AStar: Make get_closest_point() deterministic for equidistant points

Closes godotengine/godot-docs#3667.
Supersedes #39405.

core/math/a_star.cpp

@@ -280,10 +280,16 @@ int AStar::get_closest_point(const Vector3 &p_point, bool p_include_disabled) co
 			continue; // Disabled points should not be considered.
 		}
 
+		// Keep the closest point's ID, and in case of multiple closest IDs,
+		// the smallest one (makes it deterministic).
 		real_t d = p_point.distance_squared_to((*it.value)->pos);
-		if (closest_id < 0 || d < closest_dist) {
+		int id = *(it.key);
+		if (d <= closest_dist) {
+			if (d == closest_dist && id > closest_id) { // Keep lowest ID.
+				continue;
+			}
 			closest_dist = d;
-			closest_id = *(it.key);
+			closest_id = id;
 		}
 	}
 
@@ -291,7 +297,6 @@ int AStar::get_closest_point(const Vector3 &p_point, bool p_include_disabled) co
 }
 
 Vector3 AStar::get_closest_position_in_segment(const Vector3 &p_point) const {
-	bool found = false;
 	real_t closest_dist = 1e20;
 	Vector3 closest_point;
 
@@ -311,10 +316,9 @@ Vector3 AStar::get_closest_position_in_segment(const Vector3 &p_point) const {
 
 		Vector3 p = Geometry3D::get_closest_point_to_segment(p_point, segment);
 		real_t d = p_point.distance_squared_to(p);
-		if (!found || d < closest_dist) {
+		if (d < closest_dist) {
 			closest_point = p;
 			closest_dist = d;
-			found = true;
 		}
 	}
 

doc/classes/AStar.xml

@@ -131,7 +131,8 @@
 			<argument index="1" name="include_disabled" type="bool" default="false">
 			</argument>
 			<description>
-				Returns the ID of the closest point to [code]to_position[/code], optionally taking disabled points into account. Returns -1 if there are no points in the points pool.
+				Returns the ID of the closest point to [code]to_position[/code], optionally taking disabled points into account. Returns [code]-1[/code] if there are no points in the points pool.
+				[b]Note:[/b] If several points are the closest to [code]to_position[/code], the one with the smallest ID will be returned, ensuring a deterministic result.
 			</description>
 		</method>
 		<method name="get_closest_position_in_segment" qualifiers="const">

doc/classes/AStar2D.xml

@@ -114,7 +114,8 @@
 			<argument index="1" name="include_disabled" type="bool" default="false">
 			</argument>
 			<description>
-				Returns the ID of the closest point to [code]to_position[/code], optionally taking disabled points into account. Returns -1 if there are no points in the points pool.
+				Returns the ID of the closest point to [code]to_position[/code], optionally taking disabled points into account. Returns [code]-1[/code] if there are no points in the points pool.
+				[b]Note:[/b] If several points are the closest to [code]to_position[/code], the one with the smallest ID will be returned, ensuring a deterministic result.
 			</description>
 		</method>
 		<method name="get_closest_position_in_segment" qualifiers="const">