1082 lines
32 KiB
C++
1082 lines
32 KiB
C++
/*******************************************************************************
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* Author : Angus Johnson *
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* Date : 12 May 2024 *
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* Website : https://www.angusj.com *
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* Copyright : Angus Johnson 2010-2024 *
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* Purpose : Core Clipper Library structures and functions *
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* License : https://www.boost.org/LICENSE_1_0.txt *
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*******************************************************************************/
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#ifndef CLIPPER_CORE_H
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#define CLIPPER_CORE_H
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#include "clipper2/clipper.version.h"
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#include <cstdint>
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#include <vector>
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#include <string>
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#include <iostream>
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#include <algorithm>
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#include <numeric>
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#include <cmath>
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#define CLIPPER2_THROW(exception) std::abort()
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namespace Clipper2Lib
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{
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#if (defined(__cpp_exceptions) && __cpp_exceptions) || (defined(__EXCEPTIONS) && __EXCEPTIONS)
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class Clipper2Exception : public std::exception {
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public:
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explicit Clipper2Exception(const char* description) :
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m_descr(description) {}
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virtual const char* what() const noexcept override { return m_descr.c_str(); }
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private:
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std::string m_descr;
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};
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static const char* precision_error =
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"Precision exceeds the permitted range";
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static const char* range_error =
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"Values exceed permitted range";
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static const char* scale_error =
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"Invalid scale (either 0 or too large)";
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static const char* non_pair_error =
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"There must be 2 values for each coordinate";
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static const char* undefined_error =
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"There is an undefined error in Clipper2";
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#endif
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// error codes (2^n)
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const int precision_error_i = 1; // non-fatal
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const int scale_error_i = 2; // non-fatal
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const int non_pair_error_i = 4; // non-fatal
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const int undefined_error_i = 32; // fatal
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const int range_error_i = 64;
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#ifndef PI
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static const double PI = 3.141592653589793238;
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#endif
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#ifdef CLIPPER2_MAX_DECIMAL_PRECISION
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const int CLIPPER2_MAX_DEC_PRECISION = CLIPPER2_MAX_DECIMAL_PRECISION;
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#else
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const int CLIPPER2_MAX_DEC_PRECISION = 8; // see Discussions #564
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#endif
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static const int64_t MAX_COORD = INT64_MAX >> 2;
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static const int64_t MIN_COORD = -MAX_COORD;
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static const int64_t INVALID = INT64_MAX;
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const double max_coord = static_cast<double>(MAX_COORD);
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const double min_coord = static_cast<double>(MIN_COORD);
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static const double MAX_DBL = (std::numeric_limits<double>::max)();
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static void DoError([[maybe_unused]] int error_code)
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{
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#if (defined(__cpp_exceptions) && __cpp_exceptions) || (defined(__EXCEPTIONS) && __EXCEPTIONS)
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switch (error_code)
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{
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case precision_error_i:
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CLIPPER2_THROW(Clipper2Exception(precision_error));
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case scale_error_i:
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CLIPPER2_THROW(Clipper2Exception(scale_error));
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case non_pair_error_i:
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CLIPPER2_THROW(Clipper2Exception(non_pair_error));
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case undefined_error_i:
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CLIPPER2_THROW(Clipper2Exception(undefined_error));
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case range_error_i:
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CLIPPER2_THROW(Clipper2Exception(range_error));
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// Should never happen, but adding this to stop a compiler warning
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default:
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CLIPPER2_THROW(Clipper2Exception("Unknown error"));
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}
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#else
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if(error_code) {}; // only to stop compiler 'parameter not used' warning
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#endif
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}
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// can we call std::round on T? (default false) (#824)
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template <typename T, typename = void>
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struct is_round_invocable : std::false_type {};
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template <typename T>
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struct is_round_invocable<T, std::void_t<decltype(std::round(std::declval<T>()))>> : std::true_type {};
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//By far the most widely used filling rules for polygons are EvenOdd
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//and NonZero, sometimes called Alternate and Winding respectively.
