844 lines
24 KiB
C++
844 lines
24 KiB
C++
/*******************************************************************************
|
|
* Author : Angus Johnson *
|
|
* Date : 24 November 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 <cstdint>
|
|
#include <cstdlib>
|
|
#include <cmath>
|
|
#include <vector>
|
|
#include <string>
|
|
#include <iostream>
|
|
#include <algorithm>
|
|
#include <climits>
|
|
#include <numeric>
|
|
#include "clipper2/clipper.version.h"
|
|
|
|
#define CLIPPER2_THROW(exception) std::abort()
|
|
|
|
namespace Clipper2Lib
|
|
{
|
|
|
|
#if (defined(__cpp_exceptions) && __cpp_exceptions) || (defined(__EXCEPTIONS) && __EXCEPTIONS)
|
|
|
|
class Clipper2Exception : public std::exception {
|
|
public:
|
|
explicit Clipper2Exception(const char* description) :
|
|
m_descr(description) {}
|
|
virtual const char* what() const throw() override { 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";
|
|
static const char* scale_error =
|
|
"Invalid scale (either 0 or too large)";
|
|
static const char* non_pair_error =
|
|
"There must be 2 values for each coordinate";
|
|
static const char* undefined_error =
|
|
"There is an undefined error in Clipper2";
|
|
#endif
|
|
|
|
// error codes (2^n)
|
|
const int precision_error_i = 1; // non-fatal
|
|
const int scale_error_i = 2; // non-fatal
|
|
const int non_pair_error_i = 4; // non-fatal
|
|
const int undefined_error_i = 32; // fatal
|
|
const int range_error_i = 64;
|
|
|
|
#ifndef PI
|
|
static const double PI = 3.141592653589793238;
|
|
#endif
|
|
|
|
#ifdef CLIPPER2_MAX_PRECISION
|
|
const int MAX_DECIMAL_PRECISION = CLIPPER2_MAX_PRECISION;
|
|
#else
|
|
const int MAX_DECIMAL_PRECISION = 8; // see Discussions #564
|
|
#endif
|
|
|
|
static const int64_t MAX_COORD = INT64_MAX >> 2;
|
|
static const int64_t MIN_COORD = -MAX_COORD;
|
|
static const int64_t INVALID = INT64_MAX;
|
|
const double max_coord = static_cast<double>(MAX_COORD);
|
|
const double min_coord = static_cast<double>(MIN_COORD);
|
|
|
|
static const double MAX_DBL = (std::numeric_limits<double>::max)();
|
|
|
|
static void DoError(int error_code)
|
|
{
|
|
#if (defined(__cpp_exceptions) && __cpp_exceptions) || (defined(__EXCEPTIONS) && __EXCEPTIONS)
|
|
switch (error_code)
|
|
{
|
|
case precision_error_i:
|
|
CLIPPER2_THROW(Clipper2Exception(precision_error));
|
|
case scale_error_i:
|
|
CLIPPER2_THROW(Clipper2Exception(scale_error));
|
|
case non_pair_error_i:
|
|
CLIPPER2_THROW(Clipper2Exception(non_pair_error));
|
|
case undefined_error_i:
|
|
CLIPPER2_THROW(Clipper2Exception(undefined_error));
|
|
case range_error_i:
|
|
CLIPPER2_THROW(Clipper2Exception(range_error));
|
|
}
|
|
#else
|
|
if(error_code) {}; // only to stop compiler 'parameter not used' warning
|
|
#endif
|
|
}
|
|
|
|
|
|
//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(const Point<T2>& p)
|
|
{
|
|
Init(p.x, p.y, p.z);
|
|
}
|
|
|
|
Point operator * (const double scale) const
|
|
{
|
|
return Point(x * scale, y * scale, z);
|
|
}
|
|
|
|
void SetZ(const int64_t z_value) { z = z_value; }
|
|
|
|
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(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>;
|
|
|
|
static const Point64 InvalidPoint64 = Point64(
|
|
(std::numeric_limits<int64_t>::max)(),
|
|
(std::numeric_limits<int64_t>::max)());
|
|
static const PointD InvalidPointD = PointD(
|
|
(std::numeric_limits<double>::max)(),
|
|
(std::numeric_limits<double>::max)());
|
|
|
|
|
|
// 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(T l, T t, T r, T b) :
|
|
left(l),
|
|
top(t),
|
|
right(r),
|
|
bottom(b) {}
|
|
|
|
Rect(bool is_valid = true)
|
|
{
|
|
if (is_valid)
|
|
{
|
|
left = right = top = bottom = 0;
|
|
}
|
|
else
|
|
{
|
|
left = top = (std::numeric_limits<T>::max)();
|
|
right = bottom = (std::numeric_limits<T>::lowest)();
|
|
}
|
|
}
|
|
|
|
