// Copyright 2005 Google Inc. All Rights Reserved. #ifndef UTIL_GEOMETRY_S2POLYLINE_H__ #define UTIL_GEOMETRY_S2POLYLINE_H__ #include using std::vector; #include "base/logging.h" #include "base/macros.h" #include "s2.h" #include "s2region.h" #include "s2latlngrect.h" class S1Angle; // An S2Polyline represents a sequence of zero or more vertices connected by // straight edges (geodesics). Edges of length 0 and 180 degrees are not // allowed, i.e. adjacent vertices should not be identical or antipodal. class S2Polyline : public S2Region { public: // Creates an empty S2Polyline that should be initialized by calling Init() // or Decode(). S2Polyline(); // Convenience constructors that call Init() with the given vertices. S2Polyline(vector const& vertices); S2Polyline(vector const& vertices); // Initialize a polyline that connects the given vertices. Empty polylines are // allowed. Adjacent vertices should not be identical or antipodal. All // vertices should be unit length. void Init(vector const& vertices); // Convenience initialization function that accepts latitude-longitude // coordinates rather than S2Points. void Init(vector const& vertices); ~S2Polyline(); // Return true if the given vertices form a valid polyline. // Output errors to "err" if it's not NULL. static bool IsValid(vector const& vertices, string* err = NULL); int num_vertices() const { return num_vertices_; } S2Point const& vertex(int k) const { DCHECK_GE(k, 0); return vertices_[k]; } // Return the length of the polyline. S1Angle GetLength() const; // Return the true centroid of the polyline multiplied by the length of the // polyline (see s2.h for details on centroids). The result is not unit // length, so you may want to normalize it. // // Prescaling by the polyline length makes it easy to compute the centroid // of several polylines (by simply adding up their centroids). S2Point GetCentroid() const; // Return the point whose distance from vertex 0 along the polyline is the // given fraction of the polyline's total length. Fractions less than zero // or greater than one are clamped. The return value is unit length. This // cost of this function is currently linear in the number of vertices. // The polyline must not be empty. S2Point Interpolate(double fraction) const; // Like Interpolate(), but also return the index of the next polyline // vertex after the interpolated point P. This allows the caller to easily // construct a given suffix of the polyline by concatenating P with the // polyline vertices starting at "next_vertex". Note that P is guaranteed // to be different than vertex(*next_vertex), so this will never result in // a duplicate vertex. // // The polyline must not be empty. Note that if "fraction" >= 1.0, then // "next_vertex" will be set to num_vertices() (indicating that no vertices // from the polyline need to be appended). The value of "next_vertex" is // always between 1 and num_vertices(). // // This method can also be used to construct a prefix of the polyline, by // taking the polyline vertices up to "next_vertex - 1" and appending the // returned point P if it is different from the last vertex (since in this // case there is no guarantee of distinctness). S2Point GetSuffix(double fraction, int* next_vertex) const; // The inverse operation of GetSuffix/Interpolate. Given a point on the // polyline, returns the ratio of the distance to the point from the // beginning of the polyline over the length of the polyline. The return // value is always betwen 0 and 1 inclusive. See GetSuffix() for the // meaning of "next_vertex". // // The polyline should not be empty. If it has fewer than 2 vertices, the // return value is zero. double UnInterpolate(S2Point const& point, int next_vertex) const; // Given a point, returns a point on the polyline that is closest to the given // point. See GetSuffix() for the meaning of "next_vertex", which is chosen // here w.r.t. the projected point as opposed to the interpolated point in // GetSuffix(). // // The polyline must be non-empty. S2Point Project(S2Point const& point, int* next_vertex) const; // Returns true if the point given is on the right hand side of the polyline, // using a naive definition of "right-hand-sideness" where the point is on // the RHS of the polyline iff the point is on the RHS of the line segment in // the polyline which it is closest to. // // The polyline must have at least 2 vertices. bool IsOnRight(S2Point const& point) const; // Return true if this polyline intersects the given polyline. If the // polylines share a vertex they are considered to be intersecting. When a // polyline endpoint is the only intersection with the other polyline, the // function may return true or false arbitrarily. // // The running time is quadratic in the number of vertices. bool Intersects(S2Polyline const* line) const; // Reverse the order of the polyline vertices. void Reverse(); // Return a subsequence of vertex indices such that the polyline connecting // these vertices is never further than "tolerance" from the original // polyline. The first and last vertices are always preserved. // // Some useful properties of the algorithm: // // - It runs in linear time. // // - The output is always a valid polyline. In particular, adjacent // output vertices are never identical or antipodal. // // - The method is not optimal, but it tends to produce 2-3% fewer // vertices than the Douglas-Peucker algorithm with the same tolerance. // // - The output is *parametrically* equivalent to the original polyline to // within the given tolerance. For example, if a polyline backtracks on // itself and then proceeds onwards, the backtracking will be preserved // (to within the given tolerance). This is different than the // Douglas-Peucker algorithm used in maps/util/geoutil-inl.h, which only // guarantees geometric equivalence. void SubsampleVertices(S1Angle const& tolerance, vector* indices) const; // Return true if two polylines have the same number of vertices, and // corresponding vertex pairs are separated by no more than "max_error". // (For testing purposes.) bool ApproxEquals(S2Polyline const* b, double max_error = 1e-15) const; // Return true if "covered" is within "max_error" of a contiguous subpath of // this polyline over its entire length. Specifically, this method returns // true if this polyline has parameterization a:[0,1] -> S^2, "covered" has // parameterization b:[0,1] -> S^2, and there is a non-decreasing function // f:[0,1] -> [0,1] such that distance(a(f(t)), b(t)) <= max_error for all t. // // You can think of this as testing whether it is possible to drive a car // along "covered" and a car along some subpath of this polyline such that no // car ever goes backward, and the cars are always within "max_error" of each // other. bool NearlyCoversPolyline(S2Polyline const& covered, S1Angle const& max_error) const; //////////////////////////////////////////////////////////////////////// // S2Region interface (see s2region.h for details): virtual S2Polyline* Clone() const; virtual S2Cap GetCapBound() const; virtual S2LatLngRect GetRectBound() const; virtual bool Contains(S2Cell const& cell) const { return false; } virtual bool MayIntersect(S2Cell const& cell) const; // Polylines do not have a Contains(S2Point) method, because "containment" // is not numerically well-defined except at the polyline vertices. virtual bool VirtualContainsPoint(S2Point const& p) const { return false; } virtual void Encode(Encoder* const encoder) const; virtual bool Decode(Decoder* const decoder); private: // Internal constructor used only by Clone() that makes a deep copy of // its argument. S2Polyline(S2Polyline const* src); // We store the vertices in an array rather than a vector because we don't // need any STL methods, and computing the number of vertices using size() // would be relatively expensive (due to division by sizeof(S2Point) == 24). int num_vertices_; S2Point* vertices_; DISALLOW_EVIL_CONSTRUCTORS(S2Polyline); }; #endif // UTIL_GEOMETRY_S2POLYLINE_H__