pgRouting · Mohit242-bit · Aug 21, 2026 · Aug 21, 2026 · Aug 21, 2026 · Aug 21, 2026
diff --git a/NEWS.md b/NEWS.md
@@ -35,12 +35,22 @@ To see all issues & pull requests closed by this release see the
 * [#3101](https://github.com/pgRouting/pgrouting/issues/3101): pgr_edgeColoring not building graph correctly
 
 
+**New experimental functions.**
+
+* Planar
+
+  * pgr_makeMaximalPlanar
+
 **Summary of changes by function**
 
 * pgr_edgeColoring
 
   * Fix the way it builds the graph
 
+* pgr_makeMaximalPlanar
+
+  * New experimental function.
+
 ## pgRouting 4.0
 
 
@@ -272,6 +282,7 @@ Summary of changes by function
 
   * All signatures promoted to official.
 
+
 * pgr_maxCardinalityMatch
 
   .. Breaking change
@@ -463,6 +474,7 @@ New experimental functions.
   * [#2954](https://github.com/pgRouting/pgrouting/issues/2954): pgr_kingOrdering
   * [#2955](https://github.com/pgRouting/pgrouting/issues/2955): pgr_sloanOrdering
 
+
 SQL signatures and output standardization
 
 [#2904](https://github.com/pgRouting/pgrouting/issues/2904): Standardize output columns of functions with different output

diff --git a/doc/_static/page_history.js b/doc/_static/page_history.js
@@ -16,6 +16,8 @@ var titles = [
 
 
 var newpages = [
+    {v: '4.1', pages: ['pgr_makeMaximalPlanar']},
+
     {v: '4.0', pages: ['pgr_bandwidth', 'pgr_kingOrdering', 'pgr_sloanOrdering']},
 
     {v: '3.8', pages: ['pgr_contractionDeadEnd', 'pgr_contractionLinear', 'pgr_separateCrossing',

diff --git a/doc/planar/CMakeLists.txt b/doc/planar/CMakeLists.txt
@@ -3,7 +3,9 @@
 # License: GPL-2 See https://github.com/pgRouting/pgrouting/blob/main/LICENSE
 
 set(LOCAL_FILES
+    planar-family.rst
     pgr_isPlanar.rst
+    pgr_makeMaximalPlanar.rst
     )
 
 foreach (f ${LOCAL_FILES})

diff --git a/doc/planar/images/CMakeLists.txt b/doc/planar/images/CMakeLists.txt
@@ -3,6 +3,9 @@
 # License: GPL-2 See https://github.com/pgRouting/pgrouting/blob/main/LICENSE
 set(LOCAL_FILES
     nonPlanar.png
+    maximal_planar_sampledata.png
+    maximal_planar_5cycle.png
+    maximal_planar_5cycle_before.png
     )
 
 foreach (f ${LOCAL_FILES})

