diff --git a/python/core/geometry/qgsgeometry.sip.in b/python/core/geometry/qgsgeometry.sip.in
index fef378108dd..bb0ad763d6f 100644
--- a/python/core/geometry/qgsgeometry.sip.in
+++ b/python/core/geometry/qgsgeometry.sip.in
@@ -1423,10 +1423,13 @@ An empty geometry will be returned in the case of errors.
 .. versionadded:: 3.0
 %End
 
-    void convertToStraightSegment();
+    void convertToStraightSegment( double tolerance = M_PI / 180., QgsAbstractGeometry::SegmentationToleranceType toleranceType = QgsAbstractGeometry::MaximumAngle );
 %Docstring
 Converts the geometry to straight line segments, if it is a curved geometry type.
 
+:param tolerance: segmentation tolerance
+:param toleranceType: maximum segmentation angle or maximum difference between approximation and curve
+
 .. versionadded:: 2.10
 
 .. seealso:: :py:func:`requiresConversionToStraightSegments`
diff --git a/src/core/geometry/qgsgeometry.cpp b/src/core/geometry/qgsgeometry.cpp
index 10aa1326bc3..352fbd0c685 100644
--- a/src/core/geometry/qgsgeometry.cpp
+++ b/src/core/geometry/qgsgeometry.cpp
@@ -2312,14 +2312,14 @@ QgsGeometry QgsGeometry::polygonize( const QVector<QgsGeometry> &geometryList )
   return result;
 }
 
-void QgsGeometry::convertToStraightSegment()
+void QgsGeometry::convertToStraightSegment( double tolerance, QgsAbstractGeometry::SegmentationToleranceType toleranceType )
 {
   if ( !d->geometry || !requiresConversionToStraightSegments() )
   {
     return;
   }
 
-  std::unique_ptr< QgsAbstractGeometry > straightGeom( d->geometry->segmentize() );
+  std::unique_ptr< QgsAbstractGeometry > straightGeom( d->geometry->segmentize( tolerance, toleranceType ) );
   reset( std::move( straightGeom ) );
 }
 
diff --git a/src/core/geometry/qgsgeometry.h b/src/core/geometry/qgsgeometry.h
index 84802e7749e..4bc6232a19b 100644
--- a/src/core/geometry/qgsgeometry.h
+++ b/src/core/geometry/qgsgeometry.h
@@ -1413,10 +1413,12 @@ class CORE_EXPORT QgsGeometry
 
     /**
      * Converts the geometry to straight line segments, if it is a curved geometry type.
+     * \param tolerance segmentation tolerance
+     * \param toleranceType maximum segmentation angle or maximum difference between approximation and curve
      * \since QGIS 2.10
      * \see requiresConversionToStraightSegments
      */
-    void convertToStraightSegment();
+    void convertToStraightSegment( double tolerance = M_PI / 180., QgsAbstractGeometry::SegmentationToleranceType toleranceType = QgsAbstractGeometry::MaximumAngle );
 
     /**
      * Returns true if the geometry is a curved geometry type which requires conversion to