path: root/src/libslic3r/Point.hpp

#ifndef slic3r_Point_hpp_
#define slic3r_Point_hpp_

#include "libslic3r.h"
#include <cstddef>
#include <vector>
#include <cmath>
#include <string>
#include <sstream>
#include <unordered_map>

#include <Eigen/Geometry> 

namespace Slic3r {

class Line;
class MultiPoint;
class Point;
typedef Point Vector;

// Eigen types, to replace the Slic3r's own types in the future.
// Vector types with a fixed point coordinate base type.
typedef Eigen::Matrix<coord_t,  2, 1, Eigen::DontAlign> Vec2crd;
typedef Eigen::Matrix<coord_t,  3, 1, Eigen::DontAlign> Vec3crd;
typedef Eigen::Matrix<int,      2, 1, Eigen::DontAlign> Vec2i;
typedef Eigen::Matrix<int,      3, 1, Eigen::DontAlign> Vec3i;
typedef Eigen::Matrix<int32_t,  2, 1, Eigen::DontAlign> Vec2i32;
typedef Eigen::Matrix<int64_t,  2, 1, Eigen::DontAlign> Vec2i64;
typedef Eigen::Matrix<int32_t,  3, 1, Eigen::DontAlign> Vec3i32;
typedef Eigen::Matrix<int64_t,  3, 1, Eigen::DontAlign> Vec3i64;

// Vector types with a double coordinate base type.
typedef Eigen::Matrix<float,    2, 1, Eigen::DontAlign> Vec2f;
typedef Eigen::Matrix<float,    3, 1, Eigen::DontAlign> Vec3f;
typedef Eigen::Matrix<double,   2, 1, Eigen::DontAlign> Vec2d;
typedef Eigen::Matrix<double,   3, 1, Eigen::DontAlign> Vec3d;

typedef std::vector<Point>                              Points;
typedef std::vector<Point*>                             PointPtrs;
typedef std::vector<const Point*>                       PointConstPtrs;
typedef std::vector<Vec3crd>                            Points3;
typedef std::vector<Vec2d>                              Pointfs;
typedef std::vector<Vec2d>                              Vec2ds;
typedef std::vector<Vec3d>                              Pointf3s;

typedef Eigen::Matrix<float,  2, 2, Eigen::DontAlign> Matrix2f;
typedef Eigen::Matrix<double, 2, 2, Eigen::DontAlign> Matrix2d;
typedef Eigen::Matrix<float,  3, 3, Eigen::DontAlign> Matrix3f;
typedef Eigen::Matrix<double, 3, 3, Eigen::DontAlign> Matrix3d;

typedef Eigen::Transform<float,  2, Eigen::Affine, Eigen::DontAlign> Transform2f;
typedef Eigen::Transform<double, 2, Eigen::Affine, Eigen::DontAlign> Transform2d;
typedef Eigen::Transform<float,  3, Eigen::Affine, Eigen::DontAlign> Transform3f;
typedef Eigen::Transform<double, 3, Eigen::Affine, Eigen::DontAlign> Transform3d;

inline bool operator<(const Vec2d &lhs, const Vec2d &rhs) { return lhs(0) < rhs(0) || (lhs(0) == rhs(0) && lhs(1) < rhs(1)); }

inline int32_t cross2(const Vec2i32 &v1, const Vec2i32 &v2) { return v1(0) * v2(1) - v1(1) * v2(0); }
inline int64_t cross2(const Vec2i64 &v1, const Vec2i64 &v2) { return v1(0) * v2(1) - v1(1) * v2(0); }
inline float   cross2(const Vec2f   &v1, const Vec2f   &v2) { return v1(0) * v2(1) - v1(1) * v2(0); }
inline double  cross2(const Vec2d   &v1, const Vec2d   &v2) { return v1(0) * v2(1) - v1(1) * v2(0); }

template<class T, int N> Eigen::Matrix<T,  2, 1, Eigen::DontAlign>
to_2d(const Eigen::Matrix<T,  N, 1, Eigen::DontAlign> &ptN) { return {ptN(0), ptN(1)}; }