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//https://en.wikipedia.org/wiki/Nonzero-rule
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enum class FillRule { EvenOdd, NonZero, Positive, Negative };
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#ifdef USINGZ
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using z_type = int64_t;
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#endif
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// Point ------------------------------------------------------------------------
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template <typename T>
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struct Point {
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T x;
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T y;
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#ifdef USINGZ
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z_type z;
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template <typename T2>
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inline void Init(const T2 x_ = 0, const T2 y_ = 0, const z_type z_ = 0)
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{
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if constexpr (std::is_integral_v<T> &&
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is_round_invocable<T2>::value && !std::is_integral_v<T2>)
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{
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x = static_cast<T>(std::round(x_));
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y = static_cast<T>(std::round(y_));
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z = z_;
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}
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else
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{
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x = static_cast<T>(x_);
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y = static_cast<T>(y_);
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z = z_;
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}
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}
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explicit Point() : x(0), y(0), z(0) {};
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template <typename T2>
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Point(const T2 x_, const T2 y_, const z_type z_ = 0)
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{
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Init(x_, y_);
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z = z_;
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}
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template <typename T2>
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explicit Point(const Point<T2>& p)
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{
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Init(p.x, p.y, p.z);
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}
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template <typename T2>
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explicit Point(const Point<T2>& p, z_type z_)
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{
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Init(p.x, p.y, z_);
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}
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Point operator * (const double scale) const
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{
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return Point(x * scale, y * scale, z);
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}
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void SetZ(const z_type z_value) { z = z_value; }
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friend std::ostream& operator<<(std::ostream& os, const Point& point)
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{
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os << point.x << "," << point.y << "," << point.z;
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return os;
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}
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#else
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template <typename T2>
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inline void Init(const T2 x_ = 0, const T2 y_ = 0)
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{
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if constexpr (std::is_integral_v<T> &&
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is_round_invocable<T2>::value && !std::is_integral_v<T2>)
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{
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x = static_cast<T>(std::round(x_));
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y = static_cast<T>(std::round(y_));
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}
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else
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{
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x = static_cast<T>(x_);
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y = static_cast<T>(y_);
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}
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}
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explicit Point() : x(0), y(0) {};
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template <typename T2>
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Point(const T2 x_, const T2 y_) { Init(x_, y_); }
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template <typename T2>
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explicit Point(const Point<T2>& p) { Init(p.x, p.y); }
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Point operator * (const double scale) const
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{
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return Point(x * scale, y * scale);
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}
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friend std::ostream& operator<<(std::ostream& os, const Point& point)
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{
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os << point.x << "," << point.y;
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return os;
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}
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#endif
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friend bool operator==(const Point& a, const Point& b)
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{
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return a.x == b.x && a.y == b.y;
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}
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friend bool operator!=(const Point& a, const Point& b)
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{
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return !(a == b);
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}
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inline Point<T> operator-() const
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{
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return Point<T>(-x, -y);
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}
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inline Point operator+(const Point& b) const
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{
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return Point(x + b.x, y + b.y);
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}
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inline Point operator-(const Point& b) const
