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Open Source Computer Vision Library
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325 lines
12 KiB
325 lines
12 KiB
\section{Planar Subdivisions} |
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\ifCPy |
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\cvclass{CvSubdiv2D}\label{CvSubdiv2D} |
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Planar subdivision. |
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\ifC |
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\begin{lstlisting} |
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#define CV_SUBDIV2D_FIELDS() \ |
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CV_GRAPH_FIELDS() \ |
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int quad_edges; \ |
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int is_geometry_valid; \ |
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CvSubdiv2DEdge recent_edge; \ |
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CvPoint2D32f topleft; \ |
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CvPoint2D32f bottomright; |
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typedef struct CvSubdiv2D |
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{ |
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CV_SUBDIV2D_FIELDS() |
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} |
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CvSubdiv2D; |
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\end{lstlisting} |
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\else |
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\begin{description} |
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\cvarg{edges}{A \cross{CvSet} of \cross{CvSubdiv2DEdge}} |
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\end{description} |
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\fi |
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Planar subdivision is the subdivision of a plane into a set of |
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non-overlapped regions (facets) that cover the whole plane. The above |
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structure describes a subdivision built on a 2d point set, where the points |
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are linked together and form a planar graph, which, together with a few |
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edges connecting the exterior subdivision points (namely, convex hull points) |
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with infinity, subdivides a plane into facets by its edges. |
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For every subdivision there exists a dual subdivision in which facets and |
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points (subdivision vertices) swap their roles, that is, a facet is |
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treated as a vertex (called a virtual point below) of the dual subdivision and |
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the original subdivision vertices become facets. On the picture below |
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original subdivision is marked with solid lines and dual subdivision |
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with dotted lines. |
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\includegraphics[width=0.5\textwidth]{pics/subdiv.png} |
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OpenCV subdivides a plane into triangles using Delaunay's |
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algorithm. Subdivision is built iteratively starting from a dummy |
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triangle that includes all the subdivision points for sure. In this |
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case the dual subdivision is a Voronoi diagram of the input 2d point set. The |
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subdivisions can be used for the 3d piece-wise transformation of a plane, |
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morphing, fast location of points on the plane, building special graphs |
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(such as NNG,RNG) and so forth. |
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\ifC |
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\cvclass{CvQuadEdge2D}\label{CvQuadEdge2D} |
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Quad-edge of planar subdivision. |
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\begin{lstlisting} |
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/* one of edges within quad-edge, lower 2 bits is index (0..3) |
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and upper bits are quad-edge pointer */ |
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typedef long CvSubdiv2DEdge; |
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/* quad-edge structure fields */ |
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#define CV_QUADEDGE2D_FIELDS() \ |
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int flags; \ |
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struct CvSubdiv2DPoint* pt[4]; \ |
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CvSubdiv2DEdge next[4]; |
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typedef struct CvQuadEdge2D |
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{ |
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CV_QUADEDGE2D_FIELDS() |
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} |
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CvQuadEdge2D; |
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\end{lstlisting} |
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Quad-edge is a basic element of subdivision containing four edges (e, eRot, reversed e and reversed eRot): |
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\includegraphics[width=0.5\textwidth]{pics/quadedge.png} |
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\fi |
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\cvclass{CvSubdiv2DPoint}\label{CvSubdiv2DPoint} |
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\ifC |
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Point of original or dual subdivision. |
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\begin{lstlisting} |
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#define CV_SUBDIV2D_POINT_FIELDS()\ |
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int flags; \ |
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CvSubdiv2DEdge first; \ |
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CvPoint2D32f pt; \ |
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int id; |
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#define CV_SUBDIV2D_VIRTUAL_POINT_FLAG (1 << 30) |
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typedef struct CvSubdiv2DPoint |
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{ |
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CV_SUBDIV2D_POINT_FIELDS() |
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} |
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CvSubdiv2DPoint; |
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\end{lstlisting} |
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\begin{itemize} |
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\item[id] This integer can be used to index auxillary data associated with each vertex of the planar subdivision |
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\end{itemize} |
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\else |
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Point of original or dual subdivision. |
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\begin{description} |
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\cvarg{first}{A connected \cross{CvSubdiv2DEdge}} |
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\cvarg{pt}{Position, as a \cross{CvPoint2D32f}} |
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\end{description} |
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\fi |
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\cvCPyFunc{CalcSubdivVoronoi2D} |
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Calculates the coordinates of Voronoi diagram cells. |
