# OpenGraph DrawingFramework

v. 2022.02 (Dogwood)

ogdf::SchnyderLayout Class Reference

The class SchnyderLayout represents the layout algorithm by Schnyder [Sch90]. More...

#include <ogdf/planarlayout/SchnyderLayout.h>

Inheritance diagram for ogdf::SchnyderLayout:

## Public Types

enum  CombinatorialObjects { CombinatorialObjects::VerticesMinusDepth, CombinatorialObjects::Faces }
Each node in a Schnyder wood splits the graph into three regions. More...

## Public Member Functions

SchnyderLayout ()

CombinatorialObjects getCombinatorialObjects ()
Returns the type of combinatorial objects whose number corresponds to the node coordinates. More...

void setCombinatorialObjects (CombinatorialObjects combinatorialObjects)
Sets the type of combinatorial objects whose number corresponds to the node coordinates. More...

Public Member Functions inherited from ogdf::PlanarGridLayoutModule
PlanarGridLayoutModule ()
Initializes a planar grid layout module. More...

virtual ~PlanarGridLayoutModule ()

Calls the grid layout algorithm with a fixed planar embedding (general call). More...

Calls the grid layout algorithm with a fixed planar embedding (call for GridLayout). More...

Public Member Functions inherited from ogdf::GridLayoutModule
GridLayoutModule ()
Initializes a grid layout module. More...

virtual ~GridLayoutModule ()

virtual void call (GraphAttributes &GA) override final
Calls the grid layout algorithm (general call). More...

void callGrid (const Graph &G, GridLayout &gridLayout)
Calls the grid layout algorithm (call for GridLayout). More...

const IPointgridBoundingBox () const

double separation () const
Returns the current setting of the minimum distance between nodes. More...

void separation (double sep)
Sets the minimum distance between nodes. More...

Public Member Functions inherited from ogdf::LayoutModule
LayoutModule ()
Initializes a layout module. More...

virtual ~LayoutModule ()

void operator() (GraphAttributes &GA)
Computes a layout of graph GA. More...

## Protected Member Functions

virtual void doCall (const Graph &G, adjEntry adjExternal, GridLayout &gridLayout, IPoint &boundingBox, bool fixEmbedding) override
Implements the algorithm call. More...

Protected Member Functions inherited from ogdf::PlanarGridLayoutModule
virtual void doCall (const Graph &G, GridLayout &gridLayout, IPoint &boundingBox) override
Implements the GridLayoutModule::doCall(). More...

bool handleTrivial (const Graph &G, GridLayout &gridLayout, IPoint &boundingBox)
Handles the special cases of graphs with less than 3 nodes. More...

## Private Member Functions

void contract (Graph &G, node a, node b, node c, List< node > &L)

void prefixSum (EdgeArray< int > &rValues, int i, node r, const NodeArray< int > &val, NodeArray< int > &sum)

void realizer (GraphCopy &G, const List< node > &L, node a, node b, node c, EdgeArray< int > &rValues, GraphCopy &T)

void subtreeSizes (EdgeArray< int > &rValues, int i, node r, NodeArray< int > &size)

## Private Attributes

CombinatorialObjects m_combinatorialObjects
Determines how the barycentric coordinates of each node are computed. More...

Protected Attributes inherited from ogdf::GridLayoutModule
IPoint m_gridBoundingBox
The computed bounding box of the grid layout. More...

## Detailed Description

The class SchnyderLayout represents the layout algorithm by Schnyder [Sch90].

This algorithm draws a planar graph G straight-line without crossings. G (with |V| ≥ 3) must not contain self-loops or multiple edges. The algorithm runs in three phases. In the first phase, the graph is augmented by adding new artificial edges to get a triangulated plane graph. Then, a partition of the set of interior edges in three trees (also called Schnyder trees) with special orientation properties is derived. In the third step, the actual coordinates are computed. See:

[Sch90] Schnyder, Walter. "Embedding planar graphs on the grid." Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, 1990.

[Sch89] Schnyder, Walter. "Planar graphs and poset dimension." Order 5.4 (1989): 323-343.

Definition at line 60 of file SchnyderLayout.h.

## ◆ CombinatorialObjects

 strong

Each node in a Schnyder wood splits the graph into three regions.

The barycentric coordinates of the nodes are given by the count of combinatorial objects in these regions.

Enumerator
VerticesMinusDepth

Count the number of vertices in each region i and subtract the depth of the (i-1)-path of the node.

This approach is outlined in [Sch90]. The grid layout size is (n - 2) × (n - 2).

Faces

Count the number of faces in each region i.

This approach is outlined in [Sch89]. The grid layout size is (2n - 5) × (2n - 5).

Definition at line 70 of file SchnyderLayout.h.

## ◆ SchnyderLayout()

 ogdf::SchnyderLayout::SchnyderLayout ( )

## ◆ contract()

 void ogdf::SchnyderLayout::contract ( Graph & G, node a, node b, node c, List< node > & L )
private

## ◆ doCall()

 virtual void ogdf::SchnyderLayout::doCall ( const Graph & G, adjEntry adjExternal, GridLayout & gridLayout, IPoint & boundingBox, bool fixEmbedding )
overrideprotectedvirtual

Implements the algorithm call.

A derived algorithm must implement this method and return the computed grid layout in gridLayout.

Parameters
 G is the input graph. adjExternal is an adjacency entry on the external face, or 0 if no external face is specified. gridLayout is assigned the computed grid layout. boundingBox returns the bounding box of the grid layout. The lower left corner of the bounding box is always (0,0), thus this IPoint defines the upper right corner as well as the width and height of the grid layout. fixEmbedding determines if the input graph is embedded and that embedding has to be preserved (true), or if an embedding needs to be computed (false).

Implements ogdf::PlanarGridLayoutModule.

## ◆ getCombinatorialObjects()

 CombinatorialObjects ogdf::SchnyderLayout::getCombinatorialObjects ( )
inline

Returns the type of combinatorial objects whose number corresponds to the node coordinates.

Definition at line 81 of file SchnyderLayout.h.

## ◆ prefixSum()

 void ogdf::SchnyderLayout::prefixSum ( EdgeArray< int > & rValues, int i, node r, const NodeArray< int > & val, NodeArray< int > & sum )
private

## ◆ realizer()

 void ogdf::SchnyderLayout::realizer ( GraphCopy & G, const List< node > & L, node a, node b, node c, EdgeArray< int > & rValues, GraphCopy & T )
private

## ◆ schnyderEmbedding()

 void ogdf::SchnyderLayout::schnyderEmbedding ( GraphCopy & GC, GridLayout & gridLayout, adjEntry adjExternal )
private

## ◆ setCombinatorialObjects()

 void ogdf::SchnyderLayout::setCombinatorialObjects ( CombinatorialObjects combinatorialObjects )
inline

Sets the type of combinatorial objects whose number corresponds to the node coordinates.

Definition at line 84 of file SchnyderLayout.h.

## ◆ subtreeSizes()

 void ogdf::SchnyderLayout::subtreeSizes ( EdgeArray< int > & rValues, int i, node r, NodeArray< int > & size )
private

## ◆ m_combinatorialObjects

 CombinatorialObjects ogdf::SchnyderLayout::m_combinatorialObjects
private

Determines how the barycentric coordinates of each node are computed.

Definition at line 127 of file SchnyderLayout.h.

The documentation for this class was generated from the following file: