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From dsmi...@apache.org
Subject [12/16] lucene-solr git commit: LUCENE-7056: Geo3D package re-org
Date Tue, 08 Mar 2016 01:15:12 GMT
http://git-wip-us.apache.org/repos/asf/lucene-solr/blob/f7f81c32/lucene/spatial3d/src/java/org/apache/lucene/geo3d/LinearDistance.java
----------------------------------------------------------------------
diff --git a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/LinearDistance.java b/lucene/spatial3d/src/java/org/apache/lucene/geo3d/LinearDistance.java
deleted file mode 100644
index 9cbedba..0000000
--- a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/LinearDistance.java
+++ /dev/null
@@ -1,56 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements.  See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License.  You may obtain a copy of the License at
- *
- *     http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-package org.apache.lucene.geo3d;
-
-/**
- * Linear distance computation style.
- *
- * @lucene.experimental
- */
-public class LinearDistance implements DistanceStyle {
-  
-  /** A convenient instance */
-  public final static LinearDistance INSTANCE = new LinearDistance();
-  
-  /** Constructor.
-   */
-  public LinearDistance() {
-  }
-  
-  @Override
-  public double computeDistance(final GeoPoint point1, final GeoPoint point2) {
-    return point1.linearDistance(point2);
-  }
-  
-  @Override
-  public double computeDistance(final GeoPoint point1, final double x2, final double y2, final double z2) {
-    return point1.linearDistance(x2,y2,z2);
-  }
-
-  @Override
-  public double computeDistance(final PlanetModel planetModel, final Plane plane, final GeoPoint point, final Membership... bounds) {
-    return plane.linearDistance(planetModel, point, bounds);
-  }
-  
-  @Override
-  public double computeDistance(final PlanetModel planetModel, final Plane plane, final double x, final double y, final double z, final Membership... bounds) {
-    return plane.linearDistance(planetModel, x,y,z, bounds);
-  }
-
-}
-
-

http://git-wip-us.apache.org/repos/asf/lucene-solr/blob/f7f81c32/lucene/spatial3d/src/java/org/apache/lucene/geo3d/LinearSquaredDistance.java
----------------------------------------------------------------------
diff --git a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/LinearSquaredDistance.java b/lucene/spatial3d/src/java/org/apache/lucene/geo3d/LinearSquaredDistance.java
deleted file mode 100644
index 028d3c4..0000000
--- a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/LinearSquaredDistance.java
+++ /dev/null
@@ -1,56 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements.  See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License.  You may obtain a copy of the License at
- *
- *     http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-package org.apache.lucene.geo3d;
-
-/**
- * Linear squared distance computation style.
- *
- * @lucene.experimental
- */
-public class LinearSquaredDistance implements DistanceStyle {
-  
-  /** A convenient instance */
-  public final static LinearSquaredDistance INSTANCE = new LinearSquaredDistance();
-  
-  /** Constructor.
-   */
-  public LinearSquaredDistance() {
-  }
-  
-  @Override
-  public double computeDistance(final GeoPoint point1, final GeoPoint point2) {
-    return point1.linearDistanceSquared(point2);
-  }
-  
-  @Override
-  public double computeDistance(final GeoPoint point1, final double x2, final double y2, final double z2) {
-    return point1.linearDistanceSquared(x2,y2,z2);
-  }
-
-  @Override
-  public double computeDistance(final PlanetModel planetModel, final Plane plane, final GeoPoint point, final Membership... bounds) {
-    return plane.linearDistanceSquared(planetModel, point, bounds);
-  }
-  
-  @Override
-  public double computeDistance(final PlanetModel planetModel, final Plane plane, final double x, final double y, final double z, final Membership... bounds) {
-    return plane.linearDistanceSquared(planetModel, x,y,z, bounds);
-  }
-
-}
-
-