//inline Vec2i32 to_2d(const Vec3i32 &pt3) { return Vec2i32(pt3(0), pt3(1)); }
//inline Vec2i64 to_2d(const Vec3i64 &pt3) { return Vec2i64(pt3(0), pt3(1)); }
//inline Vec2f   to_2d(const Vec3f   &pt3) { return Vec2f  (pt3(0), pt3(1)); }
//inline Vec2d   to_2d(const Vec3d   &pt3) { return Vec2d  (pt3(0), pt3(1)); }

inline Vec3d   to_3d(const Vec2d &v, double z) { return Vec3d(v(0), v(1), z); }
inline Vec3f   to_3d(const Vec2f &v, float z) { return Vec3f(v(0), v(1), z); }
inline Vec3i64 to_3d(const Vec2i64 &v, float z) { return Vec3i64(int64_t(v(0)), int64_t(v(1)), int64_t(z)); }
inline Vec3crd to_3d(const Vec3crd &p, coord_t z) { return Vec3crd(p(0), p(1), z); }

inline Vec2d   unscale(coord_t x, coord_t y) { return Vec2d(unscale<double>(x), unscale<double>(y)); }
inline Vec2d   unscale(const Vec2crd &pt) { return Vec2d(unscale<double>(pt(0)), unscale<double>(pt(1))); }
inline Vec2d   unscale(const Vec2d   &pt) { return Vec2d(unscale<double>(pt(0)), unscale<double>(pt(1))); }
inline Vec3d   unscale(coord_t x, coord_t y, coord_t z) { return Vec3d(unscale<double>(x), unscale<double>(y), unscale<double>(z)); }
inline Vec3d   unscale(const Vec3crd &pt) { return Vec3d(unscale<double>(pt(0)), unscale<double>(pt(1)), unscale<double>(pt(2))); }
inline Vec3d   unscale(const Vec3d   &pt) { return Vec3d(unscale<double>(pt(0)), unscale<double>(pt(1)), unscale<double>(pt(2))); }

inline std::string to_string(const Vec2crd &pt) { return std::string("[") + std::to_string(pt(0)) + ", " + std::to_string(pt(1)) + "]"; }
inline std::string to_string(const Vec2d   &pt) { return std::string("[") + std::to_string(pt(0)) + ", " + std::to_string(pt(1)) + "]"; }
inline std::string to_string(const Vec3crd &pt) { return std::string("[") + std::to_string(pt(0)) + ", " + std::to_string(pt(1)) + ", " + std::to_string(pt(2)) + "]"; }
inline std::string to_string(const Vec3d   &pt) { return std::string("[") + std::to_string(pt(0)) + ", " + std::to_string(pt(1)) + ", " + std::to_string(pt(2)) + "]"; }

std::vector<Vec3f> transform(const std::vector<Vec3f>& points, const Transform3f& t);
Pointf3s transform(const Pointf3s& points, const Transform3d& t);

template<int N, class T> using Vec = Eigen::Matrix<T,  N, 1, Eigen::DontAlign, N, 1>;

class Point : public Vec2crd
{
public:
    typedef coord_t coord_type;

    Point() : Vec2crd(0, 0) {}
    Point(int32_t x, int32_t y) : Vec2crd(coord_t(x), coord_t(y)) {}
    Point(int64_t x, int64_t y) : Vec2crd(coord_t(x), coord_t(y)) {}
    Point(double x, double y) : Vec2crd(coord_t(lrint(x)), coord_t(lrint(y))) {}
    Point(const Point &rhs) { *this = rhs; }
	explicit Point(const Vec2d& rhs) : Vec2crd(coord_t(lrint(rhs.x())), coord_t(lrint(rhs.y()))) {}
	// This constructor allows you to construct Point from Eigen expressions
    template<typename OtherDerived>
    Point(const Eigen::MatrixBase<OtherDerived> &other) : Vec2crd(other) {}
    static Point new_scale(coordf_t x, coordf_t y) { return Point(coord_t(scale_(x)), coord_t(scale_(y))); }

    // This method allows you to assign Eigen expressions to MyVectorType
    template<typename OtherDerived>
    Point& operator=(const Eigen::MatrixBase<OtherDerived> &other)
    {
        this->Vec2crd::operator=(other);
        return *this;
    }

    bool operator< (const Point& rhs) const { return (*this)(0) < rhs(0) || ((*this)(0) == rhs(0) && (*this)(1) < rhs(1)); }

