diff --git a/src/main/java/pythagoras/f/AbstractDimension.java b/src/main/java/pythagoras/f/AbstractDimension.java
new file mode 100644
index 0000000..06e81cd
--- /dev/null
+++ b/src/main/java/pythagoras/f/AbstractDimension.java
@@ -0,0 +1,38 @@
+//
+// $Id$
+
+package pythagoras.f;
+
+/**
+ * Provides most of the implementation of {@link IDimension}, obtaining only width and height from
+ * the derived class.
+ */
+public abstract class AbstractDimension implements IDimension
+{
+    @Override // from interface IDimension
+    public Dimension clone () {
+        return new Dimension(this);
+    }
+
+    @Override
+    public int hashCode () {
+        return Float.floatToIntBits(getWidth()) ^ Float.floatToIntBits(getHeight());
+    }
+
+    @Override
+    public boolean equals (Object obj) {
+        if (obj == this) {
+            return true;
+        }
+        if (obj instanceof AbstractDimension) {
+            AbstractDimension d = (AbstractDimension)obj;
+            return (d.getWidth() == getWidth() && d.getHeight() == getHeight());
+        }
+        return false;
+    }
+
+    @Override
+    public String toString () {
+        return Geometry.dimenToString(getWidth(), getHeight());
+    }
+}
diff --git a/src/main/java/pythagoras/f/AbstractLine.java b/src/main/java/pythagoras/f/AbstractLine.java
new file mode 100644
index 0000000..89128e5
--- /dev/null
+++ b/src/main/java/pythagoras/f/AbstractLine.java
@@ -0,0 +1,130 @@
+//
+// $Id$
+
+package pythagoras.f;
+
+/**
+ * Provides most of the implementation of {@link ILine}, obtaining only the start and end points
+ * from the derived class.
+ */
+public abstract class AbstractLine implements ILine
+{
+    @Override // from interface ILine
+    public IPoint p1 () {
+        return new AbstractPoint() {
+            @Override public float getX () {
+                return getX1();
+            }
+            @Override public float getY () {
+                return getY1();
+            }
+        };
+    }
+
+    @Override // from interface ILine
+    public Point getP1 () {
+        return new Point(getX1(), getY1());
+    }
+
+    @Override // from interface ILine
+    public IPoint p2 () {
+        return new AbstractPoint() {
+            @Override public float getX () {
+                return getX2();
+            }
+            @Override public float getY () {
+                return getY2();
+            }
+        };
+    }
+
+    @Override // from interface ILine
+    public Point getP2 () {
+        return new Point(getX2(), getY2());
+    }
+
+    @Override // from interface ILine
+    public Line clone () {
+        return new Line(getX1(), getY1(), getX2(), getY2());
+    }
+
+    @Override // from interface IShape
+    public boolean isEmpty () {
+        return false;
+    }
+
+    @Override // from interface IShape
+    public boolean contains (float x, float y) {
+        return false;
+    }
+
+    @Override // from interface IShape
+    public boolean contains (IPoint point) {
+        return false;
+    }
+
+    @Override // from interface IShape
+    public boolean contains (float x, float y, float w, float h) {
+        return false;
+    }
+
+    @Override // from interface IShape
+    public boolean contains (IRectangle r) {
+        return false;
+    }
+
+    @Override // from interface IShape
+    public boolean intersects (float rx, float ry, float rw, float rh) {
+        return Geometry.lineIntersectsRect(getX1(), getY1(), getX2(), getY2(), rx, ry, rw, rh);
+    }
+
+    @Override // from interface IShape
+    public boolean intersects (IRectangle r) {
+        return r.intersectsLine(this);
+    }
+
+    @Override // from interface IShape
+    public IRectangle bounds () {
+        return new AbstractRectangle() {
+            @Override public float getX () {
+                return Math.min(getX1(), getX2());
+            }
+            @Override public float getY () {
+                return Math.min(getY1(), getY2());
+            }
+            @Override public float getWidth () {
+                float x1 = getX1(), x2 = getX2();
+                return (x1 < x2) ? (x2 - x1) : (x1 - x2);
+            }
+            @Override public float getHeight () {
+                float y1 = getY1(), y2 = getY2();
+                return (y1 < y2) ? (y2 - y1) : (y1 - y2);
+            }
+            // this isn't visible in the type, so won't be called by non-combatants
+            @Override public void setFrame (float x, float y, float w, float h) {
+                throw new UnsupportedOperationException();
+            }
+        };
+    }
+
+    @Override // from interface IShape
+    public Rectangle getBounds () {
+        float x1 = getX1(), x2 = getX2(), y1 = getY1(), y2 = getY2();
+        float rx, ry, rw, rh;
+        if (x1 < x2) {
+            rx = x1;
+            rw = x2 - x1;
+        } else {
+            rx = x2;
+            rw = x1 - x2;
+        }
+        if (y1 < y2) {
+            ry = y1;
+            rh = y2 - y1;
+        } else {
+            ry = y2;
+            rh = y1 - y2;
+        }
+        return new Rectangle(rx, ry, rw, rh);
+    }
+}
diff --git a/src/main/java/pythagoras/f/AbstractPoint.java b/src/main/java/pythagoras/f/AbstractPoint.java
new file mode 100644
index 0000000..347ff58
--- /dev/null
+++ b/src/main/java/pythagoras/f/AbstractPoint.java
@@ -0,0 +1,58 @@
+//
+// $Id$
+
+package pythagoras.f;
+
+/**
+ * Provides most of the implementation of {@link IPoint}, obtaining only the location from the
+ * derived class.
+ */
+public abstract class AbstractPoint implements IPoint
+{
+    @Override // from interface IPoint
+    public float distanceSq (float px, float py) {
+        return Geometry.distanceSq(getX(), getY(), px, py);
+    }
+
+    @Override // from interface IPoint
+    public float distanceSq (IPoint p) {
+        return Geometry.distanceSq(getX(), getY(), p.getX(), p.getY());
+    }
+
+    @Override // from interface IPoint
+    public float distance (float px, float py) {
+        return Geometry.distance(getX(), getY(), px, py);
+    }
+
+    @Override // from interface IPoint
+    public float distance (IPoint p) {
+        return Geometry.distance(getX(), getY(), p.getX(), p.getY());
+    }
+
+    @Override // from interface IPoint
+    public Point clone () {
+        return new Point(this);
+    }
+
+    @Override
+    public boolean equals (Object obj) {
+        if (obj == this) {
+            return true;
+        }
+        if (obj instanceof AbstractPoint) {
+            AbstractPoint p = (AbstractPoint)obj;
+            return getX() == p.getX() && getY() == p.getY();
+        }
+        return false;
+    }
+
+    @Override
+    public int hashCode () {
+        return Float.floatToIntBits(getX()) ^ Float.floatToIntBits(getY());
+    }
+
+    @Override
+    public String toString () {
+        return Geometry.pointToString(getX(), getY());
+    }
+}
diff --git a/src/main/java/pythagoras/f/AbstractRectangle.java b/src/main/java/pythagoras/f/AbstractRectangle.java
new file mode 100644
index 0000000..0cc5e29
--- /dev/null
+++ b/src/main/java/pythagoras/f/AbstractRectangle.java
@@ -0,0 +1,172 @@
+//
+// $Id$
+
+package pythagoras.f;
+
+/**
+ * Provides most of the implementation of {@link IRectangle}, obtaining only the location and
+ * dimensions from the derived class.
+ */
+public abstract class AbstractRectangle extends RectangularShape implements IRectangle
+{
+    @Override // from interface IRectangle
+    public IPoint location () {
+        return new AbstractPoint() {
+            @Override public float getX () {
+                return AbstractRectangle.this.getX();
+            }
+            @Override public float getY () {
+                return AbstractRectangle.this.getY();
+            }
+        };
+    }
+
+    @Override // from interface IRectangle
+    public Point getLocation () {
+        return new Point(getX(), getY());
+    }
+
+    @Override // from interface IRectangle
+    public IDimension size () {
+        return new AbstractDimension() {
+            @Override public float getWidth () {
+                return AbstractRectangle.this.getWidth();
+            }
+            @Override public float getHeight () {
+                return AbstractRectangle.this.getHeight();
+            }
+        };
+    }
+
+    @Override // from interface IRectangle
+    public Dimension getSize () {
+        return new Dimension(getWidth(), getHeight());
+    }
+
+    @Override // from interface IRectangle
+    public Rectangle intersection (float rx, float ry, float rw, float rh) {
+        float x1 = Math.max(getX(), rx);
+        float y1 = Math.max(getY(), ry);
+        float x2 = Math.min(getMaxX(), rx + rw);
+        float y2 = Math.min(getMaxY(), ry + rh);
+        return new Rectangle(x1, y1, x2 - x1, y2 - y1);
+    }
+
+    @Override // from interface IRectangle
+    public Rectangle intersection (IRectangle r) {
+        return intersection(r.getX(), r.getY(), r.getWidth(), r.getHeight());
+    }
+
+    @Override // from interface IRectangle
+    public Rectangle union (IRectangle r) {
+        Rectangle rect = new Rectangle(this);
+        rect.add(r);
+        return rect;
+    }
+
+    @Override // from interface IRectangle
+    public boolean intersectsLine (float x1, float y1, float x2, float y2) {
+        return Geometry.lineIntersectsRect(x1, y1, x2, y2, getX(), getY(), getWidth(), getHeight());
+    }
+
+    @Override // from interface IRectangle
+    public boolean intersectsLine (ILine l) {
+        return intersectsLine(l.getX1(), l.getY1(), l.getX2(), l.getY2());
+    }
+
+    @Override // from interface IRectangle
+    public int outcode (float px, float py) {
+        int code = 0;
+
+        if (getWidth() <= 0) {
+            code |= OUT_LEFT | OUT_RIGHT;
+        } else if (px < getX()) {
+            code |= OUT_LEFT;
+        } else if (px > getMaxX()) {
+            code |= OUT_RIGHT;
+        }
+
+        if (getHeight() <= 0) {
+            code |= OUT_TOP | OUT_BOTTOM;
+        } else if (py < getY()) {
+            code |= OUT_TOP;
+        } else if (py > getMaxY()) {
+            code |= OUT_BOTTOM;
+        }
+
+        return code;
+    }
+
+    @Override // from interface IRectangle
+    public int outcode (IPoint p) {
+        return outcode(p.getX(), p.getY());
+    }
+
+    @Override // from interface IRectangle
+    public Rectangle clone () {
+        return new Rectangle(this);
+    }
+
+    @Override // from interface IShape
+    public boolean contains (float px, float py) {
+        if (isEmpty()) return false;
+
+        float x = getX(), y = getY();
+        if (px < x || py < y) return false;
+
+        px -= x;
+        py -= y;
+        return px < getWidth() && py < getHeight();
+    }
+
+    @Override // from interface IShape
+    public boolean contains (float rx, float ry, float rw, float rh) {
+        if (isEmpty()) return false;
+
+        double x1 = getX(), y1 = getY(), x2 = x1 + getWidth(), y2 = y1 + getHeight();
+        return (x1 <= rx) && (rx + rw <= x2) && (y1 <= ry) && (ry + rh <= y2);
+    }
+
+    @Override // from interface IShape
+    public boolean intersects (float rx, float ry, float rw, float rh) {
+        if (isEmpty()) return false;
+
+        double x1 = getX(), y1 = getY(), x2 = x1 + getWidth(), y2 = y1 + getHeight();
+        return (rx + rw > x1) && (rx < x2) && (ry + rh > y1) && (ry < y2);
+    }
+
+    @Override // from RectangularShape
+    public IRectangle frame () {
+        return this;
+    }
+
+    @Override // from RectangularShape
+    public IRectangle bounds () {
+        return this;
+    }
+
+    @Override // from Object
+    public boolean equals (Object obj) {
+        if (obj == this) {
+            return true;
+        }
+        if (obj instanceof AbstractRectangle) {
+            AbstractRectangle r = (AbstractRectangle)obj;
+            return r.getX() == getX() && r.getY() == getY() &&
+                r.getWidth() == getWidth() && r.getHeight() == getHeight();
+        }
+        return false;
+    }
+
+    @Override // from Object
+    public int hashCode () {
+        return Float.floatToIntBits(getX()) ^ Float.floatToIntBits(getY()) ^
+            Float.floatToIntBits(getWidth()) ^ Float.floatToIntBits(getHeight());
+    }
+
+    @Override // from Object
+    public String toString () {
+        return Geometry.dimenToString(getWidth(), getHeight()) +
+            Geometry.pointToString(getX(), getY());
+    }
+}
diff --git a/src/main/java/pythagoras/f/Dimension.java b/src/main/java/pythagoras/f/Dimension.java
index fd8c618..8df3803 100644
--- a/src/main/java/pythagoras/f/Dimension.java
+++ b/src/main/java/pythagoras/f/Dimension.java
@@ -9,7 +9,7 @@ import java.io.Serializable;
 /**
  * Represents a magnitude in two dimensions.
  */
-public class Dimension implements IDimension, Serializable
+public class Dimension extends AbstractDimension implements Serializable
 {
     /** The magnitude in the x-dimension. */
     public float width;
@@ -62,35 +62,4 @@ public class Dimension implements IDimension, Serializable
     public float getHeight () {
         return height;
     }
-
-    @Override // from interface IDimension
-    public Dimension clone () {
-        try {
-            return (Dimension)super.clone();
-        } catch (CloneNotSupportedException cnse) {
-            throw new AssertionError(cnse);
-        }
-    }
-
-    @Override
-    public int hashCode () {
-        return Float.floatToIntBits(width) ^ Float.floatToIntBits(height);
-    }
-
-    @Override
-    public boolean equals (Object obj) {
-        if (obj == this) {
-            return true;
-        }
-        if (obj instanceof Dimension) {
-            Dimension d = (Dimension)obj;
-            return (d.width == width && d.height == height);
-        }
-        return false;
-    }
-
-    @Override
-    public String toString () {
-        return Geometry.dimenToString(width, height);
-    }
 }
diff --git a/src/main/java/pythagoras/f/Geometry.java b/src/main/java/pythagoras/f/Geometry.java
index d4fc77c..8e054cf 100644
--- a/src/main/java/pythagoras/f/Geometry.java
+++ b/src/main/java/pythagoras/f/Geometry.java
@@ -25,6 +25,61 @@ public class Geometry
         return (float)Math.sqrt(distanceSq(x1, y1, x2, y2));
     }
 
