--- /dev/null
+Planar Subdivisions (C API)
+============================
+
+.. highlight:: c
+
+CvSubdiv2D
+----------
+
+.. ocv:struct:: CvSubdiv2D
+
+Planar subdivision.
+
+::
+
+ #define CV_SUBDIV2D_FIELDS() \
+ CV_GRAPH_FIELDS() \
+ int quad_edges; \
+ int is_geometry_valid; \
+ CvSubdiv2DEdge recent_edge; \
+ CvPoint2D32f topleft; \
+ CvPoint2D32f bottomright;
+
+ typedef struct CvSubdiv2D
+ {
+ CV_SUBDIV2D_FIELDS()
+ }
+ CvSubdiv2D;
+
+..
+
+Planar subdivision is the subdivision of a plane into a set of
+non-overlapped regions (facets) that cover the whole plane. The above
+structure describes a subdivision built on a 2d point set, where the points
+are linked together and form a planar graph, which, together with a few
+edges connecting the exterior subdivision points (namely, convex hull points)
+with infinity, subdivides a plane into facets by its edges.
+
+For every subdivision there exists a dual subdivision in which facets and
+points (subdivision vertices) swap their roles, that is, a facet is
+treated as a vertex (called a virtual point below) of the dual subdivision and
+the original subdivision vertices become facets. On the picture below
+original subdivision is marked with solid lines and dual subdivision
+with dotted lines.
+
+.. image:: pics/subdiv.png
+
+OpenCV subdivides a plane into triangles using Delaunay's
+algorithm. Subdivision is built iteratively starting from a dummy
+triangle that includes all the subdivision points for sure. In this
+case the dual subdivision is a Voronoi diagram of the input 2d point set. The
+subdivisions can be used for the 3d piece-wise transformation of a plane,
+morphing, fast location of points on the plane, building special graphs
+(such as NNG,RNG) and so forth.
+
+CvQuadEdge2D
+------------
+
+.. ocv:struct:: CvQuadEdge2D
+
+Quad-edge of planar subdivision.
+
+::
+
+ /* one of edges within quad-edge, lower 2 bits is index (0..3)
+ and upper bits are quad-edge pointer */
+ typedef long CvSubdiv2DEdge;
+
+ /* quad-edge structure fields */
+ #define CV_QUADEDGE2D_FIELDS() \
+ int flags; \
+ struct CvSubdiv2DPoint* pt[4]; \
+ CvSubdiv2DEdge next[4];
+
+ typedef struct CvQuadEdge2D
+ {
+ CV_QUADEDGE2D_FIELDS()
+ }
+ CvQuadEdge2D;
+
+..
+
+Quad-edge is a basic element of subdivision containing four edges (e, eRot, reversed e and reversed eRot):
+
+.. image:: pics/quadedge.png
+
+CvSubdiv2DPoint
+---------------
+
+.. ocv:struct:: CvSubdiv2DPoint
+
+Point of original or dual subdivision.
+
+::
+
+ #define CV_SUBDIV2D_POINT_FIELDS()\
+ int flags; \
+ CvSubdiv2DEdge first; \
+ CvPoint2D32f pt; \
+ int id;
+
+ #define CV_SUBDIV2D_VIRTUAL_POINT_FLAG (1 << 30)
+
+ typedef struct CvSubdiv2DPoint
+ {
+ CV_SUBDIV2D_POINT_FIELDS()
+ }
+ CvSubdiv2DPoint;
+
+..
+
+* id
+ This integer can be used to index auxillary data associated with each vertex of the planar subdivision
+
+CalcSubdivVoronoi2D
+-------------------
+Calculates the coordinates of Voronoi diagram cells.
+
+.. ocv:cfunction:: void cvCalcSubdivVoronoi2D( CvSubdiv2D* subdiv )
+.. ocv:pyoldfunction:: cv.CalcSubdivVoronoi2D(subdiv)-> None
+
+ :param subdiv: Delaunay subdivision, in which all the points are already added
+
+The function calculates the coordinates
+of virtual points. All virtual points corresponding to some vertex of the
+original subdivision form (when connected together) a boundary of the Voronoi
+cell at that point.
