ln1b.x - ln1a.x);
double dy1 = static_cast<double>(ln1b.y - ln1a.y);
double dx2 = static_cast<double>(ln2b.x - ln2a.x);
double dy2 = static_cast<double>(ln2b.y - ln2a.y);
double det = dy1 * dx2 - dy2 * dx1;
if (det == 0.0) return 0;
double qx = dx1 * ln1a.y - dy1 * ln1a.x;
double qy = dx2 * ln2a.y - dy2 * ln2a.x;
ip.x = CheckCastInt64((dx1 * qy - dx2 * qx) / det);
ip.y = CheckCastInt64((dy1 * qy - dy2 * qx) / det);
return (ip.x != INVALID && ip.y != INVALID);
}
inline bool SegmentsIntersect(const Point64& seg1a, const Point64& seg1b,
const Point64& seg2a, const Point64& seg2b, bool inclusive = false)
{
if (inclusive)
{
double res1 = CrossProduct(seg1a, seg2a, seg2b);
double res2 = CrossProduct(seg1b, seg2a, seg2b);
if (res1 * res2 > 0) return false;
double res3 = CrossProduct(seg2a, seg1a, seg1b);
double res4 = CrossProduct(seg2b, seg1a, seg1b);
if (res3 * res4 > 0) return false;
return (res1 || res2 || res3 || res4); // ensures not collinear
}
else {
return (CrossProduct(seg1a, seg2a, seg2b) *
CrossProduct(seg1b, seg2a, seg2b) < 0) &&
(CrossProduct(seg2a, seg1a, seg1b) *
CrossProduct(seg2b, seg1a, seg1b) < 0);
}
}
inline Point64 GetClosestPointOnSegment(const Point64& offPt,
const Point64& seg1, const Point64& seg2)
{
if (seg1.x == seg2.x && seg1.y == seg2.y) return seg1;
double dx = static_cast<double>(seg2.x - seg1.x);
double dy = static_cast<double>(seg2.y - seg1.y);
double q =
(static_cast<double>(offPt.x - seg1.x) * dx +
static_cast<double>(offPt.y - seg1.y) * dy) /
(Sqr(dx) + Sqr(dy));
if (q < 0) q = 0; else if (q > 1) q = 1;
return Point64(
seg1.x + static_cast<int64_t>(nearbyint(q * dx)),
seg1.y + static_cast<int64_t>(nearbyint(q * dy)));
}
enum class PointInPolygonResult { IsOn, IsInside, IsOutside };
template <typename T>
inline PointInPolygonResult PointInPolygon(const Point<T>& pt, const Path<T>& polygon)
{
if (polygon.size() < 3)
return PointInPolygonResult::IsOutside;
int val = 0;
typename Path<T>::const_iterator start = polygon.cbegin(), cit = start;
typename Path<T>::const_iterator cend = polygon.cend(), pit = cend - 1;
while (pit->y == pt.y)
{
if (pit == start) return PointInPolygonResult::IsOutside;
--pit;
}
bool is_above = pit->y < pt.y;
while (cit != cend)
{
if (is_above)
{
while (cit != cend && cit->y < pt.y) ++cit;
if (cit == cend) break;
}
else
{
while (cit != cend && cit->y > pt.y) ++cit;
if (cit == cend) break;
}
if (cit == start) pit = cend - 1;
else pit = cit - 1;
if (cit->y == pt.y)
{
if (cit->x == pt.x || (cit->y == pit->y &&
((pt.x < pit->x) != (pt.x < cit->x))))
return PointInPolygonResult::IsOn;
++cit;
continue;
}
if (pt.x < cit->x && pt.x < pit->x)
{
// we're only interested in edges crossing on the left
}
else if (pt.x > pit->x && pt.x > cit->x)
val = 1 - val; // toggle val
else
{
double d = CrossProduct(*pit, *cit, pt);
if (d == 0) return PointInPolygonResult::IsOn;
if ((d < 0) == is_above) val = 1 - val;
}
is_above = !is_above;
++cit;
}
return (val == 0) ?
PointInPolygonResult::IsOutside :
PointInPolygonResult::IsInside;
}
} // namespace
#endif // CLIPPER_CORE_H