+    /**
+     * Returns true if the specified two line segments intersect.
+     */
+    public static boolean linesIntersect (float x1, float y1, float x2, float y2,
+                                          float x3, float y3, float x4, float y4) {
+        // A = (x2-x1, y2-y1)
+        // B = (x3-x1, y3-y1)
+        // C = (x4-x1, y4-y1)
+        // D = (x4-x3, y4-y3) = C-B
+        // E = (x1-x3, y1-y3) = -B
+        // F = (x2-x3, y2-y3) = A-B
+        //
+        // Result is ((AxB) * (AxC) <= 0) and ((DxE) * (DxF) <= 0)
+        // 
+        // DxE = (C-B)x(-B) = BxB-CxB = BxC
+        // DxF = (C-B)x(A-B) = CxA-CxB-BxA+BxB = AxB+BxC-AxC
+        x2 -= x1; // A
+        y2 -= y1;
+        x3 -= x1; // B
+        y3 -= y1;
+        x4 -= x1; // C
+        y4 -= y1;
+
+        float AvB = x2 * y3 - x3 * y2;
+        float AvC = x2 * y4 - x4 * y2;
+
+        // online
+        if (AvB == 0 && AvC == 0) {
+            if (x2 != 0) {
+                return (x4 * x3 <= 0) ||
+                    ((x3 * x2 >= 0) && (x2 > 0 ? x3 <= x2 || x4 <= x2 : x3 >= x2 || x4 >= x2));
+            }
+            if (y2 != 0) {
+                return (y4 * y3 <= 0) ||
+                    ((y3 * y2 >= 0) && (y2 > 0 ? y3 <= y2 || y4 <= y2 : y3 >= y2 || y4 >= y2));
+            }
+            return false;
+        }
+
+        float BvC = x3 * y4 - x4 * y3;
+        return (AvB * AvC <= 0) && (BvC * (AvB + BvC - AvC) <= 0);
+    }
+
+    /**
+     * Returns true if the specified line segment intersects the specified rectangle.
+     */
+    public static boolean lineIntersectsRect (float x1, float y1, float x2, float y2,
+                                              float rx, float ry, float rw, float rh) {
+        float rr = rx + rw, rb = ry + rh;
+        return (rx <= x1 && x1 <= rr && ry <= y1 && y1 <= rb)
+            || (rx <= x2 && x2 <= rr && ry <= y2 && y2 <= rb)
+            || linesIntersect(rx, ry, rr, rb, x1, y1, x2, y2)
+            || linesIntersect(rr, ry, rx, rb, x1, y1, x2, y2);
+    }
+
     /**
      * Returns a string describing the supplied point, of the form <code>+x+y</code>,
      * <code>+x-y</code>, <code>-x-y</code>, etc.
diff --git a/src/main/java/pythagoras/f/IDimension.java b/src/main/java/pythagoras/f/IDimension.java
index d546383..40b7411 100644
--- a/src/main/java/pythagoras/f/IDimension.java
+++ b/src/main/java/pythagoras/f/IDimension.java
@@ -20,7 +20,7 @@ public interface IDimension extends Cloneable
     float getHeight ();
 