+
+ClearSubdivVoronoi2D
+--------------------
+
+.. ocv:cfunction:: void cvClearSubdivVoronoi2D( CvSubdiv2D* subdiv )
+.. ocv:pyoldfunction:: cv.ClearSubdivVoronoi2D(subdiv)-> None
+
+ Removes all virtual points.
+
+ :param subdiv: Delaunay subdivision
+
+The function removes all of the virtual points. It
+is called internally in
+:ref:`CalcSubdivVoronoi2D`
+if the subdivision
+was modified after previous call to the function.
+
+CreateSubdivDelaunay2D
+----------------------
+Creates an empty Delaunay triangulation.
+
+.. ocv:cfunction:: CvSubdiv2D* cvCreateSubdivDelaunay2D( CvRect rect, CvMemStorage* storage )
+.. ocv:pyoldfunction:: cv.CreateSubdivDelaunay2D(rect, storage)-> emptyDelaunayTriangulation
+
+ :param rect: Rectangle that includes all of the 2d points that are to be added to the subdivision
+
+ :param storage: Container for subdivision
+
+The function creates an empty Delaunay
+subdivision, where 2d points can be added using the function
+:ref:`SubdivDelaunay2DInsert`
+. All of the points to be added must be within
+the specified rectangle, otherwise a runtime error will be raised.
+
+Note that the triangulation is a single large triangle that covers the given rectangle. Hence the three vertices of this triangle are outside the rectangle
+``rect``
+.
+
+FindNearestPoint2D
+------------------
+Finds the closest subdivision vertex to the given point.
+
+.. ocv:cfunction:: CvSubdiv2DPoint* cvFindNearestPoint2D( CvSubdiv2D* subdiv, CvPoint2D32f pt )
+.. ocv:pyoldfunction:: cv.FindNearestPoint2D(subdiv, pt)-> point
+
+ :param subdiv: Delaunay or another subdivision
+
+ :param pt: Input point
+
+The function is another function that
+locates the input point within the subdivision. It finds the subdivision vertex that
+is the closest to the input point. It is not necessarily one of vertices
+of the facet containing the input point, though the facet (located using
+:ref:`Subdiv2DLocate`
+) is used as a starting
+point. The function returns a pointer to the found subdivision vertex.
+
+Subdiv2DEdgeDst
+---------------
+Returns the edge destination.
+
+.. ocv:cfunction:: CvSubdiv2DPoint* cvSubdiv2DEdgeDst( CvSubdiv2DEdge edge )
+.. ocv:pyoldfunction:: cv.Subdiv2DEdgeDst(edge)-> point
+
+ :param edge: Subdivision edge (not a quad-edge)
+
+The function returns the edge destination. The
+returned pointer may be NULL if the edge is from dual subdivision and
+the virtual point coordinates are not calculated yet. The virtual points
+can be calculated using the function
+:ref:`CalcSubdivVoronoi2D`
+.
+
+Subdiv2DGetEdge
+---------------
+Returns one of the edges related to the given edge.
+
+.. ocv:cfunction:: CvSubdiv2DEdge cvSubdiv2DGetEdge( CvSubdiv2DEdge edge, CvNextEdgeType type )
+.. ocv:pyoldfunction:: cv.Subdiv2DGetEdge(edge, type)-> CvSubdiv2DEdge
+
+ :param edge: Subdivision edge (not a quad-edge)
+
+ :param type: Specifies which of the related edges to return, one of the following:
+
+ * **CV_NEXT_AROUND_ORG** next around the edge origin ( ``eOnext`` on the picture below if ``e`` is the input edge)
+
+ * **CV_NEXT_AROUND_DST** next around the edge vertex ( ``eDnext`` )
+
+ * **CV_PREV_AROUND_ORG** previous around the edge origin (reversed ``eRnext`` )
+
+ * **CV_PREV_AROUND_DST** previous around the edge destination (reversed ``eLnext`` )
+
+ * **CV_NEXT_AROUND_LEFT** next around the left facet ( ``eLnext`` )
+
+ * **CV_NEXT_AROUND_RIGHT** next around the right facet ( ``eRnext`` )
+
+ * **CV_PREV_AROUND_LEFT** previous around the left facet (reversed ``eOnext`` )
+
+ * **CV_PREV_AROUND_RIGHT** previous around the right facet (reversed ``eDnext`` )
+
+.. image:: pics/quadedge.png
+
+The function returns one of the edges related to the input edge.
