diff --git a/doc/classes/Curve2D.xml b/doc/classes/Curve2D.xml
index 01a011021f2..f15c0d74caa 100644
--- a/doc/classes/Curve2D.xml
+++ b/doc/classes/Curve2D.xml
@@ -15,10 +15,10 @@
 			<param index="0" name="position" type="Vector2" />
 			<param index="1" name="in" type="Vector2" default="Vector2(0, 0)" />
 			<param index="2" name="out" type="Vector2" default="Vector2(0, 0)" />
-			<param index="3" name="at_position" type="int" default="-1" />
+			<param index="3" name="index" type="int" default="-1" />
 			<description>
-				Adds a point to a curve at [param position] relative to the [Curve2D]'s position, with control points [param in] and [param out].
-				If [param at_position] is given, the point is inserted before the point number [param at_position], moving that point (and every point after) after the inserted point. If [param at_position] is not given, or is an illegal value ([code]at_position &lt;0[/code] or [code]at_position &gt;= [method get_point_count][/code]), the point will be appended at the end of the point list.
+				Adds a point with the specified [param position] relative to the curve's own position, with control points [param in] and [param out]. Appends the new point at the end of the point list.
+				If [param index] is given, the new point is inserted before the existing point identified by index [param index]. Every existing point starting from [param index] is shifted further down the list of points. The index must be greater than or equal to [code]0[/code] and must not exceed the number of existing points in the line. See [member point_count].
 			</description>
 		</method>
 		<method name="clear_points">
diff --git a/doc/classes/Curve3D.xml b/doc/classes/Curve3D.xml
index ca3ce1cb645..08434538202 100644
--- a/doc/classes/Curve3D.xml
+++ b/doc/classes/Curve3D.xml
@@ -15,10 +15,10 @@
 			<param index="0" name="position" type="Vector3" />
 			<param index="1" name="in" type="Vector3" default="Vector3(0, 0, 0)" />
 			<param index="2" name="out" type="Vector3" default="Vector3(0, 0, 0)" />
-			<param index="3" name="at_position" type="int" default="-1" />
+			<param index="3" name="index" type="int" default="-1" />
 			<description>
-				Adds a point to a curve at [param position] relative to the [Curve3D]'s position, with control points [param in] and [param out].
-				If [param at_position] is given, the point is inserted before the point number [param at_position], moving that point (and every point after) after the inserted point. If [param at_position] is not given, or is an illegal value ([code]at_position &lt;0[/code] or [code]at_position &gt;= [method get_point_count][/code]), the point will be appended at the end of the point list.
+				Adds a point with the specified [param position] relative to the curve's own position, with control points [param in] and [param out]. Appends the new point at the end of the point list.
+				If [param index] is given, the new point is inserted before the existing point identified by index [param index]. Every existing point starting from [param index] is shifted further down the list of points. The index must be greater than or equal to [code]0[/code] and must not exceed the number of existing points in the line. See [member point_count].
 			</description>
 		</method>
 		<method name="clear_points">
diff --git a/doc/classes/Line2D.xml b/doc/classes/Line2D.xml
index f6aea83b7f2..f4bf8035546 100644
--- a/doc/classes/Line2D.xml
+++ b/doc/classes/Line2D.xml
@@ -14,10 +14,10 @@
 		<method name="add_point">
 			<return type="void" />
 			<param index="0" name="position" type="Vector2" />
-			<param index="1" name="at_position" type="int" default="-1" />
+			<param index="1" name="index" type="int" default="-1" />
 			<description>
-				Adds a point at the [param position]. Appends the point at the end of the line.
-				If [param at_position] is given, the point is inserted before the point number [param at_position], moving that point (and every point after) after the inserted point. If [param at_position] is not given, or is an illegal value ([code]at_position &lt; 0[/code] or [code]at_position &gt;= [method get_point_count][/code]), the point will be appended at the end of the point list.
+				Adds a point with the specified [param position] relative to the line's own position. Appends the new point at the end of the point list.
+				If [param index] is given, the new point is inserted before the existing point identified by index [param index]. Every existing point starting from [param index] is shifted further down the list of points. The index must be greater than or equal to [code]0[/code] and must not exceed the number of existing points in the line. See [method get_point_count].
 			</description>
 		</method>
 		<method name="clear_points">
@@ -29,29 +29,29 @@
 		<method name="get_point_count" qualifiers="const">
 			<return type="int" />
 			<description>
-				Returns the Line2D's amount of points.
+				Returns the amount of points in the line.
 			</description>
 		</method>
 		<method name="get_point_position" qualifiers="const">
 			<return type="Vector2" />
-			<param index="0" name="i" type="int" />
+			<param index="0" name="index" type="int" />
 			<description>
-				Returns point [param i]'s position.
+				Returns the position of the point at index [param index].
 			</description>
 		</method>
 		<method name="remove_point">
 			<return type="void" />
-			<param index="0" name="i" type="int" />
+			<param index="0" name="index" type="int" />
 			<description>
-				Removes the point at index [param i] from the line.
+				Removes the point at index [param index] from the line.
 			</description>
 		</method>
 		<method name="set_point_position">
 			<return type="void" />
-			<param index="0" name="i" type="int" />
+			<param index="0" name="index" type="int" />
 			<param index="1" name="position" type="Vector2" />
 			<description>
-				Overwrites the position in point [param i] with the supplied [param position].
+				Overwrites the position of the point at index [param index] with the supplied [param position].
 			</description>
 		</method>
 	</methods>
diff --git a/scene/2d/line_2d.cpp b/scene/2d/line_2d.cpp
index 06e5cbc97e0..837f3061f12 100644
--- a/scene/2d/line_2d.cpp
+++ b/scene/2d/line_2d.cpp
@@ -346,13 +346,13 @@ void Line2D::_bind_methods() {
 	ClassDB::bind_method(D_METHOD("set_points", "points"), &Line2D::set_points);
 	ClassDB::bind_method(D_METHOD("get_points"), &Line2D::get_points);
 
