WIP: Elongation and Centroid work

Author: gselzer

src/main/java/net/imglib2/mesh/MeshStats.java

@@ -256,7 +256,7 @@ public static double compactness( final Mesh mesh )
 	 * @param input
 	 *            the input mesh.
 	 * @return the centroid of the mesh.
-	 * @implNote op names='geom.centroid', priority='10000.'
+	 * @implNote op names='geom.centerOfGravity', priority='10000.'
 	 */
 	public static RealPoint centroid( final Mesh input )
 	{
@@ -314,6 +314,49 @@ public static RealPoint centroid( final Mesh input )
 		return new RealPoint( m100 / v, m010 / v, m001 / v );
 	}
 
+	/**
+	 * Describes the elongation of the two <b>larger</b> axes of the minimum box containing a {@link Mesh}. i.e. for a bounding box with side radii of {@code a}, {@code b}, and {@code c}, where {@code a}&ge;{@code b}&ge;{@code c}, this method returns
+	 * @param input a {@link Mesh}
+	 * @return the elongation of a cross-section of
+	 * @implNote op names='geom.mainElongation', label='Geometric (3D): Main
+	 *           Elongation', priority='10000.'
+	 */
+	public static double mainElongation(final Mesh input) {
+		final RealMatrix it = InertiaTensor.calculate(input);
+		final EigenDecomposition ed = new EigenDecomposition(it);
+
+		final double l1 = ed.getRealEigenvalue(0) - ed.getRealEigenvalue(2) + ed
+				.getRealEigenvalue(1);
+		final double l2 = ed.getRealEigenvalue(0) - ed.getRealEigenvalue(1) + ed
+				.getRealEigenvalue(2);
+		final double l3 = ed.getRealEigenvalue(2) - ed.getRealEigenvalue(0) + ed
+				.getRealEigenvalue(1);
+
+		final double g = 1 / (8 * Math.PI / 15);
+
+		final double a = Math.pow(g * l1 * l1 / Math.sqrt(l2 * l3), 1 / 5d);
+		final double b = Math.pow(g * l2 * l2 / Math.sqrt(l1 * l3), 1 / 5d);
+		return 1 - (b / a);
+	}
+
+	public static double medianElongation(final Mesh input) {
+		final RealMatrix it = InertiaTensor.calculate(input);
+		final EigenDecomposition ed = new EigenDecomposition(it);
+
+		final double l1 = ed.getRealEigenvalue(0) - ed.getRealEigenvalue(2) + ed
+				.getRealEigenvalue(1);
+		final double l2 = ed.getRealEigenvalue(0) - ed.getRealEigenvalue(1) + ed
+				.getRealEigenvalue(2);
+		final double l3 = ed.getRealEigenvalue(2) - ed.getRealEigenvalue(0) + ed
+				.getRealEigenvalue(1);
+
+		final double g = 1 / (8 * Math.PI / 15);
+
+		final double b = Math.pow(g * l2 * l2 / Math.sqrt(l1 * l3), 1 / 5d);
+		final double c = Math.pow(g * l3 * l3 / Math.sqrt(l1 * l2), 1 / 5d);
+		return 1 - (c / b);
+	}
+
 	private MeshStats()
 	{}
 }

src/main/java/net/imglib2/mesh/Meshes.java

@@ -59,6 +59,7 @@ public class Meshes
 	 * Finds the center of a mesh using vertices.
 	 *
 	 * @return a RealPoint representing the mesh's center
+	 * @implNote op names='geom.centroid', priority='10000.'
 	 */
 	public static RealPoint center( final Mesh m )
 	{