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{
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return Point(x - b.x, y - b.y);
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}
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inline void Negate() { x = -x; y = -y; }
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};
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//nb: using 'using' here (instead of typedef) as they can be used in templates
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using Point64 = Point<int64_t>;
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using PointD = Point<double>;
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template <typename T>
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using Path = std::vector<Point<T>>;
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template <typename T>
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using Paths = std::vector<Path<T>>;
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using Path64 = Path<int64_t>;
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using PathD = Path<double>;
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using Paths64 = std::vector< Path64>;
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using PathsD = std::vector< PathD>;
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static const Point64 InvalidPoint64 = Point64(
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(std::numeric_limits<int64_t>::max)(),
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(std::numeric_limits<int64_t>::max)());
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static const PointD InvalidPointD = PointD(
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(std::numeric_limits<double>::max)(),
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(std::numeric_limits<double>::max)());
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template<typename T>
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static inline Point<T> MidPoint(const Point<T>& p1, const Point<T>& p2)
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{
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Point<T> result;
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result.x = (p1.x + p2.x) / 2;
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result.y = (p1.y + p2.y) / 2;
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return result;
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}
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// Rect ------------------------------------------------------------------------
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template <typename T>
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struct Rect;
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using Rect64 = Rect<int64_t>;
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using RectD = Rect<double>;
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template <typename T>
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struct Rect {
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T left;
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T top;
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T right;
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T bottom;
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Rect(T l, T t, T r, T b) :
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left(l),
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top(t),
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right(r),
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bottom(b) {}
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Rect(bool is_valid = true)
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{
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if (is_valid)
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{
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left = right = top = bottom = 0;
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}
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else
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{
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left = top = (std::numeric_limits<T>::max)();
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right = bottom = std::numeric_limits<T>::lowest();
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}
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}
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static Rect<T> InvalidRect()
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{
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return {
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(std::numeric_limits<T>::max)(),
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(std::numeric_limits<T>::max)(),
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std::numeric_limits<T>::lowest(),
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std::numeric_limits<T>::lowest() };
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}
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bool IsValid() const { return left != (std::numeric_limits<T>::max)(); }
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T Width() const { return right - left; }
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T Height() const { return bottom - top; }
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void Width(T width) { right = left + width; }
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void Height(T height) { bottom = top + height; }
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Point<T> MidPoint() const
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{
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return Point<T>((left + right) / 2, (top + bottom) / 2);
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}
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Path<T> AsPath() const
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{
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Path<T> result;
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result.reserve(4);
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result.emplace_back(left, top);
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result.emplace_back(right, top);
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result.emplace_back(right, bottom);
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result.emplace_back(left, bottom);
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return result;
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}
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bool Contains(const Point<T>& pt) const
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{
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return pt.x > left && pt.x < right&& pt.y > top && pt.y < bottom;
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}
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bool Contains(const Rect<T>& rec) const
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{
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return rec.left >= left && rec.right <= right &&
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rec.top >= top && rec.bottom <= bottom;
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}
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void Scale(double scale) {
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left *= scale;
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top *= scale;
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right *= scale;
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bottom *= scale;
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}
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bool IsEmpty() const { return bottom <= top || right <= left; };
