diff --git a/modules/core/src/main/java/org/locationtech/jts/algorithm/Centroid.java b/modules/core/src/main/java/org/locationtech/jts/algorithm/Centroid.java
index d8aa8558d4..50712ec4a0 100644
--- a/modules/core/src/main/java/org/locationtech/jts/algorithm/Centroid.java
+++ b/modules/core/src/main/java/org/locationtech/jts/algorithm/Centroid.java
@@ -15,8 +15,6 @@
 import org.locationtech.jts.geom.Coordinate;
 import org.locationtech.jts.geom.Geometry;
 import org.locationtech.jts.geom.GeometryCollection;
-import org.locationtech.jts.geom.LineString;
-import org.locationtech.jts.geom.Point;
 import org.locationtech.jts.geom.Polygon;
 
 /**
@@ -92,22 +90,22 @@ private void add(Geometry geom)
   {
     if (geom.isEmpty())
       return;
-    if (geom instanceof Point) {
+    if (geom instanceof GeometryCollection) {
+      GeometryCollection gc = (GeometryCollection) geom;
+      for (int i = 0; i < gc.getNumGeometries(); i++) {
+        add(gc.getGeometryN(i));
+      }
+    }
+    else if (geom.getDimension() == 0) {
       addPoint(geom.getCoordinate());
     }
-    else if (geom instanceof LineString) {
+    else if (geom.getDimension() == 1) {
       addLineSegments(geom.getCoordinates());
     }
-    else if (geom instanceof Polygon) {
+    else if (geom.getDimension() == 2) {
       Polygon poly = (Polygon) geom;
       add(poly);
     }
-    else if (geom instanceof GeometryCollection) {
-      GeometryCollection gc = (GeometryCollection) geom;
-      for (int i = 0; i < gc.getNumGeometries(); i++) {
-        add(gc.getGeometryN(i));
-      }
-    }
   }
 
   /**
diff --git a/modules/core/src/main/java/org/locationtech/jts/algorithm/InteriorPointLine.java b/modules/core/src/main/java/org/locationtech/jts/algorithm/InteriorPointLine.java
index 1971d5da6f..c550758083 100644
--- a/modules/core/src/main/java/org/locationtech/jts/algorithm/InteriorPointLine.java
+++ b/modules/core/src/main/java/org/locationtech/jts/algorithm/InteriorPointLine.java
@@ -57,7 +57,7 @@ public Coordinate getInteriorPoint()
    */
   private void addInterior(Geometry geom)
   {
-    if (geom instanceof LineString) {
+    if (geom.getDimension() == 1) {
       addInterior(geom.getCoordinates());
     }
     else if (geom instanceof GeometryCollection) {
diff --git a/modules/core/src/main/java/org/locationtech/jts/algorithm/InteriorPointPoint.java b/modules/core/src/main/java/org/locationtech/jts/algorithm/InteriorPointPoint.java
index 71e14ce811..30afc1719a 100644
--- a/modules/core/src/main/java/org/locationtech/jts/algorithm/InteriorPointPoint.java
+++ b/modules/core/src/main/java/org/locationtech/jts/algorithm/InteriorPointPoint.java
@@ -15,7 +15,6 @@
 import org.locationtech.jts.geom.Coordinate;
 import org.locationtech.jts.geom.Geometry;
 import org.locationtech.jts.geom.GeometryCollection;
-import org.locationtech.jts.geom.Point;
 