     /**
-     * Clones this dimension.
+     * Returns a mutable copy of this dimension.
      */
     Dimension clone ();
 }
diff --git a/src/main/java/pythagoras/f/ILine.java b/src/main/java/pythagoras/f/ILine.java
new file mode 100644
index 0000000..f5a772c
--- /dev/null
+++ b/src/main/java/pythagoras/f/ILine.java
@@ -0,0 +1,59 @@
+//
+// $Id$
+
+package pythagoras.f;
+
+/**
+ * Provides read-only access to a {@link Line}.
+ */
+public interface ILine extends IShape, Cloneable
+{
+    /**
+     * Returns the x-coordinate of the start of this line.
+     */
+    float getX1 ();
+
+    /**
+     * Returns the y-coordinate of the start of this line.
+     */
+    float getY1 ();
+
+    /**
+     * Returns the x-coordinate of the end of this line.
+     */
+    float getX2 ();
+
+    /**
+     * Returns the y-coordinate of the end of this line.
+     */
+    float getY2 ();
+
+    /**
+     * Returns a view of the starting point of this line. Subsequent changes to the starting point
+     * will be visible in the returned point.
+     */
+    IPoint p1 ();
+
+    /**
+     * Returns a copy of the starting point of this line. Subsequent changes to the starting point
+     * will not be visible in the returned point.
+     */
+    Point getP1 ();
+
+    /**
+     * Returns a view of the ending point of this line. Subsequent changes to the ending point will
+     * be visible in the returned point.
+     */
+    IPoint p2 ();
+
+    /**
+     * Returns a copy of the ending point of this line. Subsequent changes to the ending point will
+     * not be visible in the returned point.
+     */
+    Point getP2 ();
+
+    /**
+     * Returns a mutable copy of this line.
+     */
+    Line clone ();
+}
diff --git a/src/main/java/pythagoras/f/IPoint.java b/src/main/java/pythagoras/f/IPoint.java
index 7a4359f..365b12a 100644
--- a/src/main/java/pythagoras/f/IPoint.java
+++ b/src/main/java/pythagoras/f/IPoint.java
@@ -40,7 +40,7 @@ public interface IPoint extends Cloneable
     float distance (IPoint p);
 
