3 files changed, 27 insertions, 5 deletions
diff --git a/core/math/a_star.cpp b/core/math/a_star.cpp
index 110185c2d2..c82a40f30d 100644
--- a/core/math/a_star.cpp
+++ b/core/math/a_star.cpp
@@ -28,6 +28,8 @@
 /*************************************************************************/
 #include "a_star.h"
 #include "geometry.h"
+#include "scene/scene_string_names.h"
+#include "script_language.h"
 
 int AStar::get_available_point_id() const {
 
@@ -187,7 +189,7 @@ bool AStar::_solve(Point *begin_point, Point *end_point) {
 
 		Point *n = begin_point->neighbours[i];
 		n->prev_point = begin_point;
-		n->distance = n->pos.distance_to(begin_point->pos);
+		n->distance = _compute_cost(n->id, begin_point->id);
 		n->distance *= n->weight_scale;
 		n->last_pass = pass;
 		open_list.add(&n->list);
@@ -215,7 +217,7 @@ bool AStar::_solve(Point *begin_point, Point *end_point) {
 			Point *p = E->self();
 
 			real_t cost = p->distance;
-			cost += p->pos.distance_to(end_point->pos);
+			cost += _estimate_cost(p->id, end_point->id);
 			cost *= p->weight_scale;
 
 			if (cost < least_cost) {
@@ -233,7 +235,7 @@ bool AStar::_solve(Point *begin_point, Point *end_point) {
 
 			Point *e = p->neighbours[i];
 
-			real_t distance = p->pos.distance_to(e->pos) + p->distance;
+			real_t distance = _compute_cost(p->id, e->id) + p->distance;
 			distance *= e->weight_scale;
 
 			if (e->last_pass == pass) {
@@ -274,6 +276,20 @@ bool AStar::_solve(Point *begin_point, Point *end_point) {
 	return found_route;
 }
 
+float AStar::_estimate_cost(int p_from_id, int p_to_id) {
+	if (get_script_instance() && get_script_instance()->has_method(SceneStringNames::get_singleton()->_estimate_cost))
+		return get_script_instance()->call(SceneStringNames::get_singleton()->_estimate_cost, p_from_id, p_to_id);
+
+	return points[p_from_id]->pos.distance_to(points[p_to_id]->pos);
+}
+
+float AStar::_compute_cost(int p_from_id, int p_to_id) {
+	if (get_script_instance() && get_script_instance()->has_method(SceneStringNames::get_singleton()->_compute_cost))
+		return get_script_instance()->call(SceneStringNames::get_singleton()->_compute_cost, p_from_id, p_to_id);
+
+	return points[p_from_id]->pos.distance_to(points[p_to_id]->pos);
+}
+
 PoolVector<Vector3> AStar::get_point_path(int p_from_id, int p_to_id) {
 
 	ERR_FAIL_COND_V(!points.has(p_from_id), PoolVector<Vector3>());
@@ -395,6 +411,9 @@ void AStar::_bind_methods() {
 
 	ClassDB::bind_method(D_METHOD("get_point_path", "from_id", "to_id"), &AStar::get_point_path);
 	ClassDB::bind_method(D_METHOD("get_id_path", "from_id", "to_id"), &AStar::get_id_path);
+
+	BIND_VMETHOD(MethodInfo("_estimate_cost", PropertyInfo(Variant::INT, "from_id"), PropertyInfo(Variant::INT, "to_id")));
+	BIND_VMETHOD(MethodInfo("_compute_cost", PropertyInfo(Variant::INT, "from_id"), PropertyInfo(Variant::INT, "to_id")));
 }
 
 AStar::AStar() {
diff --git a/core/math/a_star.h b/core/math/a_star.h
index 2ac855737c..43c9c4457a 100644
--- a/core/math/a_star.h
+++ b/core/math/a_star.h
@@ -93,6 +93,9 @@ class AStar : public Reference {
 protected:
 	static void _bind_methods();
 
+	virtual float _estimate_cost(int p_from_id, int p_to_id);
+	virtual float _compute_cost(int p_from_id, int p_to_id);
+
 public:
 	int get_available_point_id() const;
 
diff --git a/core/math/math_2d.cpp b/core/math/math_2d.cpp
index 021b1fbf55..8f942c423f 100644
--- a/core/math/math_2d.cpp
+++ b/core/math/math_2d.cpp
@@ -449,7 +449,7 @@ real_t Transform2D::get_rotation() const {
 	real_t det = basis_determinant();
 	Transform2D m = orthonormalized();
 	if (det < 0) {
-		m.scale_basis(Size2(-1, -1));
+		m.scale_basis(Size2(1, -1)); // convention to separate rotation and reflection for 2D is to absorb a flip along y into scaling.
 	}
 	return Math::atan2(m[0].y, m[0].x);
 }
@@ -477,7 +477,7 @@ Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) {
 
 Size2 Transform2D::get_scale() const {
 	real_t det_sign = basis_determinant() > 0 ? 1 : -1;
-	return det_sign * Size2(elements[0].length(), elements[1].length());
+	return Size2(elements[0].length(), det_sign * elements[1].length());
 }
 
 void Transform2D::scale(const Size2 &p_scale) {