+
+Subdiv2DNextEdge
+----------------
+Returns next edge around the edge origin
+
+.. ocv:cfunction:: CvSubdiv2DEdge cvSubdiv2DNextEdge( CvSubdiv2DEdge edge )
+.. ocv:pyoldfunction:: cv.Subdiv2DNextEdge(edge)-> CvSubdiv2DEdge
+
+ :param edge: Subdivision edge (not a quad-edge)
+
+The function returns the next edge around the edge origin:
+``eOnext``
+on the picture above if
+``e``
+is the input edge)
+
+Subdiv2DLocate
+--------------
+Returns the location of a point within a Delaunay triangulation.
+
+.. ocv:cfunction:: CvSubdiv2DPointLocation cvSubdiv2DLocate( CvSubdiv2D* subdiv, CvPoint2D32f pt, CvSubdiv2DEdge* edge, CvSubdiv2DPoint** vertex=NULL )
+.. ocv:pyoldfunction:: cv.Subdiv2DLocate(subdiv, pt) -> (loc, where)
+
+ :param subdiv: Delaunay or another subdivision
+
+ :param pt: The point to locate
+
+ :param edge: The output edge the point falls onto or right to
+
+ :param vertex: Optional output vertex double pointer the input point coinsides with
+
+The function locates the input point within the subdivision. There are 5 cases:
+
+*
+ The point falls into some facet. The function returns
+ ``CV_PTLOC_INSIDE``
+ and
+ ``*edge``
+ will contain one of edges of the facet.
+
+*
+ The point falls onto the edge. The function returns
+ ``CV_PTLOC_ON_EDGE``
+ and
+ ``*edge``
+ will contain this edge.
+
+*
+ The point coincides with one of the subdivision vertices. The function returns
+ ``CV_PTLOC_VERTEX``
+ and
+ ``*vertex``
+ will contain a pointer to the vertex.
+
+*
+ The point is outside the subdivsion reference rectangle. The function returns
+ ``CV_PTLOC_OUTSIDE_RECT``
+ and no pointers are filled.
+
+*
+ One of input arguments is invalid. A runtime error is raised or, if silent or "parent" error processing mode is selected,
+ ``CV_PTLOC_ERROR``
+ is returnd.
+
+Subdiv2DRotateEdge
+------------------
+Returns another edge of the same quad-edge.
+
+.. ocv:cfunction:: CvSubdiv2DEdge cvSubdiv2DRotateEdge( CvSubdiv2DEdge edge, int rotate )
+.. ocv:pyoldfunction:: cv.Subdiv2DRotateEdge(edge, rotate)-> CvSubdiv2DEdge
+
+ :param edge: Subdivision edge (not a quad-edge)
+
+ :param rotate: Specifies which of the edges of the same quad-edge as the input one to return, one of the following:
+
+ * **0** the input edge ( ``e`` on the picture below if ``e`` is the input edge)
+
+ * **1** the rotated edge ( ``eRot`` )
+
+ * **2** the reversed edge (reversed ``e`` (in green))
+
+ * **3** the reversed rotated edge (reversed ``eRot`` (in green))
+
+The function returns one of the edges of the same quad-edge as the input edge.
+
+SubdivDelaunay2DInsert
+----------------------
+Inserts a single point into a Delaunay triangulation.
+
+.. ocv:cfunction:: CvSubdiv2DPoint* cvSubdivDelaunay2DInsert( CvSubdiv2D* subdiv, CvPoint2D32f pt)
+.. ocv:pyoldfunction:: cv.SubdivDelaunay2DInsert(subdiv, pt)-> point
+
+ :param subdiv: Delaunay subdivision created by the function :ref:`CreateSubdivDelaunay2D`
+
+ :param pt: Inserted point
+
+The function inserts a single point into a subdivision and modifies the subdivision topology appropriately. If a point with the same coordinates exists already, no new point is added. The function returns a pointer to the allocated point. No virtual point coordinates are calculated at this stage.
+
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