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bool Intersects(const Rect<T>& rec) const
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{
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return ((std::max)(left, rec.left) <= (std::min)(right, rec.right)) &&
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((std::max)(top, rec.top) <= (std::min)(bottom, rec.bottom));
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};
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bool operator==(const Rect<T>& other) const {
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return left == other.left && right == other.right &&
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top == other.top && bottom == other.bottom;
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}
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Rect<T>& operator+=(const Rect<T>& other)
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{
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left = (std::min)(left, other.left);
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top = (std::min)(top, other.top);
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right = (std::max)(right, other.right);
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bottom = (std::max)(bottom, other.bottom);
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return *this;
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}
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Rect<T> operator+(const Rect<T>& other) const
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{
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Rect<T> result = *this;
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result += other;
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return result;
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}
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friend std::ostream& operator<<(std::ostream& os, const Rect<T>& rect) {
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os << "(" << rect.left << "," << rect.top << "," << rect.right << "," << rect.bottom << ") ";
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return os;
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}
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};
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template <typename T1, typename T2>
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inline Rect<T1> ScaleRect(const Rect<T2>& rect, double scale)
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{
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Rect<T1> result;
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if constexpr (std::is_integral_v<T1> &&
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is_round_invocable<T2>::value && !std::is_integral_v<T2>)
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{
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result.left = static_cast<T1>(std::round(rect.left * scale));
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result.top = static_cast<T1>(std::round(rect.top * scale));
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result.right = static_cast<T1>(std::round(rect.right * scale));
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result.bottom = static_cast<T1>(std::round(rect.bottom * scale));
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}
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else
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{
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result.left = static_cast<T1>(rect.left * scale);
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result.top = static_cast<T1>(rect.top * scale);
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result.right = static_cast<T1>(rect.right * scale);
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result.bottom = static_cast<T1>(rect.bottom * scale);
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}
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return result;
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}
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static const Rect64 InvalidRect64 = Rect64::InvalidRect();
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static const RectD InvalidRectD = RectD::InvalidRect();
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template <typename T>
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Rect<T> GetBounds(const Path<T>& path)
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{
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T xmin = (std::numeric_limits<T>::max)();
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T ymin = (std::numeric_limits<T>::max)();
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T xmax = std::numeric_limits<T>::lowest();
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T ymax = std::numeric_limits<T>::lowest();
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for (const auto& p : path)
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{
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if (p.x < xmin) xmin = p.x;
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if (p.x > xmax) xmax = p.x;
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if (p.y < ymin) ymin = p.y;
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if (p.y > ymax) ymax = p.y;
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}
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return Rect<T>(xmin, ymin, xmax, ymax);
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}
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template <typename T>
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Rect<T> GetBounds(const Paths<T>& paths)
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{
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T xmin = (std::numeric_limits<T>::max)();
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T ymin = (std::numeric_limits<T>::max)();
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T xmax = std::numeric_limits<T>::lowest();
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T ymax = std::numeric_limits<T>::lowest();
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for (const Path<T>& path : paths)
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for (const Point<T>& p : path)
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{
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if (p.x < xmin) xmin = p.x;
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if (p.x > xmax) xmax = p.x;
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if (p.y < ymin) ymin = p.y;
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if (p.y > ymax) ymax = p.y;
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}
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return Rect<T>(xmin, ymin, xmax, ymax);
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}
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template <typename T, typename T2>
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Rect<T> GetBounds(const Path<T2>& path)
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{
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T xmin = (std::numeric_limits<T>::max)();
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T ymin = (std::numeric_limits<T>::max)();
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T xmax = std::numeric_limits<T>::lowest();
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T ymax = std::numeric_limits<T>::lowest();
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for (const auto& p : path)
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{
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if (p.x < xmin) xmin = static_cast<T>(p.x);