 /**
  * Computes a point in the interior of an point geometry.
@@ -44,15 +43,15 @@ public InteriorPointPoint(Geometry g)
    */
   private void add(Geometry geom)
   {
-    if (geom instanceof Point) {
-      add(geom.getCoordinate());
-    }
-    else if (geom instanceof GeometryCollection) {
+    if (geom instanceof GeometryCollection) {
       GeometryCollection gc = (GeometryCollection) geom;
       for (int i = 0; i < gc.getNumGeometries(); i++) {
         add(gc.getGeometryN(i));
       }
     }
+    else if (geom.getDimension() == 0) {
+      add(geom.getCoordinate());
+    }
   }
   private void add(Coordinate point)
   {
diff --git a/modules/core/src/main/java/org/locationtech/jts/geom/LineString.java b/modules/core/src/main/java/org/locationtech/jts/geom/LineString.java
index 13624b3859..84768c38de 100644
--- a/modules/core/src/main/java/org/locationtech/jts/geom/LineString.java
+++ b/modules/core/src/main/java/org/locationtech/jts/geom/LineString.java
@@ -102,11 +102,16 @@ public Coordinate getCoordinate()
   }
 
   public int getDimension() {
-    return 1;
+    // Test if geometry is non empty and has several distinct coordinates
+    if (new CoordinateList(points.toCoordinateArray(),false).size()==1)
+      return 0;
+    else
+      // valid or empty LineString return 1
+      return 1;
   }
 
   public int getBoundaryDimension() {
-    if (isClosed()) {
+    if (isClosed() || getDimension() == 0) {
       return Dimension.FALSE;
     }
     return 0;
diff --git a/modules/core/src/main/java/org/locationtech/jts/geom/MultiLineString.java b/modules/core/src/main/java/org/locationtech/jts/geom/MultiLineString.java
index 15ce502a0b..f7ec4dc50f 100644
--- a/modules/core/src/main/java/org/locationtech/jts/geom/MultiLineString.java
+++ b/modules/core/src/main/java/org/locationtech/jts/geom/MultiLineString.java
@@ -55,10 +55,16 @@ public MultiLineString(LineString[] lineStrings, GeometryFactory factory) {
     super(lineStrings, factory);
   }
 
+
   public int getDimension() {
-    return 1;
+    if (isEmpty())
+      return 1;
+    else
+      // super will get the heighest dimension of components
+      return super.getDimension();
   }
 
+
   public int getBoundaryDimension() {
     if (isClosed()) {
       return Dimension.FALSE;
diff --git a/modules/core/src/main/java/org/locationtech/jts/geom/MultiPolygon.java b/modules/core/src/main/java/org/locationtech/jts/geom/MultiPolygon.java
index 67df633248..41a4a09404 100644
--- a/modules/core/src/main/java/org/locationtech/jts/geom/MultiPolygon.java
+++ b/modules/core/src/main/java/org/locationtech/jts/geom/MultiPolygon.java
@@ -67,7 +67,11 @@ public MultiPolygon(Polygon[] polygons, GeometryFactory factory) {
   }
 
   public int getDimension() {
-    return 2;
+    if (isEmpty())
+      return 2;
+    else
+      // super will get the heighest dimension of components
+      return super.getDimension();
   }
 
   public int getBoundaryDimension() {
diff --git a/modules/core/src/main/java/org/locationtech/jts/geom/Polygon.java b/modules/core/src/main/java/org/locationtech/jts/geom/Polygon.java
index bf389c6460..3ef47963c4 100644
--- a/modules/core/src/main/java/org/locationtech/jts/geom/Polygon.java
+++ b/modules/core/src/main/java/org/locationtech/jts/geom/Polygon.java
@@ -164,11 +164,20 @@ public int getNumPoints() {
   }
 
   public int getDimension() {
-    return 2;
+    if (getExteriorRing().getDimension() == 0)
+      return 0;
+    else
+      // Does not handle the case of 1-dimension collapsed polygon
+      // if exteriorRing is empty, returns 2 (not sure why)
+      return 2;
   }
 
   public int getBoundaryDimension() {
-    return 1;
+    if (isEmpty())
+      // Return the same dimension as an empty LinearRing
+      return 1;
+    else
+      return getExteriorRing().getDimension();
   }
 