     /**
-     * Clones this point.
+     * Returns a mutable copy of this point.
      */
     Point clone ();
 }
diff --git a/src/main/java/pythagoras/f/IRectangle.java b/src/main/java/pythagoras/f/IRectangle.java
index 5e8eaf2..990a4ac 100644
--- a/src/main/java/pythagoras/f/IRectangle.java
+++ b/src/main/java/pythagoras/f/IRectangle.java
@@ -7,7 +7,7 @@ package pythagoras.f;
 /**
  * Provides read-only access to a {@link Rectangle}.
  */
-public interface IRectangle extends Shape, Cloneable
+public interface IRectangle extends IRectangularShape, Cloneable
 {
     /** The bitmask that indicates that a point lies to the left of this rectangle.
      * See {@link #outcode}. */
@@ -24,41 +24,26 @@ public interface IRectangle extends Shape, Cloneable
     int OUT_BOTTOM = 8;
 
     /**
-     * Returns the x-coordinate of the rectangle's upper left corner.
+     * Returns a view of this rectangle's upper-left corner. Subsequent changes to this rectangle's
+     * location will be reflected in the returned point.
      */
-    float getX ();
+    IPoint location ();
 
     /**
-     * Returns the y-coordinate of the rectangle's upper left corner.
-     */
-    float getY ();
-
-    /**
-     * Returns the width of the rectangle.
-     */
-    float getWidth ();
-
-    /**
-     * Returns the height of the rectangle.
-     */
-    float getHeight ();
-
-    /**
-     * Returns true if this rectangle does not have > 0 width and height.
-     */
-    boolean isEmpty ();
-
-    /**
-     * Returns this rectangle's upper-left corner. Note that this constructs a new instance,
-     * because a {@link Rectangle} is not an {@link IPoint} and cannot efficiently masquerade as
-     * one.
+     * Returns a copy of this rectangle's upper-left corner. Subsequent changes to this rectangle's
+     * location will not be reflected in the returned point.
      */
     Point getLocation ();
 
     /**
-     * Returns the size of this rectangle as a newly constructed dimension. Note that this
-     * constructs a new instance, because a {@link Rectangle} is not an {@link IDimension} and
-     * cannot efficiently masquerade as one.
+     * Returns a view of this rectangle's size. Subsequent changes to this rectangle's size will be
+     * reflected in the returned dimension.
+     */
+    IDimension size ();
+
+    /**
+     * Returns a copy of this rectangle's size. Subsequent changes to this rectangle's size will
+     * not be reflected in the returned dimension.
      */
     Dimension getSize ();
 