-	ClassDB::bind_method(D_METHOD("set_point_position", "i", "position"), &Line2D::set_point_position);
-	ClassDB::bind_method(D_METHOD("get_point_position", "i"), &Line2D::get_point_position);
+	ClassDB::bind_method(D_METHOD("set_point_position", "index", "position"), &Line2D::set_point_position);
+	ClassDB::bind_method(D_METHOD("get_point_position", "index"), &Line2D::get_point_position);
 
 	ClassDB::bind_method(D_METHOD("get_point_count"), &Line2D::get_point_count);
 
-	ClassDB::bind_method(D_METHOD("add_point", "position", "at_position"), &Line2D::add_point, DEFVAL(-1));
-	ClassDB::bind_method(D_METHOD("remove_point", "i"), &Line2D::remove_point);
+	ClassDB::bind_method(D_METHOD("add_point", "position", "index"), &Line2D::add_point, DEFVAL(-1));
+	ClassDB::bind_method(D_METHOD("remove_point", "index"), &Line2D::remove_point);
 
 	ClassDB::bind_method(D_METHOD("clear_points"), &Line2D::clear_points);
 
diff --git a/scene/resources/curve.cpp b/scene/resources/curve.cpp
index 5de92acb752..18356042855 100644
--- a/scene/resources/curve.cpp
+++ b/scene/resources/curve.cpp
@@ -1167,7 +1167,7 @@ void Curve2D::_get_property_list(List<PropertyInfo> *p_list) const {
 void Curve2D::_bind_methods() {
 	ClassDB::bind_method(D_METHOD("get_point_count"), &Curve2D::get_point_count);
 	ClassDB::bind_method(D_METHOD("set_point_count", "count"), &Curve2D::set_point_count);
-	ClassDB::bind_method(D_METHOD("add_point", "position", "in", "out", "at_position"), &Curve2D::add_point, DEFVAL(Vector2()), DEFVAL(Vector2()), DEFVAL(-1));
+	ClassDB::bind_method(D_METHOD("add_point", "position", "in", "out", "index"), &Curve2D::add_point, DEFVAL(Vector2()), DEFVAL(Vector2()), DEFVAL(-1));
 	ClassDB::bind_method(D_METHOD("set_point_position", "idx", "position"), &Curve2D::set_point_position);
 	ClassDB::bind_method(D_METHOD("get_point_position", "idx"), &Curve2D::get_point_position);
 	ClassDB::bind_method(D_METHOD("set_point_in", "idx", "position"), &Curve2D::set_point_in);
@@ -1972,7 +1972,7 @@ void Curve3D::_get_property_list(List<PropertyInfo> *p_list) const {
 void Curve3D::_bind_methods() {
 	ClassDB::bind_method(D_METHOD("get_point_count"), &Curve3D::get_point_count);
 	ClassDB::bind_method(D_METHOD("set_point_count", "count"), &Curve3D::set_point_count);
-	ClassDB::bind_method(D_METHOD("add_point", "position", "in", "out", "at_position"), &Curve3D::add_point, DEFVAL(Vector3()), DEFVAL(Vector3()), DEFVAL(-1));
+	ClassDB::bind_method(D_METHOD("add_point", "position", "in", "out", "index"), &Curve3D::add_point, DEFVAL(Vector3()), DEFVAL(Vector3()), DEFVAL(-1));
 	ClassDB::bind_method(D_METHOD("set_point_position", "idx", "position"), &Curve3D::set_point_position);
 	ClassDB::bind_method(D_METHOD("get_point_position", "idx"), &Curve3D::get_point_position);
 	ClassDB::bind_method(D_METHOD("set_point_tilt", "idx", "tilt"), &Curve3D::set_point_tilt);