Describes path which consists of segments where each segment could be line or bezier curve.

You can find more information in comments below.

template<class PointType, class FloatType> // Type is a data type of points(usually it's an integer) 
    class TPath
    {
    public:
        struct SEGMENT // Describes segment 
        {
            SEGMENT_TYPE SegmentType; // Segment type 
            size_t Index; // Start point index 
            size_t Equation; // Equation index 
            math::TRect<PointType> Bounds; // Bounding rectangle 
        };
    public:
        TPath(); // Create empty 
        TPath(const math::TPoint<PointType> &start_point); // Create with start point 
        TPath(const TPath &other) = default;
        TPath(TPath &&other) = default;
    
        // STL 
        typename std::vector<SEGMENT>::size_type size() const;
        typename std::vector<SEGMENT>::const_iterator cbegin() const;
        typename std::vector<SEGMENT>::const_iterator cend() const;
        typename std::vector<SEGMENT>::const_iterator begin() const;
        typename std::vector<SEGMENT>::const_iterator end() const;
        typename std::vector<SEGMENT>::const_reverse_iterator crbegin() const;
        typename std::vector<SEGMENT>::const_reverse_iterator crend() const;
        typename std::vector<SEGMENT>::const_reverse_iterator rbegin() const;
        typename std::vector<SEGMENT>::const_reverse_iterator rend() const;
        const math::TPoint<PointType> &operator[](const typename std::vector<math::TPoint<PointType>>::size_type index) const;
        void clear();
    
        bool isClosed() const; // Return whether it is closed(last point is equal to first one) 
        math::TRect<PointType> getBounds() const; // Calculate bounding rectangle 
        const TLineEquation<FloatType> &getLineEquation(const size_t index) const; // Return line equation by index 
        const TBezierEquation<PointType> &getBezierEquation(const size_t index) const; // Return bezier equation by index 
    
        void AddStartPoint(const math::TPoint<PointType> &p); // Add start point. Can be called only on empty path 
        void LineTo(const math::TPoint<PointType> &p); // Add line from last point to specified one 
        void BezierTo(const math::TPoint<PointType> &p2, const math::TPoint<PointType> &p3); // Add bezier segment using last added point and two specified points 
    
        typename std::vector<SEGMENT>::const_iterator FirstSegment(const FloatType hline, FloatType &x); // Find segment index which intersects with hline. Stores intersection x-coordinate in x argument 
        typename std::vector<SEGMENT>::const_iterator NextSegment(const FloatType hline, const FloatType min_x, FloatType &x); // Find next the nearest segment which intersects horizontal line with hline y-coordinate and intersection point is >= min_x. If found, x is intersection point 
        std::vector<FloatType> Intersections(const FloatType hline, const bool sort); // Find all segments which intersect with hline. Optionally sort them by X-coordinate 
        bool TestPoint(const math::TPoint<PointType> &p); // Check whether point is inside path or not 
    };