@@ -80,11 +65,21 @@ public interface IRectangle extends Shape, Cloneable
      */
     Rectangle union (IRectangle r);
 
+    /**
+     * Returns true if the specified line segment intersects this rectangle.
+     */
+    boolean intersectsLine (float x1, float y1, float x2, float y2);
+
+    /**
+     * Returns true if the supplied line segment intersects this rectangle.
+     */
+    boolean intersectsLine (ILine l);
+
     /**
      * Returns a set of flags indicating where the specified point lies in relation to the bounds
      * of this rectangle. See {@link #OUT_LEFT}, etc.
      */
-    int outcode (double px, double py);
+    int outcode (float px, float py);
 
     /**
      * Returns a set of flags indicating where the supplied point lies in relation to the bounds of
@@ -93,7 +88,7 @@ public interface IRectangle extends Shape, Cloneable
     int outcode (IPoint point);
 
     /**
-     * Clones this rectangle.
+     * Returns a mutable copy of this rectangle.
      */
     Rectangle clone ();
 }
diff --git a/src/main/java/pythagoras/f/IRectangularShape.java b/src/main/java/pythagoras/f/IRectangularShape.java
new file mode 100644
index 0000000..7844878
--- /dev/null
+++ b/src/main/java/pythagoras/f/IRectangularShape.java
@@ -0,0 +1,75 @@
+//
+// Pythagoras - a collection of geometry classes
+// http://github.com/samskivert/pythagoras
+
+package pythagoras.f;
+
+/**
+ * An interface implemented by {@link Shape} classes whose geometry is defined by a rectangular
+ * frame. The framing rectangle <em>defines</em> the geometry, but may in some cases differ from
+ * the <em>bounding</em> rectangle of the shape.
+ */
+public interface IRectangularShape extends IShape
+{
+    /**
+     * Returns the x-coordinate of the upper-left corner of the framing rectangle.
+     */
+    float getX ();
+
+    /**
+     * Returns the y-coordinate of the upper-left corner of the framing rectangle.
+     */
+    float getY ();
+
+    /**
+     * Returns the width of the framing rectangle.
+     */
+    float getWidth ();
+
+    /**
+     * Returns the height of the framing rectangle.
+     */
+    float getHeight ();
+
+    /**
+     * Returns the minimum x-coordinate of the framing rectangle.
+     */
+    float getMinX ();
+
+    /**
+     * Returns the minimum y-coordinate of the framing rectangle.
+     */
+    float getMinY ();
+
+    /**
+     * Returns the maximum x-coordinate of the framing rectangle.
+     */
+    float getMaxX ();
+
+    /**
+     * Returns the maximum y-coordinate of the framing rectangle.
+     */
+    float getMaxY ();
+
+    /**
+     * Returns the x-coordinate of the center of the framing rectangle.
+     */
+    float getCenterX ();
+
+    /**
+     * Returns the y-coordinate of the center of the framing rectangle.
+     */
+    float getCenterY ();
+
+    /**
+     * Returns a view of this shape's framing rectangle. Subsequent changes to the shape will be
+     * reflected in the returned rectangle.
+     */
+    IRectangle frame ();
+
+    /**
+     * Returns a copy of this shape's framing rectangle. Subsequent changes to the shape will be
+     * reflected in the returned rectangle.
+     */
+    Rectangle getFrame ();
+}
diff --git a/src/main/java/pythagoras/f/Shape.java b/src/main/java/pythagoras/f/IShape.java
similarity index 77%
rename from src/main/java/pythagoras/f/Shape.java
rename to src/main/java/pythagoras/f/IShape.java
index 426d5dc..0f9dd9f 100644
--- a/src/main/java/pythagoras/f/Shape.java
+++ b/src/main/java/pythagoras/f/IShape.java
@@ -7,8 +7,13 @@ package pythagoras.f;
 /**
  * An interface provided by all shapes.
  */
-public interface Shape
+public interface IShape
 {
+    /**
+     * Returns true if this shape encloses no area.
+     */
+    boolean isEmpty ();
+
     /**
      * Returns true if this shape contains the specified point.
      */
@@ -40,9 +45,16 @@ public interface Shape
     boolean intersects (IRectangle r);
 
     /**
-     * Returns the bounding rectangle for this shape.
+     * Returns a view of the bounding rectangle for this shape. Subsequent changes to the bounding
+     * rectangle will be reflected in the returned rectangle.
      */
-    IRectangle getBounds ();
+    IRectangle bounds();
+
+    /**
+     * Returns a copy of the bounding rectangle for this shape. Subsequent changes to the bounding
+     * rectangle will not be reflected in the returned rectangle.
+     */
+    Rectangle getBounds ();
 
