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I would like to know on which method (e.g. Douglas-Peucker line simplification) the modules qgis:simplifygeometries and qgis:smoothgeometry are built on.

I cannot find further information on these modules.

5

Simplifying and smoothing operations are related to the QgsGeometry() Class: this means that you can run them when dealing with the geometry of the current feature.

As far as I know, the Simplify geometries algorithm literally simplifies the current geometry by reducing the number of vertices on the basis of a tolerance value (so, there isn't any particular method applied).

Instead, the Smooth geometry algorithm is based on the Chaikin algorithm, as reported in the smooth() module:

Smooths a geometry by rounding off corners using the Chaikin algorithm.

This operation roughly doubles the number of vertices in a geometry.

EDIT

The Simplify geometries algorithm is based on the simplify() module which, as brilliantly noted by @user30184 in its comment, leads to GEOS. From the following links:

geos::simplify::DouglasPeuckerLineSimplifier Class Reference

geos::simplify::TopologyPreservingSimplifier Class Reference

it seems that there is an explicit reference to the Douglas-Peucker algorithm. More in detail, from the first link above:

Simplifies a linestring (sequence of points) using the standard Douglas-Peucker algorithm.

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