diff --git a/include/libweston/matrix.h b/include/libweston/matrix.h
index 08310003..ffa5b755 100644
--- a/include/libweston/matrix.h
+++ b/include/libweston/matrix.h
@@ -77,6 +77,12 @@ bool
 weston_matrix_to_transform(const struct weston_matrix *mat,
 			   enum wl_output_transform *transform);
 
+void
+weston_matrix_init_transform(struct weston_matrix *matrix,
+			     enum wl_output_transform transform,
+			     int x, int y, int width, int height,
+			     int scale);
+
 #ifdef  __cplusplus
 }
 #endif
diff --git a/libweston/compositor.c b/libweston/compositor.c
index 14ffc974..b967f01d 100644
--- a/libweston/compositor.c
+++ b/libweston/compositor.c
@@ -6269,46 +6269,10 @@ weston_region_global_to_output(pixman_region32_t *dst,
 WESTON_EXPORT_FOR_TESTS void
 weston_output_update_matrix(struct weston_output *output)
 {
-	weston_matrix_init(&output->matrix);
-	weston_matrix_translate(&output->matrix, -output->x, -output->y, 0);
-
-	switch (output->transform) {
-	case WL_OUTPUT_TRANSFORM_FLIPPED:
-	case WL_OUTPUT_TRANSFORM_FLIPPED_90:
-	case WL_OUTPUT_TRANSFORM_FLIPPED_180:
-	case WL_OUTPUT_TRANSFORM_FLIPPED_270:
-		weston_matrix_translate(&output->matrix, -output->width, 0, 0);
-		weston_matrix_scale(&output->matrix, -1, 1, 1);
-		break;
-	}
-
-	switch (output->transform) {
-	default:
-	case WL_OUTPUT_TRANSFORM_NORMAL:
-	case WL_OUTPUT_TRANSFORM_FLIPPED:
-		break;
-	case WL_OUTPUT_TRANSFORM_90:
-	case WL_OUTPUT_TRANSFORM_FLIPPED_90:
-		weston_matrix_translate(&output->matrix, -output->width, 0, 0);
-		weston_matrix_rotate_xy(&output->matrix, 0, -1);
-		break;
-	case WL_OUTPUT_TRANSFORM_180:
-	case WL_OUTPUT_TRANSFORM_FLIPPED_180:
-		weston_matrix_translate(&output->matrix,
-					-output->width, -output->height, 0);
-		weston_matrix_rotate_xy(&output->matrix, -1, 0);
-		break;
-	case WL_OUTPUT_TRANSFORM_270:
-	case WL_OUTPUT_TRANSFORM_FLIPPED_270:
-		weston_matrix_translate(&output->matrix, 0, -output->height, 0);
-		weston_matrix_rotate_xy(&output->matrix, 0, 1);
-		break;
-	}
-
-	if (output->current_scale != 1)
-		weston_matrix_scale(&output->matrix,
-				    output->current_scale,
-				    output->current_scale, 1);
+	weston_matrix_init_transform(&output->matrix, output->transform,
+				     output->x, output->y,
+				     output->width, output->height,
+				     output->current_scale);
 
 	weston_matrix_invert(&output->inverse_matrix, &output->matrix);
 }
diff --git a/shared/matrix.c b/shared/matrix.c
index 72717f37..f41abe76 100644
--- a/shared/matrix.c
+++ b/shared/matrix.c
@@ -516,3 +516,51 @@ weston_matrix_to_transform(const struct weston_matrix *mat,
 
 	return true;
 }
+
+WL_EXPORT void
+weston_matrix_init_transform(struct weston_matrix *matrix,
+			     enum wl_output_transform transform,
+			     int x, int y, int width, int height,
+			     int scale)
+{
+	weston_matrix_init(matrix);
+
+	weston_matrix_translate(matrix, -x, -y, 0);
+
+	switch (transform) {
+	case WL_OUTPUT_TRANSFORM_FLIPPED:
+	case WL_OUTPUT_TRANSFORM_FLIPPED_90:
+	case WL_OUTPUT_TRANSFORM_FLIPPED_180:
+	case WL_OUTPUT_TRANSFORM_FLIPPED_270:
+		weston_matrix_scale(matrix, -1, 1, 1);
+		weston_matrix_translate(matrix, width, 0, 0);
+		break;
+	default:
+		break;
+	}
+
+	switch (transform) {
+	default:
+	case WL_OUTPUT_TRANSFORM_NORMAL:
+	case WL_OUTPUT_TRANSFORM_FLIPPED:
+		break;
+	case WL_OUTPUT_TRANSFORM_90:
+	case WL_OUTPUT_TRANSFORM_FLIPPED_90:
+		weston_matrix_rotate_xy(matrix, 0, -1);
+		weston_matrix_translate(matrix, 0, width, 0);
+		break;
+	case WL_OUTPUT_TRANSFORM_180:
+	case WL_OUTPUT_TRANSFORM_FLIPPED_180:
+		weston_matrix_rotate_xy(matrix, -1, 0);
+		weston_matrix_translate(matrix,
+					width, height, 0);
+		break;
+	case WL_OUTPUT_TRANSFORM_270:
+	case WL_OUTPUT_TRANSFORM_FLIPPED_270:
+		weston_matrix_rotate_xy(matrix, 0, 1);
+		weston_matrix_translate(matrix, height, 0, 0);
+		break;
+	}
+
+	weston_matrix_scale(matrix, scale, scale, 1);
+}