     // /**
     //  * Returns an iterator over the path described by this shape.
diff --git a/src/main/java/pythagoras/f/Line.java b/src/main/java/pythagoras/f/Line.java
new file mode 100644
index 0000000..fd6e553
--- /dev/null
+++ b/src/main/java/pythagoras/f/Line.java
@@ -0,0 +1,74 @@
+//
+// $Id$
+
+package pythagoras.f;
+
+import java.io.Serializable;
+
+/**
+ * Represents a line segment.
+ */
+public class Line extends AbstractLine implements Serializable
+{
+    public float x1;
+    public float y1;
+    public float x2;
+    public float y2;
+
+    /**
+     * Creates a line from (0,0) to (0,0).
+     */
+    public Line () {
+    }
+
+    /**
+     * Creates a line from (x1,y1), to (x2,y2).
+     */
+    public Line (float x1, float y1, float x2, float y2) {
+        setLine(x1, y1, x2, y2);
+    }
+
+    /**
+     * Creates a line from p1 to p2.
+     */
+    public Line (IPoint p1, IPoint p2) {
+        setLine(p1, p2);
+    }
+
+    /**
+     * Sets the start and end point of this line to the specified values.
+     */
+    public void setLine (float x1, float y1, float x2, float y2) {
+        this.x1 = x1;
+        this.y1 = y1;
+        this.x2 = x2;
+        this.y2 = y2;
+    }
+
+    /**
+     * Sets the start and end of this line to the specified points.
+     */
+    public void setLine (IPoint p1, IPoint p2) {
+        setLine(p1.getX(), p1.getY(), p2.getY(), p2.getY());
+    }
+
+    @Override // from interface ILine
+    public float getX1 () {
+        return x1;
+    }
+
+    @Override // from interface ILine
+    public float getY1 () {
+        return y1;
+    }
+
+    @Override // from interface ILine
+    public float getX2 () {
+        return x2;
+    }
+
+    @Override // from interface ILine
+    public float getY2 () {
+        return y2;
+    }
+}
diff --git a/src/main/java/pythagoras/f/Point.java b/src/main/java/pythagoras/f/Point.java
index 59e9c65..bfe0ddd 100644
--- a/src/main/java/pythagoras/f/Point.java
+++ b/src/main/java/pythagoras/f/Point.java
@@ -9,7 +9,7 @@ import java.io.Serializable;
 /**
  * Represents a point on a plane.
  */
-public class Point implements IPoint, Serializable
+public class Point extends AbstractPoint implements Serializable
 {
     /** The x-coordinate of the point. */
     public float x;
@@ -77,55 +77,4 @@ public class Point implements IPoint, Serializable
     public float getY () {
         return y;
     }
-
-    @Override // from interface IPoint
-    public float distanceSq (float px, float py) {
-        return Geometry.distanceSq(x, y, px, py);
-    }
-
-    @Override // from interface IPoint
-    public float distanceSq (IPoint p) {
-        return Geometry.distanceSq(x, y, p.getX(), p.getY());
-    }
-
-    @Override // from interface IPoint
-    public float distance (float px, float py) {
-        return Geometry.distance(x, y, px, py);
-    }
-
-    @Override // from interface IPoint
-    public float distance (IPoint p) {
-        return Geometry.distance(x, y, p.getX(), p.getY());
-    }
-
-    @Override // from interface IPoint
-    public Point clone () {
-        try {
-            return (Point)super.clone();
-        } catch (CloneNotSupportedException cnse) {
-            throw new AssertionError(cnse);
-        }
-    }
-
-    @Override
-    public boolean equals (Object obj) {
-        if (obj == this) {
-            return true;
-        }
-        if (obj instanceof Point) {
-            Point p = (Point)obj;
-            return x == p.x && y == p.y;
-        }
-        return false;
-    }
-
-    @Override
-    public int hashCode () {
-        return Float.floatToIntBits(x) ^ Float.floatToIntBits(y);
-    }
-
-    @Override
-    public String toString () {
-        return Geometry.pointToString(x, y);
-    }
 }
diff --git a/src/main/java/pythagoras/f/Rectangle.java b/src/main/java/pythagoras/f/Rectangle.java
index ef4d965..a55c15f 100644
--- a/src/main/java/pythagoras/f/Rectangle.java
+++ b/src/main/java/pythagoras/f/Rectangle.java
@@ -9,7 +9,7 @@ import java.io.Serializable;
 /**
  * Represents an area in two dimensions.
  */
-public class Rectangle implements IRectangle, Serializable
+public class Rectangle extends AbstractRectangle implements Serializable
 {
     /** The x-coordinate of the rectangle's upper left corner. */
     public float x;
@@ -33,23 +33,23 @@ public class Rectangle implements IRectangle, Serializable
     /**
      * Constructs a rectangle with the supplied upper-left corner and dimensions (0,0).
      */
-    public Rectangle (Point p) {
-        setBounds(p.x, p.y, 0, 0);
+    public Rectangle (IPoint p) {
+        setBounds(p.getX(), p.getY(), 0, 0);
     }
 
     /**
      * Constructs a rectangle with upper-left corner at (0,) and the supplied dimensions.
      */
-    public Rectangle (Dimension d) {
-        setBounds(0, 0, d.width, d.height);
+    public Rectangle (IDimension d) {
+        setBounds(0, 0, d.getWidth(), d.getHeight());
     }
 
     /**
      * Constructs a rectangle with upper-left corner at the supplied point and with the supplied
      * dimensions.
      */
-    public Rectangle (Point p, Dimension d) {
-        setBounds(p.x, p.y, d.width, d.height);
+    public Rectangle (IPoint p, IDimension d) {
+        setBounds(p.getX(), p.getY(), d.getWidth(), d.getHeight());
     }
 
     /**
@@ -62,23 +62,8 @@ public class Rectangle implements IRectangle, Serializable
     /**
      * Constructs a rectangle with bounds equal to the supplied rectangle.
      */
-    public Rectangle (Rectangle r) {
-        setBounds(r.x, r.y, r.width, r.height);
-    }
-
-    /**
-     * Sets the size of this rectangle to the specified dimensions.
-     */
-    public void setSize (float width, float height) {
-        this.width = width;
-        this.height = height;
-    }
-
-    /**
-     * Sets the size of this rectangle to the supplied dimensions.
-     */
-    public void setSize (Dimension d) {
-        setSize(d.width, d.height);
+    public Rectangle (IRectangle r) {
+        setBounds(r.getX(), r.getY(), r.getWidth(), r.getHeight());
     }
 