   public boolean isEmpty() {
diff --git a/modules/core/src/main/java/org/locationtech/jts/geomgraph/GeometryGraph.java b/modules/core/src/main/java/org/locationtech/jts/geomgraph/GeometryGraph.java
index caa8e83175..c583ffd840 100644
--- a/modules/core/src/main/java/org/locationtech/jts/geomgraph/GeometryGraph.java
+++ b/modules/core/src/main/java/org/locationtech/jts/geomgraph/GeometryGraph.java
@@ -292,6 +292,10 @@ private void addLineString(LineString line)
     if (coord.length < 2) {
       hasTooFewPoints = true;
       invalidPoint = coord[0];
+      // If line is made of a single point, geometry is invalid (hasTooFewPoint),
+      // but the point must still be added to the graph in order to be able to be
+      // compute correct predicate (e.g. intersects) with another GeometryGraphe
+      addPoint(coord[0]);
       return;
     }
 
diff --git a/modules/core/src/test/java/org/locationtech/jts/algorithm/InteriorPointTest.java b/modules/core/src/test/java/org/locationtech/jts/algorithm/InteriorPointTest.java
index 1419157229..f4ff867675 100644
--- a/modules/core/src/test/java/org/locationtech/jts/algorithm/InteriorPointTest.java
+++ b/modules/core/src/test/java/org/locationtech/jts/algorithm/InteriorPointTest.java
@@ -89,4 +89,34 @@ private void checkInteriorPoint(Geometry g)
     assertTrue(g.contains(ip));
   }
 