bool IsValid() const { return left != (std::numeric_limits<T>::max)(); }
|
|
|
|
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));
|
|
};
|
|
|
|
bool operator==(const Rect<T>& other) const {
|
|
return left == other.left && right == other.right &&
|
|
top == other.top && bottom == other.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 InvalidRect64 = Rect64(
|
|
(std::numeric_limits<int64_t>::max)(),
|
|
(std::numeric_limits<int64_t>::max)(),
|
|
(std::numeric_limits<int64_t>::lowest)(),
|
|
(std::numeric_limits<int64_t>::lowest)());
|
|
static const RectD InvalidRectD = RectD(
|
|
(std::numeric_limits<double>::max)(),
|
|
(std::numeric_limits<double>::max)(),
|
|
(std::numeric_limits<double>::lowest)(),
|
|
(std::numeric_limits<double>::lowest)());
|
|
|
|
template <typename T>
|
|
Rect<T> GetBounds(const Path<T>& path)
|
|
{
|
|
auto xmin = (std::numeric_limits<T>::max)();
|
|
auto ymin = (std::numeric_limits<T>::max)();
|
|
auto xmax = std::numeric_limits<T>::lowest();
|
|
auto ymax = std::numeric_limits<T>::lowest();
|
|
for (const auto& p : path)
|
|
{
|
|
if (p.x < xmin) xmin = p.x;
|
|
if (p.x > xmax) xmax = p.x;
|
|
if (p.y < ymin) ymin = p.y;
|
|
if (p.y > ymax) ymax = p.y;
|
|
}
|
|
return Rect<T>(xmin, ymin, xmax, ymax);
|
|
}
|
|
|
|
template <typename T>
|
|
Rect<T> GetBounds(const Paths<T>& paths)
|
|
{
|
|
auto xmin = (std::numeric_limits<T>::max)();
|
|
auto ymin = (std::numeric_limits<T>::max)();
|
|
auto xmax = std::numeric_limits<T>::lowest();
|
|
auto ymax = std::numeric_limits<T>::lowest();
|
|
for (const Path<T>& path : paths)
|
|
for (const Point<T>& p : path)
|
|
{
|
|
if (p.x < xmin) xmin = p.x;
|
|
if (p.x > xmax) xmax = p.x;
|
|
if (p.y < ymin) ymin = p.y;
|
|
if (p.y > ymax) ymax = p.y;
|
|
}
|
|
return Rect<T>(xmin, ymin, xmax, ymax);
|
|
}
|
|
|
|
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, int& error_code)
|
|
{
|
|
Path<T1> result;
|
|
if (scale_x == 0 || scale_y == 0)
|
|
{
|
|
error_code |= scale_error_i;
|
|
DoError(scale_error_i);
|
|
// if no exception, treat as non-fatal error
|
|
if (scale_x == 0) scale_x = 1.0;
|
|
if (scale_y == 0) scale_y = 1.0;
|
|
}
|
|
|
|
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, int& error_code)
|
|
{
|
|
return ScalePath<T1, T2>(path, scale, scale, error_code);
|
|
}
|
|
|
|
template <typename T1, typename T2>
|
|
inline Paths<T1> ScalePaths(const Paths<T2>& paths,
|
|
double scale_x, double scale_y, int& error_code)
|
|
{
|
|
Paths<T1> result;
|
|
|
|
if constexpr (std::numeric_limits<T1>::is_integer &&
|
|
!std::numeric_limits<T2>::is_integer)
|
|
{
|
|
RectD r = GetBounds(paths);
|
|
if ((r.left * scale_x) < min_coord ||
|
|
(r.right * scale_x) > max_coord ||
|
|
(r.top * scale_y) < min_coord ||
|
|
(r.bottom * scale_y) > max_coord)
|
|
{
|
|
error_code |= range_error_i;
|
|
DoError(range_error_i);
|
|
return result; // empty path
|
|
}
|
|
}
|
|
|
|
result.reserve(paths.size());
|
|
std::transform(paths.begin(), paths.end(), back_inserter(result),
|
|
[=, &error_code](const auto& path)
|
|
{ return ScalePath<T1, T2>(path, scale_x, scale_y, error_code); });
|
|
return result;
|
|
}
|
|
|
|
template <typename T1, typename T2>
|
|
inline Paths<T1> ScalePaths(const Paths<T2>& paths,
|
|
double scale, int& error_code)
|
|
{
|
|
return ScalePaths<T1, T2>(paths, scale, scale, error_code);
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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 void StripDuplicates( Path<T>& path, bool is_closed_path)
|
|
{
|
|
//https://stackoverflow.com/questions/1041620/whats-the-most-efficient-way-to-erase-duplicates-and-sort-a-vector#:~:text=Let%27s%20compare%20three%20approaches%3A
|
|
path.erase(std::unique(path.begin(), path.end()), path.end());
|
|
if (is_closed_path)
|
|
while (path.size() > 1 && path.back() == path.front()) path.pop_back();
|
|
}
|
|
|
|
template<typename T>
|
|