     /**
@@ -96,6 +81,21 @@ public class Rectangle implements IRectangle, Serializable
         setLocation(p.getX(), p.getY());
     }
 
+    /**
+     * Sets the size of this rectangle to the specified dimensions.
+     */
+    public void setSize (float width, float height) {
+        this.width = width;
+        this.height = height;
+    }
+
+    /**
+     * Sets the size of this rectangle to the supplied dimensions.
+     */
+    public void setSize (Dimension d) {
+        setSize(d.width, d.height);
+    }
+
     /**
      * Sets the bounds of this rectangle to the specified bounds.
      */
@@ -162,166 +162,28 @@ public class Rectangle implements IRectangle, Serializable
         setBounds(x1, y1, x2 - x1, y2 - y1);
     }
 
-    @Override // from interface IRectangle
-    public float getX ()
-    {
+    @Override // from interface IRectangularShape
+    public float getX () {
         return x;
     }
 
-    @Override // from interface IRectangle
-    public float getY ()
-    {
+    @Override // from interface IRectangularShape
+    public float getY () {
         return y;
     }
 
-    @Override // from interface IRectangle
-    public float getWidth ()
-    {
+    @Override // from interface IRectangularShape
+    public float getWidth () {
         return width;
     }
 
-    @Override // from interface IRectangle
-    public float getHeight ()
-    {
+    @Override // from interface IRectangularShape
+    public float getHeight () {
         return height;
     }
 