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\cvdefC{ |
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void cvCalcSubdivVoronoi2D( \par CvSubdiv2D* subdiv ); |
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} |
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\cvdefPy{CalcSubdivVoronoi2D(subdiv)-> None} |
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\begin{description} |
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\cvarg{subdiv}{Delaunay subdivision, in which all the points are already added} |
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\end{description} |
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The function calculates the coordinates |
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of virtual points. All virtual points corresponding to some vertex of the |
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original subdivision form (when connected together) a boundary of the Voronoi |
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cell at that point. |
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\cvCPyFunc{ClearSubdivVoronoi2D} |
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Removes all virtual points. |
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\cvdefC{ |
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void cvClearSubdivVoronoi2D( CvSubdiv2D* subdiv ); |
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}\cvdefPy{ClearSubdivVoronoi2D(subdiv)-> None} |
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\begin{description} |
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\cvarg{subdiv}{Delaunay subdivision} |
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\end{description} |
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The function removes all of the virtual points. It |
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is called internally in \cvCPyCross{CalcSubdivVoronoi2D} if the subdivision |
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was modified after previous call to the function. |
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\cvCPyFunc{CreateSubdivDelaunay2D} |
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Creates an empty Delaunay triangulation. |
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\cvdefC{ |
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CvSubdiv2D* cvCreateSubdivDelaunay2D( \par CvRect rect,\par CvMemStorage* storage ); |
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}\cvdefPy{CreateSubdivDelaunay2D(rect,storage)-> delaunay\_triangulation} |
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\begin{description} |
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\cvarg{rect}{Rectangle that includes all of the 2d points that are to be added to the subdivision} |
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\cvarg{storage}{Container for subdivision} |
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\end{description} |
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The function creates an empty Delaunay |
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subdivision, where 2d points can be added using the function |
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\cvCPyCross{SubdivDelaunay2DInsert}. All of the points to be added must be within |
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the specified rectangle, otherwise a runtime error will be raised. |
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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 \texttt{rect}. |
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\cvCPyFunc{FindNearestPoint2D} |
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Finds the closest subdivision vertex to the given point. |
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\cvdefC{ |
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CvSubdiv2DPoint* cvFindNearestPoint2D( \par CvSubdiv2D* subdiv,\par CvPoint2D32f pt ); |
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}\cvdefPy{FindNearestPoint2D(subdiv,pt)-> point} |
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\begin{description} |
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\cvarg{subdiv}{Delaunay or another subdivision} |
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\cvarg{pt}{Input point} |
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\end{description} |
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The function is another function that |
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locates the input point within the subdivision. It finds the subdivision vertex that |
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is the closest to the input point. It is not necessarily one of vertices |
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of the facet containing the input point, though the facet (located using |
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\cvCPyCross{Subdiv2DLocate}) is used as a starting |
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point. The function returns a pointer to the found subdivision vertex. |
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\cvCPyFunc{Subdiv2DEdgeDst} |
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Returns the edge destination. |
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\cvdefC{ |
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CvSubdiv2DPoint* cvSubdiv2DEdgeDst( \par CvSubdiv2DEdge edge ); |
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} |
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\cvdefPy{Subdiv2DEdgeDst(edge)-> point} |
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\begin{description} |
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\cvarg{edge}{Subdivision edge (not a quad-edge)} |
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\end{description} |
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The function returns the edge destination. The |
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returned pointer may be NULL if the edge is from dual subdivision and |
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the virtual point coordinates are not calculated yet. The virtual points |
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can be calculated using the function \cvCPyCross{CalcSubdivVoronoi2D}. |
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\cvCPyFunc{Subdiv2DGetEdge} |
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Returns one of the edges related to the given edge. |
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\cvdefC{ |
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CvSubdiv2DEdge cvSubdiv2DGetEdge( CvSubdiv2DEdge edge, CvNextEdgeType type ); |
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}\cvdefPy{Subdiv2DGetEdge(edge,type)-> CvSubdiv2DEdge} |
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\begin{description} |
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\cvarg{edge}{Subdivision edge (not a quad-edge)} |
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\cvarg{type}{Specifies which of the related edges to return, one of the following:} |
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\begin{description} |
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\cvarg{CV\_NEXT\_AROUND\_ORG}{next around the edge origin (\texttt{eOnext} on the picture below if \texttt{e} is the input edge)} |
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\cvarg{CV\_NEXT\_AROUND\_DST}{next around the edge vertex (\texttt{eDnext})} |
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\cvarg{CV\_PREV\_AROUND\_ORG}{previous around the edge origin (reversed \texttt{eRnext})} |
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\cvarg{CV\_PREV\_AROUND\_DST}{previous around the edge destination (reversed \texttt{eLnext})} |
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\cvarg{CV\_NEXT\_AROUND\_LEFT}{next around the left facet (\texttt{eLnext})} |
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\cvarg{CV\_NEXT\_AROUND\_RIGHT}{next around the right facet (\texttt{eRnext})} |
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\cvarg{CV\_PREV\_AROUND\_LEFT}{previous around the left facet (reversed \texttt{eOnext})} |
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\cvarg{CV\_PREV\_AROUND\_RIGHT}{previous around the right facet (reversed \texttt{eDnext})} |