+  /**
+  public void testPointInteriorPoint() throws ParseException {
+    Geometry point = rdr.read("Point(10 10)");
+    assertTrue(point.getInteriorPoint().equals(rdr.read("POINT(10 10)")));
+  }
+
+  public void testMultiPointInteriorPoint() throws ParseException {
+    Geometry point = rdr.read("MULTIPOINT ((60 300), (200 200), (240 240), (200 300), (40 140), (80 240), (140 240), (100 160), (140 200), (60 200))");
+    assertTrue(point.getInteriorPoint().equals(rdr.read("POINT (140 240)")));
+  }
+
+  public void testRelate() throws ParseException {
+    Geometry point = rdr.read("POINT (10 10)");
+    Geometry line = rdr.read("LINESTRING (10 10, 10 10)");
+    assertTrue(point.equalsTopo(line));
+  }
+
+  public void testGeometryCollection() throws ParseException {
+    Geometry gc = rdr.read("GEOMETRYCOLLECTION (POLYGON ((10 10, 10 10, 10 10, 10 10)), \n" +
+            "  LINESTRING (20 20, 30 30))");
+    assertTrue(gc.getInteriorPoint().equals(rdr.read("POINT(20 20)")));
+  }
+
+
+  public void testZeroLengthLineStringInteriorPoint() throws ParseException {
+    Geometry line = rdr.read("LineString(10 10, 10 10)");
+    assertTrue(line.getInteriorPoint().equals(rdr.read("POINT(10 10)")));
+  }
+   **/
+
 }
diff --git a/modules/core/src/test/java/org/locationtech/jts/geom/CollapsedGeometryDimensionTest.java b/modules/core/src/test/java/org/locationtech/jts/geom/CollapsedGeometryDimensionTest.java
new file mode 100644
index 0000000000..5c84d91499
--- /dev/null
+++ b/modules/core/src/test/java/org/locationtech/jts/geom/CollapsedGeometryDimensionTest.java
@@ -0,0 +1,118 @@
+package org.locationtech.jts.geom;
+
+import junit.framework.TestCase;
+import junit.textui.TestRunner;
+import org.locationtech.jts.io.ParseException;
+import org.locationtech.jts.io.WKTReader;
+
+
+public class CollapsedGeometryDimensionTest extends TestCase {
+
+  public static void main(String args[]) {
+    TestRunner.run(CollapsedGeometryDimensionTest.class);
+  }
+
+  private GeometryFactory factory = new GeometryFactory();
+  private WKTReader reader = new WKTReader(factory);
+
+  public CollapsedGeometryDimensionTest(String name) { super(name); }
+
+  public void testMock()
+  {
+    assertTrue(true);
+  }
+
+  public void testPoint() throws ParseException
+  {
+    // empty
+    assertTrue(reader.read("Point Empty").getDimension() == 0);
+    // normal
+    assertTrue(reader.read("Point(0 0)").getDimension() == 0);
+    // collapsed
+    assertTrue(reader.read("Point Empty").getDimension() == 0);
+  }
+
+  public void testLineString() throws ParseException
+  {
+    // empty
+    assertTrue(reader.read("LineString Empty").getDimension() == 1);
+    // normal (open/closed)
+    assertTrue(reader.read("LineString(0 0, 1 0)").getDimension() == 1);
+    assertTrue(reader.read("LineString(0 0, 1 0, 0.5 0.5, 0 0)").getDimension() == 1);
+    // collapsed
+    assertTrue(reader.read("LineString(0 0, 0 0)").getDimension() == 0);
+  }
+
+  public void testPolygon() throws ParseException
+  {
+    // empty
+    assertTrue(reader.read("Polygon Empty").getDimension() == 2);
+    // normal
+    assertTrue(reader.read("Polygon((0 0, 1 0, 0.5 0.5, 0 0))").getDimension() == 2);
+    // collapsed in dimension 1 (not yet detected -> dimension 2)
+    assertTrue(reader.read("Polygon((0 0, 1 0, 2 0, 0 0))").getDimension() == 2);
+    // collapsed
+    assertTrue(reader.read("Polygon((0 0, 0 0, 0 0, 0 0))").getDimension() == 0);
+    // cannot be initialized (linear ring not closed)
+    //assertTrue(reader.read("Polygon((0 0, 1 0, 1 0, 1 0))").getDimension() == 1);
+  }
+
+  public void testLinearRing() throws ParseException
+  {
+    // empty
+    assertTrue(reader.read("LinearRing Empty").getDimension() == 1);
+    // normal
+    assertTrue(reader.read("LinearRing(0 0, 1 0, 0.5 0.5, 0 0)").getDimension() == 1);
+    assertTrue(reader.read("LinearRing(0 0, 1 0, 2 0, 0 0)").getDimension() == 1);
+    // collapsed
+    assertTrue(reader.read("LinearRing(0 0, 0 0, 0 0, 0 0)").getDimension() == 0);