    Point& operator+=(const Point& rhs) { (*this)(0) += rhs(0); (*this)(1) += rhs(1); return *this; }
    Point& operator-=(const Point& rhs) { (*this)(0) -= rhs(0); (*this)(1) -= rhs(1); return *this; }
	Point& operator*=(const double &rhs) { (*this)(0) = coord_t((*this)(0) * rhs); (*this)(1) = coord_t((*this)(1) * rhs); return *this; }
    Point operator*(const double &rhs) { return Point((*this)(0) * rhs, (*this)(1) * rhs); }

    void   rotate(double angle);
    void   rotate(double angle, const Point &center);
    Point  rotated(double angle) const { Point res(*this); res.rotate(angle); return res; }
    Point  rotated(double angle, const Point &center) const { Point res(*this); res.rotate(angle, center); return res; }
    int    nearest_point_index(const Points &points) const;
    int    nearest_point_index(const PointConstPtrs &points) const;
    int    nearest_point_index(const PointPtrs &points) const;
    bool   nearest_point(const Points &points, Point* point) const;
    double ccw(const Point &p1, const Point &p2) const;
    double ccw(const Line &line) const;
    double ccw_angle(const Point &p1, const Point &p2) const;
    Point  projection_onto(const MultiPoint &poly) const;
    Point  projection_onto(const Line &line) const;
};

inline bool is_approx(const Point &p1, const Point &p2, coord_t epsilon = coord_t(SCALED_EPSILON))
{
	Point d = (p2 - p1).cwiseAbs();
	return d.x() < epsilon && d.y() < epsilon;
}

inline bool is_approx(const Vec2f &p1, const Vec2f &p2, float epsilon = float(EPSILON))
{
	Vec2f d = (p2 - p1).cwiseAbs();
	return d.x() < epsilon && d.y() < epsilon;
}

inline bool is_approx(const Vec2d &p1, const Vec2d &p2, double epsilon = EPSILON)
{
	Vec2d d = (p2 - p1).cwiseAbs();
	return d.x() < epsilon && d.y() < epsilon;
}

inline bool is_approx(const Vec3f &p1, const Vec3f &p2, float epsilon = float(EPSILON))
{
	Vec3f d = (p2 - p1).cwiseAbs();
	return d.x() < epsilon && d.y() < epsilon && d.z() < epsilon;
}

inline bool is_approx(const Vec3d &p1, const Vec3d &p2, double epsilon = EPSILON)
{
	Vec3d d = (p2 - p1).cwiseAbs();
	return d.x() < epsilon && d.y() < epsilon && d.z() < epsilon;
}

namespace int128 {
    // Exact orientation predicate,
    // returns +1: CCW, 0: collinear, -1: CW.
    int orient(const Vec2crd &p1, const Vec2crd &p2, const Vec2crd &p3);
    // Exact orientation predicate,
    // returns +1: CCW, 0: collinear, -1: CW.
    int cross(const Vec2crd &v1, const Vec2crd &v2);
}

// To be used by std::unordered_map, std::unordered_multimap and friends.
struct PointHash {
    size_t operator()(const Vec2crd &pt) const {
        return std::hash<coord_t>()(pt(0)) ^ std::hash<coord_t>()(pt(1));
    }
};

// A generic class to search for a closest Point in a given radius.
// It uses std::unordered_multimap to implement an efficient 2D spatial hashing.
// The PointAccessor has to return const Point*.
// If a nullptr is returned, it is ignored by the query.
template<typename ValueType, typename PointAccessor> class ClosestPointInRadiusLookup
{
public:
    ClosestPointInRadiusLookup(coord_t search_radius, PointAccessor point_accessor = PointAccessor()) : 
		m_search_radius(search_radius), m_point_accessor(point_accessor), m_grid_log2(0)
    {
        // Resolution of a grid, twice the search radius + some epsilon.
		coord_t gridres = 2 * m_search_radius + 4;
        m_grid_resolution = gridres;
        assert(m_grid_resolution > 0);
        assert(m_grid_resolution < (coord_t(1) << 30));
		// Compute m_grid_log2 = log2(m_grid_resolution)
		if (m_grid_resolution > 32767) {
			m_grid_resolution >>= 16;
			m_grid_log2 += 16;
		}
		if (m_grid_resolution > 127) {
			m_grid_resolution >>= 8;
			m_grid_log2 += 8;
		}
		if (m_grid_resolution > 7) {
			m_grid_resolution >>= 4;
			m_grid_log2 += 4;
		}
		if (m_grid_resolution > 1) {
			m_grid_resolution >>= 2;
			m_grid_log2 += 2;
		}
		if (m_grid_resolution > 0)
			++ m_grid_log2;
		m_grid_resolution = 1 << m_grid_log2;
		assert(m_grid_resolution >= gridres);
		assert(gridres > m_grid_resolution / 2);
    }