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\end{description} |
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\end{description} |
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\includegraphics[width=0.5\textwidth]{pics/quadedge.png} |
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The function returns one of the edges related to the input edge. |
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\cvCPyFunc{Subdiv2DNextEdge} |
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Returns next edge around the edge origin |
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\cvdefC{ |
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CvSubdiv2DEdge cvSubdiv2DNextEdge( CvSubdiv2DEdge edge ); |
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} |
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\cvdefPy{Subdiv2DNextEdge(edge)-> CvSubdiv2DEdge} |
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\begin{description} |
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\cvarg{edge}{Subdivision edge (not a quad-edge)} |
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\end{description} |
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\includegraphics[width=0.5\textwidth]{pics/quadedge.png} |
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The function returns the next edge around the edge origin: \texttt{eOnext} on the picture above if \texttt{e} is the input edge) |
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\cvCPyFunc{Subdiv2DLocate} |
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Returns the location of a point within a Delaunay triangulation. |
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\cvdefC{ |
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CvSubdiv2DPointLocation cvSubdiv2DLocate( \par CvSubdiv2D* subdiv,\par CvPoint2D32f pt,\par CvSubdiv2DEdge* edge,\par CvSubdiv2DPoint** vertex=NULL ); |
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} |
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\cvdefPy{Subdiv2DLocate(subdiv, pt) -> (loc, where)} |
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\begin{description} |
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\cvarg{subdiv}{Delaunay or another subdivision} |
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\cvarg{pt}{The point to locate} |
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\cvC{\cvarg{edge}{The output edge the point falls onto or right to}} |
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\cvC{\cvarg{vertex}{Optional output vertex double pointer the input point coinsides with}} |
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\cvPy{\cvarg{loc}{The location of the point within the triangulation}} |
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\cvPy{\cvarg{where}{The edge or vertex. See below.}} |
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\end{description} |
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The function locates the input point within the subdivision. There are 5 cases: |
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\ifC |
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\begin{itemize} |
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\item The point falls into some facet. The function returns \texttt{CV\_PTLOC\_INSIDE} and \texttt{*edge} will contain one of edges of the facet. |
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\item The point falls onto the edge. The function returns \texttt{CV\_PTLOC\_ON\_EDGE} and \texttt{*edge} will contain this edge. |
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\item The point coincides with one of the subdivision vertices. The function returns \texttt{CV\_PTLOC\_VERTEX} and \texttt{*vertex} will contain a pointer to the vertex. |
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\item The point is outside the subdivsion reference rectangle. The function returns \texttt{CV\_PTLOC\_OUTSIDE\_RECT} and no pointers are filled. |
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\item One of input arguments is invalid. A runtime error is raised or, if silent or "parent" error processing mode is selected, \texttt{CV\_PTLOC\_ERROR} is returnd. |
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\end{itemize} |
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\fi |
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\ifPy |
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\begin{itemize} |
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\item The point falls into some facet. \texttt{loc} is \texttt{CV\_PTLOC\_INSIDE} and \texttt{where} is one of edges of the facet. |
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\item The point falls onto the edge. \texttt{loc} is \texttt{CV\_PTLOC\_ON\_EDGE} and \texttt{where} is the edge. |
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\item The point coincides with one of the subdivision vertices. \texttt{loc} is \texttt{CV\_PTLOC\_VERTEX} and \texttt{where} is the vertex. |
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\item The point is outside the subdivsion reference rectangle. \texttt{loc} is \texttt{CV\_PTLOC\_OUTSIDE\_RECT} and \texttt{where} is None. |
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\item One of input arguments is invalid. The function raises an exception. |
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\end{itemize} |
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\fi |
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\cvCPyFunc{Subdiv2DRotateEdge} |
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Returns another edge of the same quad-edge. |
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\cvdefC{ |
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CvSubdiv2DEdge cvSubdiv2DRotateEdge( \par CvSubdiv2DEdge edge,\par int rotate ); |
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}\cvdefPy{Subdiv2DRotateEdge(edge,rotate)-> CvSubdiv2DEdge} |
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\begin{description} |
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\cvarg{edge}{Subdivision edge (not a quad-edge)} |
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\cvarg{rotate}{Specifies which of the edges of the same quad-edge as the input one to return, one of the following: |
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\begin{description} |
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\cvarg{0}{the input edge (\texttt{e} on the picture below if \texttt{e} is the input edge)} |
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\cvarg{1}{the rotated edge (\texttt{eRot})} |
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\cvarg{2}{the reversed edge (reversed \texttt{e} (in green))} |
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\cvarg{3}{the reversed rotated edge (reversed \texttt{eRot} (in green))} |
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\end{description}} |
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\end{description} |
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\includegraphics[width=0.5\textwidth]{pics/quadedge.png} |
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The function returns one of the edges of the same quad-edge as the input edge. |
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\cvCPyFunc{SubdivDelaunay2DInsert} |
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Inserts a single point into a Delaunay triangulation. |
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\cvdefC{ |
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CvSubdiv2DPoint* cvSubdivDelaunay2DInsert( \par CvSubdiv2D* subdiv,\par CvPoint2D32f pt); |
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}\cvdefPy{SubdivDelaunay2DInsert(subdiv,pt)-> point} |
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\begin{description} |
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\cvarg{subdiv}{Delaunay subdivision created by the function \cvCPyCross{CreateSubdivDelaunay2D}} |
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\cvarg{pt}{Inserted point} |
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\end{description} |
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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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\fi
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