+  }
+
+  public void testMultiPoint() throws ParseException
+  {
+    // empty
+    assertTrue(reader.read("MultiPoint Empty").getDimension() == 0);
+    // normal
+    assertTrue(reader.read("MultiPoint((0 0), (1 1))").getDimension() == 0);
+    // normal
+    assertTrue(reader.read("MultiPoint((0 0), (0 0))").getDimension() == 0);
+  }
+
+  public void testMultiLineString() throws ParseException
+  {
+    // empty
+    assertTrue(reader.read("MultiLineString Empty").getDimension() == 1);
+    // normal (open/closed)
+    assertTrue(reader.read("MultiLineString((0 0, 1 0), (2 0, 3 0))").getDimension() == 1);
+    assertTrue(reader.read("MultiLineString((0 0, 1 0, 0.5 0.5, 0 0))").getDimension() == 1);
+    // partially collapsed
+    assertTrue(reader.read("MultiLineString((0 0, 0 0), (1 0, 2 0))").getDimension() == 1);
+    // collapsed
+    assertTrue(reader.read("MultiLineString((0 0, 0 0), (1 0, 1 0))").getDimension() == 0);
+  }
+
+  public void testMultiPolygon() throws ParseException
+  {
+    // empty
+    assertTrue(reader.read("MultiPolygon Empty").getDimension() == 2);
+    // normal
+    assertTrue(reader.read("MultiPolygon(((0 0, 1 0, 0.5 0.5, 0 0)),((10 0, 11 0, 10.5 0.5, 10 0)))").getDimension() == 2);
+    // partially collapsed
+    assertTrue(reader.read("MultiPolygon(((0 0, 1 0, 0.5 0.5, 0 0)),((0 0, 0 0, 0 0, 0 0)))").getDimension() == 2);
+    // collapsed
+    assertTrue(reader.read("MultiPolygon(((0 0, 0 0, 0 0, 0 0)),((1 1, 1 1, 1 1, 1 1)))").getDimension() == 0);
+  }
+
+  public void tesGeometryCollection() throws ParseException
+  {
+    // empty
+    assertTrue(reader.read("GeometryCollection Empty").getDimension() == 0);
+    // normal
+    assertTrue(reader.read("GeometryCollection (Point(0 0),LineString(0 0, 1 0)").getDimension() == 1);
+    assertTrue(reader.read("GeometryCollection (Point(0 0),LineString(0 0, 1 0), Polygon((0 0, 1 0, 0.5 0.5, 0 0))").getDimension() == 2);
+    // collapsed
+    assertTrue(reader.read("GeometryCollection (Point(0 0),LineString(0 0, 0 0)").getDimension() == 0);
+    assertTrue(reader.read("GeometryCollection (Point(0 0),Polygon((0 0, 0 0, 0 0, 0 0))").getDimension() == 0);
+  }
+
+}
diff --git a/modules/core/src/test/java/org/locationtech/jts/operation/relate/ZeroLengthLineStringTest.java b/modules/core/src/test/java/org/locationtech/jts/operation/relate/ZeroLengthLineStringTest.java
new file mode 100644
index 0000000000..cf8b3c6110
--- /dev/null
+++ b/modules/core/src/test/java/org/locationtech/jts/operation/relate/ZeroLengthLineStringTest.java
@@ -0,0 +1,135 @@
+package org.locationtech.jts.operation.relate;
+
+import junit.framework.TestCase;
+import junit.textui.TestRunner;
+import org.locationtech.jts.geom.Geometry;
+import org.locationtech.jts.geom.GeometryFactory;
+import org.locationtech.jts.io.WKTReader;
+
+public class ZeroLengthLineStringTest extends TestCase {
+
+  public static void main(String args[]) {
+    TestRunner.run(ZeroLengthLineStringTest.class);
+  }
+
+  private GeometryFactory factory = new GeometryFactory();
+  private WKTReader reader = new WKTReader(factory);
+
+  public ZeroLengthLineStringTest(String name)
+  {
+    super(name);
+  }
+
+  /**
+   * From JTS #345
+   *
+   * 0-length LineString is invalid (not clear from the spec, refers
+   * to the ticket about this question)
+   *
+   * @throws Exception
+   */
+  public void testZeroLengthLineStringInvalid()
+          throws Exception
+  {
+    String a = "LINESTRING (0 0, 0 0)";
+    Geometry geom1 = reader.read(a);
+    assertTrue(!geom1.isValid());
+  }
+
+
+  /**
+   * From JTS #345
+   *
+   * Intersects a geom with itself should return true, even if geom
+   * is a 0-length (degenerated) LineString
+   *
+   * @throws Exception
+   */
+  public void testIntersectsZeroLengthLineStringWithItself()
+          throws Exception
+  {
+    String a = "LINESTRING (0 0, 0 0)";
+    Geometry geom = reader.read(a);
+    assertTrue(geom.intersects(geom));
+  }
+
+  /**
+   * From JTS #345
+   *
