diff --git a/CHANGELOG.md b/CHANGELOG.md
index f7e3bf57..82749975 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -26,6 +26,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Fixed
 * `urquhartFaces()`, `relativeNeighborFaces()`, `gabrielFaces()` and `spannerFaces()` from `PGS_Meshing` now preserve holes from the input.
+* The `from` and `to` arguments for `align()` were the wrong way round.
+* The output of `PGS_Morphology.smoothGaussian()` is no longer (slightly) affected by the vertex ordering of the input.
 
 ### Removed
 * `simplifyDCE(shape, targetNumVertices)` and `simplifyDCE(shape, vertexRemovalFraction)` in favour a single method that accepts a user-defined termination callback that is supplied with the current vertex candidate's coordinate, relevance score, and the number of vertices remaining.
diff --git a/src/main/java/micycle/pgs/commons/GaussianLineSmoothing.java b/src/main/java/micycle/pgs/commons/GaussianLineSmoothing.java
index 3765a8aa..d4d53e6e 100644
--- a/src/main/java/micycle/pgs/commons/GaussianLineSmoothing.java
+++ b/src/main/java/micycle/pgs/commons/GaussianLineSmoothing.java
@@ -1,7 +1,10 @@
 package micycle.pgs.commons;
 
+import java.util.Arrays;
+
 import org.locationtech.jts.geom.Coordinate;
 import org.locationtech.jts.geom.LineString;
+
 import net.jafama.FastMath;
 
 /**
@@ -43,6 +46,9 @@ public static LineString get(LineString line, double sigmaM, double resolution)
 			return (LineString) line.copy();
 		}
 
+		// output is sensitive to vertex order, so normalise the line (note doesn't
+		// normalise orientation)
+		line = normalise(line);
 		boolean isClosed = line.isClosed();
 		double length = line.getLength();
 		double densifiedResolution = sigmaM / 3;
@@ -165,4 +171,43 @@ public static LineString get(LineString line, double sigmaM, double resolution)
 		return lsOut;
 	}
 
+	/**
+	 * Normalises the LineString so that it starts from the coordinate with the
+	 * smallest x value. In case of a tie on the x value, the smallest y value is
+	 * used.
+	 *
+	 * @param line The open or closed LineString to be normalised.
+	 * @return A new LineString with coordinates ordered starting from the smallest
+	 *         x (and y, if tied).
+	 */
+	private static LineString normalise(LineString line) {
+		boolean isClosed = line.isClosed();
+
+		Coordinate[] originalCoords = line.getCoordinates();
+		if (isClosed && originalCoords[0].equals2D(originalCoords[originalCoords.length - 1])) {
+			// Remove last vertex if it is a duplicate of the first for closed lines
+			originalCoords = Arrays.copyOf(originalCoords, originalCoords.length - 1);
+		}
+
+		// Find index of coordinate with smallest x value, tie by y value
+		int minIndex = 0;
+		for (int i = 1; i < originalCoords.length; i++) {
+			if (originalCoords[i].x < originalCoords[minIndex].x
+					|| (originalCoords[i].x == originalCoords[minIndex].x && originalCoords[i].y < originalCoords[minIndex].y)) {
+				minIndex = i;
+			}
+		}
+
+		// Rotate array to start from vertex with smallest x (and y, if tied)
+		Coordinate[] rotatedCoords = new Coordinate[originalCoords.length + (isClosed ? 1 : 0)];
+		System.arraycopy(originalCoords, minIndex, rotatedCoords, 0, originalCoords.length - minIndex);
+		System.arraycopy(originalCoords, 0, rotatedCoords, originalCoords.length - minIndex, minIndex);
+
+		if (isClosed) {
+			rotatedCoords[rotatedCoords.length - 1] = rotatedCoords[0]; // Close the loop
+		}
+
+		return line.getFactory().createLineString(rotatedCoords);
+	}
+
 }
\ No newline at end of file