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if (p.x > xmax) xmax = static_cast<T>(p.x);
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if (p.y < ymin) ymin = static_cast<T>(p.y);
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if (p.y > ymax) ymax = static_cast<T>(p.y);
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}
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return Rect<T>(xmin, ymin, xmax, ymax);
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}
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template <typename T, typename T2>
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Rect<T> GetBounds(const Paths<T2>& paths)
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{
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T xmin = (std::numeric_limits<T>::max)();
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T ymin = (std::numeric_limits<T>::max)();
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T xmax = std::numeric_limits<T>::lowest();
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T ymax = std::numeric_limits<T>::lowest();
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for (const Path<T2>& path : paths)
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for (const Point<T2>& p : path)
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{
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if (p.x < xmin) xmin = static_cast<T>(p.x);
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if (p.x > xmax) xmax = static_cast<T>(p.x);
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if (p.y < ymin) ymin = static_cast<T>(p.y);
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if (p.y > ymax) ymax = static_cast<T>(p.y);
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}
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return Rect<T>(xmin, ymin, xmax, ymax);
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}
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template <typename T>
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std::ostream& operator << (std::ostream& outstream, const Path<T>& path)
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{
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if (!path.empty())
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{
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auto pt = path.cbegin(), last = path.cend() - 1;
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while (pt != last)
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outstream << *pt++ << ", ";
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outstream << *last << std::endl;
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}
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return outstream;
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}
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template <typename T>
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std::ostream& operator << (std::ostream& outstream, const Paths<T>& paths)
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{
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for (auto p : paths)
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outstream << p;
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return outstream;
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}
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template <typename T1, typename T2>
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inline Path<T1> ScalePath(const Path<T2>& path,
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double scale_x, double scale_y, int& error_code)
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{
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Path<T1> result;
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if (scale_x == 0 || scale_y == 0)
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{
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error_code |= scale_error_i;
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DoError(scale_error_i);
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// if no exception, treat as non-fatal error
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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::is_integral_v<T1>)
|
|
{
|
|
RectD r = GetBounds<double, T2>(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.emplace_back(first_pt);
|
|
for (; path_iter != path.cend(); ++path_iter)
|
|
{
|
|
if (!NearEqual(*path_iter, last_pt, max_dist_sqrd))
|
|
{
|
|
last_pt = *path_iter;
|
|
result.emplace_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.emplace_back(std::move(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 CheckPrecisionRange(int& precision, int& error_code)
|
|
{
|
|
if (precision >= -CLIPPER2_MAX_DEC_PRECISION &&
|
|
precision <= CLIPPER2_MAX_DEC_PRECISION) return;
|
|
error_code |= precision_error_i; // non-fatal error
|
|
DoError(precision_error_i); // does nothing when exceptions are disabled
|
|
precision = precision > 0 ? CLIPPER2_MAX_DEC_PRECISION : -CLIPPER2_MAX_DEC_PRECISION;
|
|
}
|
|
|
|
inline void CheckPrecisionRange(int& precision)
|
|
{
|
|
int error_code = 0;
|
|
CheckPrecisionRange(precision, error_code);
|
|
}
|
|
|
|
inline int TriSign(int64_t x) // returns 0, 1 or -1
|
|
{
|
|
return (x > 0) - (x < 0);
|
|
}
|
|
|
|
struct MultiplyUInt64Result
|
|
{
|
|
const uint64_t result = 0;
|
|
const uint64_t carry = 0;
|
|
|
|
bool operator==(const MultiplyUInt64Result& other) const
|
|
{
|
|
return result == other.result && carry == other.carry;
|
|
};
|
|
};
|
|
|
|
inline MultiplyUInt64Result Multiply(uint64_t a, uint64_t b) // #834, #835
|
|
{
|
|
const auto lo = [](uint64_t x) { return x & 0xFFFFFFFF; };
|
|
const auto hi = [](uint64_t x) { return x >> 32; };
|
|
|
|
const uint64_t x1 = lo(a) * lo(b);
|
|
const uint64_t x2 = hi(a) * lo(b) + hi(x1);
|
|
const uint64_t x3 = lo(a) * hi(b) + lo(x2);
|
|
const uint64_t result = lo(x3) << 32 | lo(x1);
|
|
const uint64_t carry = hi(a) * hi(b) + hi(x2) + hi(x3);
|
|
|
|
return { result, carry };
|
|
}
|
|
|
|
// returns true if (and only if) a * b == c * d
|
|
inline bool ProductsAreEqual(int64_t a, int64_t b, int64_t c, int64_t d)
|
|
{
|
|
// Work around LLVM issue: https://github.com/llvm/llvm-project/issues/16778
|
|
// Details: https://github.com/godotengine/godot/pull/95964#issuecomment-2306581804
|
|
// #if (defined(__clang__) || defined(__GNUC__)) && UINTPTR_MAX >= UINT64_MAX
|
|
// const auto ab = static_cast<__int128_t>(a) * static_cast<__int128_t>(b);
|
|
// const auto cd = static_cast<__int128_t>(c) * static_cast<__int128_t>(d);
|
|
// return ab == cd;
|
|
// #else
|
|
// nb: unsigned values needed for calculating overflow carry
|
|
const auto abs_a = static_cast<uint64_t>(std::abs(a));
|
|
const auto abs_b = static_cast<uint64_t>(std::abs(b));
|
|
const auto abs_c = static_cast<uint64_t>(std::abs(c));
|
|
const auto abs_d = static_cast<uint64_t>(std::abs(d));
|
|
|
|
const auto abs_ab = Multiply(abs_a, abs_b);
|
|
const auto abs_cd = Multiply(abs_c, abs_d);
|
|
|
|
// nb: it's important to differentiate 0 values here from other values
|
|
const auto sign_ab = TriSign(a) * TriSign(b);
|
|
const auto sign_cd = TriSign(c) * TriSign(d);
|
|
|
|
return abs_ab == abs_cd && sign_ab == sign_cd;
|
|
// #endif
|
|
}
|
|
|
|
template <typename T>
|
|
inline bool IsCollinear(const Point<T>& pt1,
|
|
const Point<T>& sharedPt, const Point<T>& pt2) // #777
|
|
{
|
|
const auto a = sharedPt.x - pt1.x;
|
|
const auto b = pt2.y - sharedPt.y;
|
|
const auto c = sharedPt.y - pt1.y;
|
|
const auto d = pt2.x - sharedPt.x;
|
|
// When checking for collinearity with very large coordinate values
|
|
// then ProductsAreEqual is more accurate than using CrossProduct.
