sakirr05
## pgr_planarFaces(): **planarFaces()**: Planar face extraction is an algorithm that takes an undirected planar graph, computes a planar embedding of it, and walks every face of that embedding. A face is a maximal connected region of the plane bounded by edges, which on a street network corresponds to the city blocks between the roads, and the exterior face is the unbounded region outside the outermost cycle. Once an embedding is fixed each edge separates exactly two faces, bordering one on its left side and the other on its right, so the function reports every edge-face incidence. This implementation uses the Boost Graph Library's `boyer_myrvold_planarity_test` to compute the embedding and `planar_face_traversal` to walk the faces, with a time complexity of O(V + E), where V is the number of vertices and E is the number of edges. This will enhance pgRouting's capabilities in topology extraction and polygon reconstruction problems. #### The algorithm: - Works on **undirected** graphs. - Edge direction and traversal costs are ignored, only the edge endpoints matter. - Requires the input graph to be planar, otherwise raises `ERROR: Graph is not planar`. Use `pgr_isPlanar` first when planarity is unknown. - Reports one row per edge side, so the result has `2|E|` rows. - Walks the outer face of every connected component separately, so on a graph with `C` components the face count satisfies `|V| - |E| + |F| = 2C`. - Running time: O(V + E) where V is the number of vertices and E is the number of edges. ### Signature: - pgr_planarFaces() ```sql pgr_planarFaces(Edges SQL) Returns set of (seq, face_id, edge_id, side) OR EMPTY SET ``` ## Parameters | Parameter | Type | Description | | --- | --- | --- | | **Edges SQL** | `TEXT` | Inner SQL query, as described below. | ### Inner Query **Edges SQL**: An SQL query returning a set of rows with the following columns: | Column | Type | Default | Description | | --- | --- | --- | --- | | **id** | `ANY-INTEGER` | | Identifier of the edge. | | **source** | `ANY-INTEGER` | | Identifier of the first endpoint vertex of the edge. | | **target** | `ANY-INTEGER` | | Identifier of the second endpoint vertex of the edge. | | **cost** | `ANY-NUMERICAL` | | Weight of the edge `(source, target)`. When negative, the edge does not exist. | | **reverse_cost** | `ANY-NUMERICAL` | `-1` | Weight of the edge `(target, source)`. When negative, the edge does not exist. | Where: - `ANY-INTEGER` = `SMALLINT`, `INTEGER`, `BIGINT` - `ANY-NUMERICAL` = `SMALLINT`, `INTEGER`, `BIGINT`, `REAL`, `FLOAT` ### Result Columns Returns `SETOF (seq, face_id, edge_id, side)`. | Column | Type | Description | | --- | --- | --- | | **seq** | `BIGINT` | Sequential value starting from 1. | | **face_id** | `BIGINT` | Identifier of the face in the computed embedding. | | **edge_id** | `BIGINT` | Identifier of the edge that borders the face. | | **side** | `INTEGER` | `1` when the edge borders the face on the left side, `2` when on the right side. |