    void insert(const ValueType &value) {
        const Vec2crd *pt = m_point_accessor(value);
        if (pt != nullptr)
            m_map.emplace(std::make_pair(Vec2crd(pt->x()>>m_grid_log2, pt->y()>>m_grid_log2), value));
    }

    void insert(ValueType &&value) {
        const Vec2crd *pt = m_point_accessor(value);
        if (pt != nullptr)
            m_map.emplace(std::make_pair(Vec2crd(pt->x()>>m_grid_log2, pt->y()>>m_grid_log2), std::move(value)));
    }

    // Erase a data point equal to value. (ValueType has to declare the operator==).
    // Returns true if the data point equal to value was found and removed.
    bool erase(const ValueType &value) {
        const Point *pt = m_point_accessor(value);
        if (pt != nullptr) {
            // Range of fragment starts around grid_corner, close to pt.
            auto range = m_map.equal_range(Point((*pt)(0)>>m_grid_log2, (*pt)(1)>>m_grid_log2));
            // Remove the first item.
            for (auto it = range.first; it != range.second; ++ it) {
                if (it->second == value) {
                    m_map.erase(it);
                    return true;
                }
            }
        }
        return false;
    }

    // Return a pair of <ValueType*, distance_squared>
    std::pair<const ValueType*, double> find(const Vec2crd &pt) {
        // Iterate over 4 closest grid cells around pt,
        // find the closest start point inside these cells to pt.
        const ValueType *value_min = nullptr;
        double           dist_min = std::numeric_limits<double>::max();
        // Round pt to a closest grid_cell corner.
        Vec2crd            grid_corner((pt(0)+(m_grid_resolution>>1))>>m_grid_log2, (pt(1)+(m_grid_resolution>>1))>>m_grid_log2);
        // For four neighbors of grid_corner:
        for (coord_t neighbor_y = -1; neighbor_y < 1; ++ neighbor_y) {
            for (coord_t neighbor_x = -1; neighbor_x < 1; ++ neighbor_x) {
                // Range of fragment starts around grid_corner, close to pt.
                auto range = m_map.equal_range(Vec2crd(grid_corner(0) + neighbor_x, grid_corner(1) + neighbor_y));
                // Find the map entry closest to pt.
                for (auto it = range.first; it != range.second; ++it) {
                    const ValueType &value = it->second;
                    const Vec2crd *pt2 = m_point_accessor(value);
                    if (pt2 != nullptr) {
                        const double d2 = (pt - *pt2).cast<double>().squaredNorm();
                        if (d2 < dist_min) {
                            dist_min = d2;
                            value_min = &value;
                        }
                    }
                }
            }
        }
        return (value_min != nullptr && dist_min < coordf_t(m_search_radius) * coordf_t(m_search_radius)) ? 
            std::make_pair(value_min, dist_min) : 
            std::make_pair(nullptr, std::numeric_limits<double>::max());
    }

private:
    typedef typename std::unordered_multimap<Vec2crd, ValueType, PointHash> map_type;
    PointAccessor m_point_accessor;
    map_type m_map;
    coord_t  m_search_radius;
    coord_t  m_grid_resolution;
    coord_t  m_grid_log2;
};

std::ostream& operator<<(std::ostream &stm, const Vec2d &pointf);


// /////////////////////////////////////////////////////////////////////////////
// Type safe conversions to and from scaled and unscaled coordinates
// /////////////////////////////////////////////////////////////////////////////

// Semantics are the following:
// Upscaling (scaled()): only from floating point types (or Vec) to either
//                       floating point or integer 'scaled coord' coordinates.
// Downscaling (unscaled()): from arithmetic (or Vec) to floating point only

// Conversion definition from unscaled to floating point scaled
template<class Tout,
         class Tin,
         class = FloatingOnly<Tin>>
inline constexpr FloatingOnly<Tout> scaled(const Tin &v) noexcept
{
    return Tout(v / Tin(SCALING_FACTOR));
}