-    @Override // from interface IRectangle
-    public boolean isEmpty () {
-        return width <= 0 || height <= 0;
-    }
-
-    @Override // from interface IRectangle
-    public Point getLocation () {
-        return new Point(x, y);
-    }
-
-    @Override // from interface IRectangle
-    public Dimension getSize () {
-        return new Dimension(width, height);
-    }
-
-    @Override // from interface IRectangle
-    public Rectangle intersection (float rx, float ry, float rw, float rh) {
-        float x1 = Math.max(x, rx);
-        float y1 = Math.max(y, ry);
-        float x2 = Math.min(x + width, rx + rw);
-        float y2 = Math.min(y + height, ry + rh);
-        return new Rectangle(x1, y1, x2 - x1, y2 - y1);
-    }
-
-    @Override // from interface IRectangle
-    public Rectangle intersection (IRectangle r) {
-        return intersection(r.getX(), r.getY(), r.getWidth(), r.getHeight());
-    }
-
-    @Override // from interface IRectangle
-    public Rectangle union (IRectangle r) {
-        Rectangle rect = new Rectangle(this);
-        rect.add(r);
-        return rect;
-    }
-
-    @Override // from interface IRectangle
-    public int outcode (double px, double py) {
-        int code = 0;
-
-        if (width <= 0) {
-            code |= OUT_LEFT | OUT_RIGHT;
-        } else if (px < x) {
-            code |= OUT_LEFT;
-        } else if (px > x + width) {
-            code |= OUT_RIGHT;
-        }
-
-        if (height <= 0) {
-            code |= OUT_TOP | OUT_BOTTOM;
-        } else if (py < y) {
-            code |= OUT_TOP;
-        } else if (py > y + height) {
-            code |= OUT_BOTTOM;
-        }
-
-        return code;
-    }
-
-    @Override // from interface IRectangle
-    public int outcode (IPoint p) {
-        return outcode(p.getX(), p.getY());
-    }
-
-    @Override // from interface IRectangle
-    public Rectangle clone () {
-        try {
-            return (Rectangle)super.clone();
-        } catch (CloneNotSupportedException cnse) {
-            throw new AssertionError(cnse);
-        }
-    }
-
-    @Override // from interface Shape
-    public boolean contains (float px, float py) {
-        if (isEmpty()) {
-            return false;
-        }
-        if (px < x || py < y) {
-            return false;
-        }
-        px -= x;
-        py -= y;
-        return px < width && py < height;
-    }
-
-    @Override // from interface Shape
-    public boolean contains (IPoint p) {
-        return contains(p.getX(), p.getY());
-    }
-
-    @Override // from interface Shape
-    public boolean contains (float rx, float ry, float rw, float rh) {
-        return contains(rx, ry) && contains(rx + rw - 1, ry + rh - 1);
-    }
-
-    @Override // from interface Shape
-    public boolean contains (IRectangle r) {
-        return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
-    }
-
-    @Override // from interface Shape
-    public boolean intersects (float rx, float ry, float rw, float rh) {
-        return !intersection(rx, ry, rw, rh).isEmpty(); // TODO: don't create garbage
-    }
-
-    @Override // from interface Shape
-    public boolean intersects (IRectangle r) {
-        return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
-    }
-
-    @Override // from interface Shape
-    public IRectangle getBounds () {
-        return this;
-    }
-
-    @Override
-    public boolean equals (Object obj) {
-        if (obj == this) {
-            return true;
-        }
-        if (obj instanceof Rectangle) {
-            Rectangle r = (Rectangle)obj;
-            return r.x == x && r.y == y && r.width == width && r.height == height;
-        }
-        return false;
-    }
-
-    @Override
-    public int hashCode () {
-        return Float.floatToIntBits(x) ^ Float.floatToIntBits(y) ^
-            Float.floatToIntBits(width) ^ Float.floatToIntBits(height);
-    }
-
-    @Override
-    public String toString () {
-        return Geometry.dimenToString(width, height) + Geometry.pointToString(x, y);
+    @Override // from RectangularShape
+    public void setFrame (float x, float y, float w, float h) {
+        setBounds(x, y, w, h);
     }
 }
diff --git a/src/main/java/pythagoras/f/RectangularShape.java b/src/main/java/pythagoras/f/RectangularShape.java
new file mode 100644
index 0000000..0083829
--- /dev/null
+++ b/src/main/java/pythagoras/f/RectangularShape.java
@@ -0,0 +1,173 @@
+//
+// Pythagoras - a collection of geometry classes
+// http://github.com/samskivert/pythagoras
+
+package pythagoras.f;
+
+/**
+ * The base class for various {@link Shape} objects whose geometry is defined by a rectangular
+ * frame.
+ */
+public abstract class RectangularShape implements IRectangularShape
+{
+    /**
+     * Sets the location and size of the framing rectangle of this shape to the specified values.
+     */
+    public abstract void setFrame (float x, float y, float w, float h);
+
+    /**
+     * Sets the location and size of the framing rectangle of this shape to the supplied values.
+     */
+    public void setFrame (IPoint loc, IDimension size) {
+        setFrame(loc.getX(), loc.getY(), size.getWidth(), size.getHeight());
+    }
+
+    /**
+     * Sets the location and size of the framing rectangle of this shape to be equal to the
+     * supplied rectangle.
+     */
+    public void setFrame (IRectangle r) {
+        setFrame(r.getX(), r.getY(), r.getWidth(), r.getHeight());
+    }
+
+    /**
+     * Sets the location and size of the framing rectangle of this shape based on the specified
+     * diagonal line.
+     */
+    public void setFrameFromDiagonal (float x1, float y1, float x2, float y2) {
+        float rx, ry, rw, rh;
+        if (x1 < x2) {
+            rx = x1;
+            rw = x2 - x1;
+        } else {
+            rx = x2;
+            rw = x1 - x2;
+        }
+        if (y1 < y2) {
+            ry = y1;
+            rh = y2 - y1;
+        } else {
+            ry = y2;
+            rh = y1 - y2;
+        }
+        setFrame(rx, ry, rw, rh);
+    }
+
+    /**
+     * Sets the location and size of the framing rectangle of this shape based on the supplied
+     * diagonal line.
+     */
+    public void setFrameFromDiagonal (IPoint p1, IPoint p2) {
+        setFrameFromDiagonal(p1.getX(), p1.getY(), p2.getX(), p2.getY());
+    }
+
+    /**
+     * Sets the location and size of the framing rectangle of this shape based on the specified
+     * center and corner points.
+     */
+    public void setFrameFromCenter (float centerX, float centerY,
+                                    float cornerX, float cornerY) {
+        float width = Math.abs(cornerX - centerX);
+        float height = Math.abs(cornerY - centerY);
+        setFrame(centerX - width, centerY - height, width * 2, height * 2);
+    }
+
+    /**
+     * Sets the location and size of the framing rectangle of this shape based on the supplied
+     * center and corner points.
+     */
+    public void setFrameFromCenter (IPoint center, IPoint corner) {
+        setFrameFromCenter(center.getX(), center.getY(), corner.getX(), corner.getY());
+    }
+
+    @Override // from IRectangularShape
+    public float getMinX () {
+        return getX();
+    }
+
+    @Override // from IRectangularShape
+    public float getMinY () {
+        return getY();
+    }
+
+    @Override // from IRectangularShape
+    public float getMaxX () {
+        return getX() + getWidth();
+    }
+
+    @Override // from IRectangularShape
+    public float getMaxY () {
+        return getY() + getHeight();
+    }
+
+    @Override // from IRectangularShape
+    public float getCenterX () {
+        return getX() + getWidth() / 2;
+    }
+
+    @Override // from IRectangularShape
+    public float getCenterY () {
+        return getY() + getHeight() / 2;
+    }
+
+    @Override // from IRectangularShape
+    public IRectangle frame () {
+        return bounds();
+    }
+
+    @Override // from IRectangularShape
+    public Rectangle getFrame () {
+        return getBounds();
+    }
+
+    @Override // from interface IShape
+    public boolean isEmpty () {
+        return getWidth() <= 0 || getHeight() <= 0;
+    }
+
+    @Override // from interface IShape
+    public boolean contains (IPoint point) {
+        return contains(point.getX(), point.getY());
+    }
+
+    @Override // from interface IShape
+    public boolean contains (IRectangle rect) {
+        return contains(rect.getX(), rect.getY(), rect.getWidth(), rect.getHeight());
+    }
+
+    @Override // from interface IShape
+    public boolean intersects (IRectangle rect) {
+        return intersects(rect.getX(), rect.getY(), rect.getWidth(), rect.getHeight());
+    }
+
+    @Override // from interface IShape
+    public IRectangle bounds () {
+        return new AbstractRectangle() {
+            @Override public float getX () {
+                return RectangularShape.this.getX();
+            }
+            @Override public float getY () {
+                return RectangularShape.this.getY();
+            }
+            @Override public float getWidth () {
+                return RectangularShape.this.getWidth();
+            }
+            @Override public float getHeight () {
+                return RectangularShape.this.getHeight();
+            }
+            // this isn't visible in the type, so won't be called by non-combatants
+            @Override public void setFrame (float x, float y, float w, float h) {
+                throw new UnsupportedOperationException();
+            }
+        };
+    }
+
+    @Override // from interface IShape
+    public Rectangle getBounds () {
+        return new Rectangle(getX(), getY(), getWidth(), getHeight());
+    }
+
+    // public PathIterator getPathIterator (AffineTransform t, float flatness) {
+    //     return new FlatteningPathIterator(getPathIterator(t), flatness);
+    // }
+}