|
|
return ProductsAreEqual(a, b, c, d);
|
|
}
|
|
|
|
|
|
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 PerpendicDistFromLineSqrd(const Point<T>& pt,
|
|
const Point<T>& line1, const Point<T>& line2)
|
|
{
|
|
//perpendicular distance of point (x³,y³) = (Ax³ + By³ + C)/Sqrt(A² + B²)
|
|
//see https://en.wikipedia.org/wiki/Perpendicular_distance
|
|
double a = static_cast<double>(pt.x - line1.x);
|
|
double b = static_cast<double>(pt.y - line1.y);
|
|
double c = static_cast<double>(line2.x - line1.x);
|
|
double d = static_cast<double>(line2.y - line1.y);
|
|
if (c == 0 && d == 0) return 0;
|
|
return Sqr(a * d - c * b) / (c * c + d * d);
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
#if CLIPPER2_HI_PRECISION
|
|
// caution: this will compromise performance
|
|
// https://github.com/AngusJohnson/Clipper2/issues/317#issuecomment-1314023253
|
|
// See also CPP/BenchMark/GetIntersectPtBenchmark.cpp
|
|
#define CC_MIN(x,y) ((x)>(y)?(y):(x))
|
|
#define CC_MAX(x,y) ((x)<(y)?(y):(x))
|
|
template<typename T>
|
|
inline bool GetSegmentIntersectPt(const Point<T>& ln1a, const Point<T>& ln1b,
|
|
const Point<T>& ln2a, const Point<T>& ln2b, Point<T>& ip)
|
|
{
|
|
double ln1dy = static_cast<double>(ln1b.y - ln1a.y);
|
|
double ln1dx = static_cast<double>(ln1a.x - ln1b.x);
|
|
double ln2dy = static_cast<double>(ln2b.y - ln2a.y);
|
|
double ln2dx = static_cast<double>(ln2a.x - ln2b.x);
|
|
double det = (ln2dy * ln1dx) - (ln1dy * ln2dx);
|
|
if (det == 0.0) return false;
|
|
T bb0minx = CC_MIN(ln1a.x, ln1b.x);
|
|
T bb0miny = CC_MIN(ln1a.y, ln1b.y);
|
|
T bb0maxx = CC_MAX(ln1a.x, ln1b.x);
|
|
T bb0maxy = CC_MAX(ln1a.y, ln1b.y);
|
|
T bb1minx = CC_MIN(ln2a.x, ln2b.x);
|
|
T bb1miny = CC_MIN(ln2a.y, ln2b.y);
|
|
T bb1maxx = CC_MAX(ln2a.x, ln2b.x);
|
|
T bb1maxy = CC_MAX(ln2a.y, ln2b.y);
|
|
|
|
if constexpr (std::is_integral_v<T>)
|
|
{
|
|
int64_t originx = (CC_MIN(bb0maxx, bb1maxx) + CC_MAX(bb0minx, bb1minx)) >> 1;
|
|
int64_t originy = (CC_MIN(bb0maxy, bb1maxy) + CC_MAX(bb0miny, bb1miny)) >> 1;
|
|
double ln0c = (ln1dy * static_cast<double>(ln1a.x - originx)) +
|
|
(ln1dx * static_cast<double>(ln1a.y - originy));
|
|
double ln1c = (ln2dy * static_cast<double>(ln2a.x - originx)) +
|
|
(ln2dx * static_cast<double>(ln2a.y - originy));
|
|
double hitx = ((ln1dx * ln1c) - (ln2dx * ln0c)) / det;
