diff --git a/gsk/gskpathpoint.c b/gsk/gskpathpoint.c
index eef0ecdfc7..a55e879b18 100644
--- a/gsk/gskpathpoint.c
+++ b/gsk/gskpathpoint.c
@@ -139,8 +139,8 @@ gsk_path_point_compare (const GskPathPoint *point1,
 
 /**
  * gsk_path_point_get_position:
- * @path: a `GskPath`
- * @point: a `GskPathPoint` on @path
+ * @point: a `GskPathPoint`
+ * @path: the path that @point is on
  * @position: (out caller-allocates): Return location for
  *   the coordinates of the point
  *
@@ -149,15 +149,15 @@ gsk_path_point_compare (const GskPathPoint *point1,
  * Since: 4.14
  */
 void
-gsk_path_point_get_position (GskPath            *path,
-                             const GskPathPoint *point,
+gsk_path_point_get_position (const GskPathPoint *point,
+                             GskPath            *path,
                              graphene_point_t   *position)
 {
   GskRealPathPoint *self = (GskRealPathPoint *) point;
   const GskContour *contour;
 
+  g_return_if_fail (self != NULL);
   g_return_if_fail (path != NULL);
-  g_return_if_fail (point != NULL);
   g_return_if_fail (position != NULL);
   g_return_if_fail (self->contour < gsk_path_get_n_contours (path));
 
@@ -167,8 +167,8 @@ gsk_path_point_get_position (GskPath            *path,
 
 /**
  * gsk_path_point_get_tangent:
- * @path: a `GskPath`
- * @point: a `GskPathPoint` on @path
+ * @point: a `GskPathPoint`
+ * @path: the path that @point is on
  * @direction: the direction for which to return the tangent
  * @tangent: (out caller-allocates): Return location for
  *   the tangent at the point
@@ -184,16 +184,16 @@ gsk_path_point_get_position (GskPath            *path,
  * Since: 4.14
  */
 void
-gsk_path_point_get_tangent (GskPath            *path,
-                            const GskPathPoint *point,
+gsk_path_point_get_tangent (const GskPathPoint *point,
+                            GskPath            *path,
                             GskPathDirection    direction,
                             graphene_vec2_t    *tangent)
 {
   GskRealPathPoint *self = (GskRealPathPoint *) point;
   const GskContour *contour;
 
+  g_return_if_fail (self != NULL);
   g_return_if_fail (path != NULL);
-  g_return_if_fail (point != NULL);
   g_return_if_fail (tangent != NULL);
   g_return_if_fail (self->contour < gsk_path_get_n_contours (path));
 
@@ -203,8 +203,8 @@ gsk_path_point_get_tangent (GskPath            *path,
 
 /**
  * gsk_path_point_get_curvature:
- * @path: a `GskPath`
- * @point: a `GskPathPoint` on @path
+ * @point: a `GskPathPoint`
+ * @path: the path that @point is on
  * @center: (out caller-allocates) (nullable): Return location for
  *   the center of the osculating circle
  *
@@ -220,15 +220,15 @@ gsk_path_point_get_tangent (GskPath            *path,
  * Since: 4.14
  */
 float
-gsk_path_point_get_curvature (GskPath            *path,
-                              const GskPathPoint *point,
+gsk_path_point_get_curvature (const GskPathPoint *point,
+                              GskPath            *path,
                               graphene_point_t   *center)
 {
   GskRealPathPoint *self = (GskRealPathPoint *) point;
   const GskContour *contour;
 
+  g_return_val_if_fail (self != NULL, 0);
   g_return_val_if_fail (path != NULL, 0);
-  g_return_val_if_fail (point != NULL, 0);
   g_return_val_if_fail (self->contour < gsk_path_get_n_contours (path), 0);
 
   contour = gsk_path_get_contour (path, self->contour);
diff --git a/gsk/gskpathpoint.h b/gsk/gskpathpoint.h
index 05f84caf49..4fdacc797e 100644
--- a/gsk/gskpathpoint.h
+++ b/gsk/gskpathpoint.h
@@ -57,19 +57,19 @@ int                     gsk_path_point_compare         (const GskPathPoint *poin
                                                         const GskPathPoint *point2);
 
 GDK_AVAILABLE_IN_4_14
-void                    gsk_path_point_get_position    (GskPath            *path,
-                                                        const GskPathPoint *point,
+void                    gsk_path_point_get_position    (const GskPathPoint *point,
+                                                        GskPath            *path,
                                                         graphene_point_t   *position);
 
 GDK_AVAILABLE_IN_4_14
-void                    gsk_path_point_get_tangent     (GskPath            *path,
-                                                        const GskPathPoint *point,
+void                    gsk_path_point_get_tangent     (const GskPathPoint *point,
+                                                        GskPath            *path,
                                                         GskPathDirection    direction,
                                                         graphene_vec2_t    *tangent);
 
 GDK_AVAILABLE_IN_4_14
-float                   gsk_path_point_get_curvature   (GskPath            *path,
-                                                        const GskPathPoint *point,
+float                   gsk_path_point_get_curvature   (const GskPathPoint *point,
+                                                        GskPath            *path,
                                                         graphene_point_t   *center);
 
 
diff --git a/testsuite/gsk/path-special-cases.c b/testsuite/gsk/path-special-cases.c
index da279a83ae..bc83ba9249 100644
--- a/testsuite/gsk/path-special-cases.c
+++ b/testsuite/gsk/path-special-cases.c
@@ -465,10 +465,10 @@ test_path_point (void)
   g_assert_true (rp->idx == 2);
   g_assert_true (rp->t == 1);
 
-  gsk_path_point_get_position (path, &point, &pos);
-  gsk_path_point_get_tangent (path, &point, GSK_PATH_START, &t1);
-  gsk_path_point_get_tangent (path, &point, GSK_PATH_END, &t2);
-  curvature = gsk_path_point_get_curvature (path, &point, &center);
+  gsk_path_point_get_position (&point, path, &pos);
+  gsk_path_point_get_tangent (&point, path, GSK_PATH_START, &t1);
+  gsk_path_point_get_tangent (&point, path, GSK_PATH_END, &t2);
+  curvature = gsk_path_point_get_curvature (&point, path, &center);
 
   g_assert_true (graphene_point_equal (&pos, &GRAPHENE_POINT_INIT (100, 100)));
   g_assert_true (graphene_vec2_equal (&t1, graphene_vec2_y_axis ()));