inline void StripDuplicates( Paths<T>& paths, bool is_closed_path)
|
|
{
|
|
for (typename Paths<T>::iterator paths_citer = paths.begin();
|
|
paths_citer != paths.end(); ++paths_citer)
|
|
{
|
|
StripDuplicates(*paths_citer, is_closed_path);
|
|
}
|
|
}
|
|
|
|
// Miscellaneous ------------------------------------------------------------
|
|
|
|
inline void CheckPrecision(int& precision, int& error_code)
|
|
{
|
|
if (precision >= -MAX_DECIMAL_PRECISION && precision <= MAX_DECIMAL_PRECISION) return;
|
|
error_code |= precision_error_i; // non-fatal error
|
|
DoError(precision_error_i); // does nothing unless exceptions enabled
|
|
precision = precision > 0 ? MAX_DECIMAL_PRECISION : -MAX_DECIMAL_PRECISION;
|
|
}
|
|
|
|
inline void CheckPrecision(int& precision)
|
|
{
|
|
int error_code = 0;
|
|
CheckPrecision(precision, error_code);
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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 false;
|
|
double t = ((ln1a.x - ln2a.x) * dy2 - (ln1a.y - ln2a.y) * dx2) / det;
|
|
if (t <= 0.0) ip = ln1a; // ?? check further (see also #568)
|
|
else if (t >= 1.0) ip = ln1b; // ?? check further
|
|
else
|
|
{
|
|
ip.x = static_cast<int64_t>(ln1a.x + t * dx1);
|
|
ip.y = static_cast<int64_t>(ln1a.y + t * dy1);
|
|
}
|
|
return true;
|
|
}
|
|
|
|
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);
|
|
}
|
|
}
|
|
|
|
template<typename T>
|
|
inline Point<T> GetClosestPointOnSegment(const Point<T>& offPt,
|
|
const Point<T>& seg1, const Point<T>& 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;
|
|
if constexpr (std::numeric_limits<T>::is_integer)
|
|
return Point<T>(
|
|
seg1.x + static_cast<T>(nearbyint(q * dx)),
|
|
seg1.y + static_cast<T>(nearbyint(q * dy)));
|
|
else
|
|
return Point<T>(
|
|
seg1.x + static_cast<T>(q * dx),
|
|
seg1.y + static_cast<T>(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 cbegin = polygon.cbegin(), first = cbegin, curr, prev;
|
|
typename Path<T>::const_iterator cend = polygon.cend();
|
|
|
|
while (first != cend && first->y == pt.y) ++first;
|
|
if (first == cend) // not a proper polygon
|
|
return PointInPolygonResult::IsOutside;
|
|
|
|
bool is_above = first->y < pt.y, starting_above = is_above;
|
|
curr = first +1;
|
|
while (true)
|
|
{
|
|
if (curr == cend)
|
|
{
|
|
if (cend == first || first == cbegin) break;
|
|
cend = first;
|
|
curr = cbegin;
|
|
}
|
|
|
|
if (is_above)
|
|
{
|
|
while (curr != cend && curr->y < pt.y) ++curr;
|
|
if (curr == cend) continue;
|
|
}
|
|
else
|
|
{
|
|
while (curr != cend && curr->y > pt.y) ++curr;
|
|
if (curr == cend) continue;
|
|
}
|
|
|
|
if (curr == cbegin)
|
|
prev = polygon.cend() - 1; //nb: NOT cend (since might equal first)
|
|
else
|
|
prev = curr - 1;
|
|
|
|
if (curr->y == pt.y)
|
|
{
|
|
if (curr->x == pt.x ||
|
|
(curr->y == prev->y &&
|
|
((pt.x < prev->x) != (pt.x < curr->x))))
|
|
return PointInPolygonResult::IsOn;
|
|
++curr;
|
|
if (curr == first) break;
|
|
continue;
|
|
}
|
|
|
|
if (pt.x < curr->x && pt.x < prev->x)
|
|
{
|
|
// we're only interested in edges crossing on the left
|
|
}
|
|
else if (pt.x > prev->x && pt.x > curr->x)
|
|
val = 1 - val; // toggle val
|
|
else
|
|
{
|
|
double d = CrossProduct(*prev, *curr, pt);
|
|
if (d == 0) return PointInPolygonResult::IsOn;
|
|
if ((d < 0) == is_above) val = 1 - val;
|
|
}
|
|
is_above = !is_above;
|
|
++curr;
|
|
}
|
|
|
|
if (is_above != starting_above)
|
|
{
|
|
cend = polygon.cend();
|
|
if (curr == cend) curr = cbegin;
|
|
if (curr == cbegin) prev = cend - 1;
|
|
else prev = curr - 1;
|
|
double d = CrossProduct(*prev, *curr, pt);
|
|
if (d == 0) return PointInPolygonResult::IsOn;
|
|
if ((d < 0) == is_above) val = 1 - val;
|
|
}
|
|
|
|
return (val == 0) ?
|
|
PointInPolygonResult::IsOutside :
|
|
PointInPolygonResult::IsInside;
|
|
}
|
|
|
|
} // namespace
|
|
|
|
#endif // CLIPPER_CORE_H
|