// Conversion definition from unscaled to integer 'scaled coord'.
// TODO: is the rounding necessary? Here it is commented  out to show that
// it can be different for integers but it does not have to be. Using
// std::round means loosing noexcept and constexpr modifiers
template<class Tout = coord_t, class Tin, class = FloatingOnly<Tin>>
inline constexpr ScaledCoordOnly<Tout> scaled(const Tin &v) noexcept
{
    //return static_cast<Tout>(std::round(v / SCALING_FACTOR));
    return Tout(v / Tin(SCALING_FACTOR));
}

// Conversion for Eigen vectors (N dimensional points)
template<class Tout = coord_t,
         class Tin,
         int N,
         class = FloatingOnly<Tin>,
         int...EigenArgs>
inline Eigen::Matrix<ArithmeticOnly<Tout>, N, EigenArgs...>
scaled(const Eigen::Matrix<Tin, N, EigenArgs...> &v)
{
    return (v / SCALING_FACTOR).template cast<Tout>();
}

// Conversion from arithmetic scaled type to floating point unscaled
template<class Tout = double,
         class Tin,
         class = ArithmeticOnly<Tin>,
         class = FloatingOnly<Tout>>
inline constexpr Tout unscaled(const Tin &v) noexcept
{
    return Tout(v * Tout(SCALING_FACTOR));
}

// Unscaling for Eigen vectors. Input base type can be arithmetic, output base
// type can only be floating point.
template<class Tout = double,
         class Tin,
         int N,
         class = ArithmeticOnly<Tin>,
         class = FloatingOnly<Tout>,
         int...EigenArgs>
inline constexpr Eigen::Matrix<Tout, N, EigenArgs...>
unscaled(const Eigen::Matrix<Tin, N, EigenArgs...> &v) noexcept
{
    return v.template cast<Tout>() * SCALING_FACTOR;
}

} // namespace Slic3r

// start Boost
#include <boost/version.hpp>
#include <boost/polygon/polygon.hpp>
namespace boost { namespace polygon {
    template <>
    struct geometry_concept<Slic3r::Point> { typedef point_concept type; };
   
    template <>
    struct point_traits<Slic3r::Point> {
        typedef coord_t coordinate_type;
    
        static inline coordinate_type get(const Slic3r::Point& point, orientation_2d orient) {
            return (coordinate_type)point((orient == HORIZONTAL) ? 0 : 1);
        }
    };
    
    template <>
    struct point_mutable_traits<Slic3r::Point> {
        typedef coord_t coordinate_type;
        static inline void set(Slic3r::Point& point, orientation_2d orient, coord_t value) {
            point((orient == HORIZONTAL) ? 0 : 1) = value;
        }
        static inline Slic3r::Point construct(coord_t x_value, coord_t y_value) {
            return Slic3r::Point(x_value, y_value);
        }
    };
} }
// end Boost

// Serialization through the Cereal library
namespace cereal {
//	template<class Archive> void serialize(Archive& archive, Slic3r::Vec2crd &v) { archive(v.x(), v.y()); }
//	template<class Archive> void serialize(Archive& archive, Slic3r::Vec3crd &v) { archive(v.x(), v.y(), v.z()); }
	template<class Archive> void serialize(Archive& archive, Slic3r::Vec2i   &v) { archive(v.x(), v.y()); }
	template<class Archive> void serialize(Archive& archive, Slic3r::Vec3i   &v) { archive(v.x(), v.y(), v.z()); }
//	template<class Archive> void serialize(Archive& archive, Slic3r::Vec2i64 &v) { archive(v.x(), v.y()); }
//	template<class Archive> void serialize(Archive& archive, Slic3r::Vec3i64 &v) { archive(v.x(), v.y(), v.z()); }
	template<class Archive> void serialize(Archive& archive, Slic3r::Vec2f   &v) { archive(v.x(), v.y()); }
	template<class Archive> void serialize(Archive& archive, Slic3r::Vec3f   &v) { archive(v.x(), v.y(), v.z()); }
	template<class Archive> void serialize(Archive& archive, Slic3r::Vec2d   &v) { archive(v.x(), v.y()); }
	template<class Archive> void serialize(Archive& archive, Slic3r::Vec3d   &v) { archive(v.x(), v.y(), v.z()); }

	template<class Archive> void load(Archive& archive, Slic3r::Matrix2f &m) { archive.loadBinary((char*)m.data(), sizeof(float) * 4); }
	template<class Archive> void save(Archive& archive, Slic3r::Matrix2f &m) { archive.saveBinary((char*)m.data(), sizeof(float) * 4); }
}

#endif