diff --git a/doc/planar/images/maximal_planar_5cycle.png b/doc/planar/images/maximal_planar_5cycle.png
diff --git a/doc/planar/images/maximal_planar_5cycle_before.png b/doc/planar/images/maximal_planar_5cycle_before.png
diff --git a/doc/planar/images/maximal_planar_sampledata.png b/doc/planar/images/maximal_planar_sampledata.png
diff --git a/doc/planar/pgr_makeMaximalPlanar.rst b/doc/planar/pgr_makeMaximalPlanar.rst
@@ -0,0 +1,163 @@
+:file: This file is part of the pgRouting project.
+:copyright: Copyright (c) 2020-2026 pgRouting developers
+:license: Creative Commons Attribution-Share Alike 3.0 https://creativecommons.org/licenses/by-sa/3.0
+
+.. index::
+   single: Planar Family ; pgr_makeMaximalPlanar - Experimental
+   single: makeMaximalPlanar - Experimental on v4.1
+
+|
+
+``pgr_makeMaximalPlanar`` - Experimental
+===============================================================================
+
+``pgr_makeMaximalPlanar`` — Returns the set of edges needed to make a planar graph maximal planar.
+
+.. include:: experimental.rst
+   :start-after: warning-begin
+   :end-before: end-warning
+
+.. rubric:: Availability
+
+.. rubric:: Version 4.1.0
+
+* New experimental function.
+
+
+Description
+-------------------------------------------------------------------------------
+
+``pgr_makeMaximalPlanar`` identifies the missing edges that need to be added to
+the connected components of a planar graph to make each eligible component maximal planar.
+
+A planar graph is considered **maximal planar** (or fully triangulated) if no additional
+edges can be added to it without violating its planarity. In a maximal planar graph,
+every face (including the outer face) is a triangle.
+
+The main characteristics are:
+
+* Works for **undirected** graphs.
+* Works for **planar** graphs only.
+* If any component of the input graph is not planar, no added edges are returned for that component.
+* Returns a list of all new edges needed to triangulate the eligible components of the graph and make them maximal planar.
+* The augmentation applies independently to eligible components (components with 3 or more vertices). Components with fewer than 3 vertices produce no added edges.
+* The algorithm does not consider traversal costs in the calculations.
+* The algorithm does not consider geometric topology in the calculations.
+* Running time: :math:`O(|V_G| + |E_G| + R \log R)` where :math:`G(V_G, E_G)` is the input graph and :math:`R` is the number of returned edges.
+
+|Boost| Boost Graph Inside
+
+Signatures
+-------------------------------------------------------------------------------
+
+.. admonition:: \ \
+   :class: signatures
+
+   | pgr_makeMaximalPlanar(`Edges SQL`_)
+
+   | Returns set of |result-component-make|
+   | OR EMPTY SET
+
+:Example: List of edges that are needed to make the sample graph maximal planar.
+
+**Sample graph before:**
+
+.. figure:: /images/Fig6-undirected.png
+   :scale: 50%
+
+   Sample graph before
+
+**Output:**
+
+.. literalinclude:: makeMaximalPlanar.queries
+   :start-after: -- q1
+   :end-before: -- q2
+
+**Sample graph after adding triangulation edges:**
+
+.. figure:: images/maximal_planar_sampledata.png
+   :scale: 75%
+
+   Sample graph after adding triangulation edges (olive = original edges, red dashed = 17 new triangulation edges).
+   Note: When a graph contains multiple disconnected components, each component is processed independently. Components (2,4) and (13,14) have < 3 vertices and cannot be triangulated; the 13-vertex component is triangulated with 17 new edges.
+
+Parameters
+-------------------------------------------------------------------------------
+
+.. include:: pgRouting-concepts.rst
+   :start-after: only_edge_param_start
+   :end-before: only_edge_param_end
+
+Inner Queries
+-------------------------------------------------------------------------------
+
+Edges SQL
+...............................................................................
+
+.. include:: pgRouting-concepts.rst
+    :start-after: basic_edges_sql_start
+    :end-before: basic_edges_sql_end
+
+Result columns
+-------------------------------------------------------------------------------
+
+Returns set of |result-component-make|
+
+.. list-table::
+   :width: 81
+   :widths: auto
+   :header-rows: 1
+
+   * - Column
+     - Type
+     - Description
+   * - ``seq``
+     - ``BIGINT``
+     - Sequential value starting from **1**.
+   * - ``start_vid``
+     - ``BIGINT``
+     - Identifier of the first end point vertex of the edge.
+   * - ``end_vid``
+     - ``BIGINT``
+     - Identifier of the second end point vertex of the edge.
+
+Additional Examples
+-------------------------------------------------------------------------------
+
+:Example: Triangulating a simple 5-cycle ring graph.
+
+.. literalinclude:: makeMaximalPlanar.queries
+   :start-after: -- q2
+   :end-before: -- q3
+
+**Sample graph before:**
+
+.. figure:: images/maximal_planar_5cycle_before.png
+   :scale: 75%
+
+   Sample 5-cycle ring graph before triangulation.
+
+**Output:**
+
+.. literalinclude:: makeMaximalPlanar.queries
+   :start-after: -- q3
+   :end-before: -- q4
+
+**Sample graph after adding triangulation edges:**
+
+.. figure:: images/maximal_planar_5cycle.png
+   :scale: 75%
+
+   Maximal planar triangulation of a simple 5-cycle ring graph (4 red dashed triangulation edges added).
+
+See Also
+-------------------------------------------------------------------------------
+
+* `Boost: make_maximal_planar
+  <https://www.boost.org/doc/libs/latest/libs/graph/doc/html/graph/algorithms/planar/make_maximal_planar.html>`__
+* :doc:`sampledata`
+
+.. rubric:: Indices and tables
+
+* :ref:`genindex`
+* :ref:`search`
diff --git a/doc/planar/planar-family.rst b/doc/planar/planar-family.rst
@@ -0,0 +1,33 @@
+:file: This file is part of the pgRouting project.
+:copyright: Copyright (c) 2020-2026 pgRouting developers
+:license: Creative Commons Attribution-Share Alike 3.0 https://creativecommons.org/licenses/by-sa/3.0
+
+.. index:: Planar Family 
+
+|
+
+Planar - Family of functions
+===============================================================================
+
+.. include:: experimental.rst
+   :start-after: warning-begin
+   :end-before: end-warning
+
+.. experimental-start
+
+* :doc:`pgr_isPlanar` - Returns a boolean depending upon the planarity of the graph.
+* :doc:`pgr_makeMaximalPlanar` - Returns edges to add to a planar graph to make its eligible components maximal planar.
+
+.. experimental-end
+
+
+.. toctree::
+    :hidden:
+
+    pgr_isPlanar
+    pgr_makeMaximalPlanar
+
+.. rubric:: Indices and tables
+
+* :ref:`genindex`
+* :ref:`search`
diff --git a/doc/src/experimental.rst b/doc/src/experimental.rst
@@ -93,13 +93,20 @@ Experimental Functions
    :start-after: experimental-start
    :end-before: experimental-end
 