|
|
double hity = ((ln2dy * ln0c) - (ln1dy * ln1c)) / det;
|
|
|
|
ip.x = originx + (T)nearbyint(hitx);
|
|
ip.y = originy + (T)nearbyint(hity);
|
|
}
|
|
else
|
|
{
|
|
double originx = (CC_MIN(bb0maxx, bb1maxx) + CC_MAX(bb0minx, bb1minx)) / 2.0;
|
|
double originy = (CC_MIN(bb0maxy, bb1maxy) + CC_MAX(bb0miny, bb1miny)) / 2.0;
|
|
double ln0c = (ln1dy * static_cast<double>(ln1a.x - originx)) +
|
|
(ln1dx * static_cast<double>(ln1a.y - originy));
|
|
double ln1c = (ln2dy * static_cast<double>(ln2a.x - originx)) +
|
|
(ln2dx * static_cast<double>(ln2a.y - originy));
|
|
double hitx = ((ln1dx * ln1c) - (ln2dx * ln0c)) / det;
|
|
double hity = ((ln2dy * ln0c) - (ln1dy * ln1c)) / det;
|
|
|
|
ip.x = originx + static_cast<T>(hitx);
|
|
ip.y = originy + static_cast<T>(hity);
|
|
}
|
|
return true;
|
|
}
|
|
#else
|
|
template<typename T>
|
|
inline bool GetSegmentIntersectPt(const Point<T>& ln1a, const Point<T>& ln1b,
|
|
const Point<T>& ln2a, const Point<T>& ln2b, Point<T>& 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;
|
|
else if (t >= 1.0) ip = ln1b;
|
|
else
|
|
{
|
|
ip.x = static_cast<T>(ln1a.x + t * dx1);
|
|
ip.y = static_cast<T>(ln1a.y + t * dy1);
|
|
}
|
|
return true;
|
|
}
|
|
#endif
|
|
|
|
template<typename T>
|
|
inline Point<T> TranslatePoint(const Point<T>& pt, double dx, double dy)
|
|
{
|
|
#ifdef USINGZ
|
|
return Point<T>(pt.x + dx, pt.y + dy, pt.z);
|
|
#else
|
|
return Point<T>(pt.x + dx, pt.y + dy);
|
|
#endif
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline Point<T> ReflectPoint(const Point<T>& pt, const Point<T>& pivot)
|
|
{
|
|
#ifdef USINGZ
|
|
return Point<T>(pivot.x + (pivot.x - pt.x), pivot.y + (pivot.y - pt.y), pt.z);
|
|
#else
|
|
return Point<T>(pivot.x + (pivot.x - pt.x), pivot.y + (pivot.y - pt.y));
|
|
#endif
|
|
}
|
|
|
|
template<typename T>
|
|
inline int GetSign(const T& val)
|
|
{
|
|
if (!val) return 0;
|
|
return (val > 0) ? 1 : -1;
|
|
}
|
|
|
|
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 (GetSign(CrossProduct(seg1a, seg2a, seg2b)) *
|
|
GetSign(CrossProduct(seg1b, seg2a, seg2b)) < 0) &&
|
|
(GetSign(CrossProduct(seg2a, seg1a, seg1b)) *
|
|
GetSign(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::is_integral_v<T>)
|
|
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
|