+   * Intersects geom with a buffer around it should return true,
+   * even if geom is a 0-length (degenerated) LineString
+   *
+   * @throws Exception
+   */
+  public void testIntersectsZeroLengthLineStringWithBuffer()
+          throws Exception
+  {
+    String a = "LINESTRING (0 0, 0 0)";
+    Geometry geom = reader.read(a);
+    assertTrue(geom.intersects(geom.buffer(1.0)));
+  }
+
+  /**
+   * From JTS #345
+   *
+   * Boundary of a zero-length LineString is empty
+   *
+   * @throws Exception
+   */
+  public void testZeroLengthLineStringBoundary()
+          throws Exception
+  {
+    String a = "LINESTRING (0 0, 0 0)";
+    Geometry geom = reader.read(a);
+    assertTrue(geom.getBoundary().isEmpty());
+  }
+
+  /**
+   * From JTS #345
+   *
+   * Intersects a valid LineString with a 0-dimensional LineString
+   * located on one of its boundary should return true
+   *
+   * @throws Exception
+   */
+  public void testIntersectsBetweenLineStringAndItsBoundary()
+          throws Exception
+  {
+    String a = "LINESTRING (0 0, 1 0)";
+    String b = "LINESTRING (0 0, 0 0)";
+    Geometry geom1 = reader.read(a);
+    Geometry geom2 = reader.read(b);
+    assertTrue(geom1.intersects(geom2));
+  }
+
+  /**
+   * From JTS #345
+   *
+   * WARNING touches between a LineString and a 0-length LineString lying
+   * on its boundary returns false but it should return true as for the
+   * punctal case.
+   * The test with 0-length linestring is deactivated.
+   * One way to return true as for the Point is to say that 0-length LineString
+   * has dimension 1. IMHO, it LineString#getDimension() should return one, but
+   * it breaks other tests which check that empty LineString#getDimension return
+   * 1 (which can probably be discussed).
+   *
+   * @throws Exception
+   */
+
+  public void testTouchesBetweenLineStringAndItsBoundary()
+          throws Exception
+  {
+    String a = "LINESTRING (0 0, 1 0)";
+    String b = "LINESTRING (0 0, 0 0)";
+    String c = "POINT (0 0)";
+    Geometry geom1 = reader.read(a);
+    Geometry geom2 = reader.read(b);
+    Geometry geom3 = reader.read(c);
+    assertTrue(geom1.touches(geom2));
+    assertTrue(geom2.touches(geom1));
+    assertTrue(geom1.touches(geom3));
+    assertTrue(geom3.touches(geom1));
+  }
+
+}
diff --git a/modules/tests/src/test/resources/testxml/general/TestInteriorPoint.xml b/modules/tests/src/test/resources/testxml/general/TestInteriorPoint.xml
index 0d765cacab..9368171187 100644
--- a/modules/tests/src/test/resources/testxml/general/TestInteriorPoint.xml
+++ b/modules/tests/src/test/resources/testxml/general/TestInteriorPoint.xml
@@ -103,7 +103,9 @@
   <a>    GEOMETRYCOLLECTION (POLYGON ((10 10, 10 10, 10 10, 10 10)), 
   LINESTRING (20 20, 30 30))
 	</a>
-<test><op name="getInteriorPoint" arg1="A" >    POINT (10 10)   </op></test>
+    <!-- Change result from 10 10 to 20 20 as interior point should belong
+    to the component with highest dimension -->
+<test><op name="getInteriorPoint" arg1="A" >    POINT (20 20)   </op></test>
 </case>
 
 <case>
diff --git a/modules/tests/src/test/resources/testxml/validate/TestRelatePL.xml b/modules/tests/src/test/resources/testxml/validate/TestRelatePL.xml
index 2e11fb7b9e..d24c7f2f43 100644
--- a/modules/tests/src/test/resources/testxml/validate/TestRelatePL.xml
+++ b/modules/tests/src/test/resources/testxml/validate/TestRelatePL.xml
@@ -40,7 +40,9 @@
   <test><op name="covers"     arg1="A" arg2="B">true</op></test>
   <test><op name="crosses"    arg1="A" arg2="B">false</op></test>
   <test><op name="disjoint"   arg1="A" arg2="B">false</op></test>
-  <test><op name="equalsTopo" arg1="A" arg2="B">false</op></test>
+  <!-- change from false to true for equalsTopo as geometries are
+  defined by the same set of points -->
+  <test><op name="equalsTopo" arg1="A" arg2="B">true</op></test>
   <test><op name="intersects" arg1="A" arg2="B">true</op></test>
   <test><op name="overlaps"   arg1="A" arg2="B">false</op></test>
   <test><op name="touches"    arg1="A" arg2="B">false</op></test>