+:doc:`planar-family`
+
+.. include:: planar-family.rst
+   :start-after: experimental-start
+   :end-before: experimental-end
+
 .. toctree::
    :hidden:
 
    chinesePostmanProblem-family
    transformation-family
    components-family
    ordering-family
+   planar-family
 
 .. rubric:: categories
 
@@ -127,14 +134,7 @@ Experimental Functions
   pgr_dagShortestPath
   pgr_edwardMoore
 
-.. rubric:: Planar Family
-
-- :doc:`pgr_isPlanar`
-
-.. toctree::
-  :hidden:
 
-  pgr_isPlanar
 
 .. rubric:: Miscellaneous Algorithms
 

diff --git a/doc/src/release_notes.rst b/doc/src/release_notes.rst
@@ -60,6 +60,12 @@ To see all issues & pull requests closed by this release see the
 * :issue:`3101`: pgr_edgeColoring not building graph correctly
 
 
+.. rubric:: New experimental functions.
+
+* Planar
+
+  * pgr_makeMaximalPlanar
+
 .. rubric:: Summary of changes by function
 
 * pgr_edgeColoring
@@ -68,6 +74,12 @@ To see all issues & pull requests closed by this release see the
      :start-after: Version 4.1.0
      :end-before: .. rubric
 
+* pgr_makeMaximalPlanar
+
+  .. include:: pgr_makeMaximalPlanar.rst
+     :start-after: Version 4.1.0
+     :end-before: Description
+
 pgRouting 4.0
 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
@@ -358,6 +370,7 @@ Summary of changes by function
      :start-after: Version 4.0.0
      :end-before: .. rubric
 
+
 * pgr_maxCardinalityMatch
 
   .. include:: pgr_maxCardinalityMatch.rst
@@ -525,6 +538,7 @@ New experimental functions.
   * :issue:`2954`: pgr_kingOrdering
   * :issue:`2955`: pgr_sloanOrdering
 
+
 SQL signatures and output standardization
 ...............................................................................
 

diff --git a/docqueries/planar/CMakeLists.txt b/docqueries/planar/CMakeLists.txt
@@ -5,6 +5,7 @@
 set(LOCAL_FILES
     boyerMyrvold
     isPlanar
+    makeMaximalPlanar
     )
 
 foreach (f ${LOCAL_FILES})

diff --git a/docqueries/planar/makeMaximalPlanar.pg b/docqueries/planar/makeMaximalPlanar.pg
@@ -0,0 +1,27 @@
+/* :file: This file is part of the pgRouting project.
+:copyright: Copyright (c) 2020-2026 pgRouting developers
+:license: Creative Commons Attribution-Share Alike 3.0 https://creativecommons.org/licenses/by-sa/3.0 */
+/* -- q1 */
+SELECT * FROM pgr_makeMaximalPlanar(
+  'SELECT id, source, target, cost, reverse_cost FROM edges'
+);
+/* -- q2 */
+CREATE TABLE example_edges1 (
+    id SERIAL PRIMARY KEY,
+    source INTEGER,
+    target INTEGER,
+    cost DOUBLE PRECISION,
+    reverse_cost DOUBLE PRECISION
+);
+INSERT INTO example_edges1 (source, target, cost, reverse_cost) VALUES
+(1, 2, 1, 1),
+(2, 3, 1, 1),
+(3, 4, 1, 1),
+(4, 5, 1, 1),
+(5, 1, 1, 1);
+
+/* -- q3 */
+SELECT * FROM pgr_makeMaximalPlanar(
+  'SELECT id, source, target, cost, reverse_cost FROM example_edges1'
+);
+/* -- q4 */