http://git-wip-us.apache.org/repos/asf/lucene-solr/blob/f7f81c32/lucene/spatial3d/src/java/org/apache/lucene/geo3d/Membership.java
----------------------------------------------------------------------
diff --git a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/Membership.java b/lucene/spatial3d/src/java/org/apache/lucene/geo3d/Membership.java
deleted file mode 100755
index 3ca6b09..0000000
--- a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/Membership.java
+++ /dev/null
@@ -1,46 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements.  See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License.  You may obtain a copy of the License at
- *
- *     http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-package org.apache.lucene.geo3d;
-
-/**
- * Implemented by Geo3D shapes that can calculate if a point is within it or not.
- *
- * @lucene.experimental
- */
-public interface Membership {
-
-  /**
-   * Check if a point is within this shape.
-   *
-   * @param point is the point to check.
-   * @return true if the point is within this shape
-   */
-  public default boolean isWithin(final Vector point) {
-    return isWithin(point.x, point.y, point.z);
-  }
-
-  /**
-   * Check if a point is within this shape.
-   *
-   * @param x is x coordinate of point to check.
-   * @param y is y coordinate of point to check.
-   * @param z is z coordinate of point to check.
-   * @return true if the point is within this shape
-   */
-  public boolean isWithin(final double x, final double y, final double z);
-
-}

http://git-wip-us.apache.org/repos/asf/lucene-solr/blob/f7f81c32/lucene/spatial3d/src/java/org/apache/lucene/geo3d/NormalDistance.java
----------------------------------------------------------------------
diff --git a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/NormalDistance.java b/lucene/spatial3d/src/java/org/apache/lucene/geo3d/NormalDistance.java
deleted file mode 100644
index cdac0d2..0000000
--- a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/NormalDistance.java
+++ /dev/null
@@ -1,56 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements.  See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License.  You may obtain a copy of the License at
- *
- *     http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-package org.apache.lucene.geo3d;
-
-/**
- * Normal distance computation style.
- *
- * @lucene.experimental
- */
-public class NormalDistance implements DistanceStyle {
-  
-  /** A convenient instance */
-  public final static NormalDistance INSTANCE = new NormalDistance();
-  
-  /** Constructor.
-   */
-  public NormalDistance() {
-  }
-  
-  @Override
-  public double computeDistance(final GeoPoint point1, final GeoPoint point2) {
-    return point1.normalDistance(point2);
-  }
-  
-  @Override
-  public double computeDistance(final GeoPoint point1, final double x2, final double y2, final double z2) {
-    return point1.normalDistance(x2,y2,z2);
-  }
-
-  @Override
-  public double computeDistance(final PlanetModel planetModel, final Plane plane, final GeoPoint point, final Membership... bounds) {
-    return plane.normalDistance(point, bounds);
-  }
-  
-  @Override
-  public double computeDistance(final PlanetModel planetModel, final Plane plane, final double x, final double y, final double z, final Membership... bounds) {
-    return plane.normalDistance(x,y,z, bounds);
-  }
-
-}
-
-

http://git-wip-us.apache.org/repos/asf/lucene-solr/blob/f7f81c32/lucene/spatial3d/src/java/org/apache/lucene/geo3d/NormalSquaredDistance.java
----------------------------------------------------------------------
diff --git a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/NormalSquaredDistance.java b/lucene/spatial3d/src/java/org/apache/lucene/geo3d/NormalSquaredDistance.java
deleted file mode 100644
index 035fd40..0000000
--- a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/NormalSquaredDistance.java
+++ /dev/null
@@ -1,56 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements.  See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License.  You may obtain a copy of the License at
- *
- *     http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-package org.apache.lucene.geo3d;
-
-/**
- * Normal squared distance computation style.
- *
- * @lucene.experimental
- */
-public class NormalSquaredDistance implements DistanceStyle {
-  
-  /** A convenient instance */
-  public final static NormalSquaredDistance INSTANCE = new NormalSquaredDistance();
-  
-  /** Constructor.
-   */
-  public NormalSquaredDistance() {
-  }
-  
-  @Override
-  public double computeDistance(final GeoPoint point1, final GeoPoint point2) {
-    return point1.normalDistanceSquared(point2);
-  }
-  
-  @Override
-  public double computeDistance(final GeoPoint point1, final double x2, final double y2, final double z2) {
-    return point1.normalDistanceSquared(x2,y2,z2);
-  }
-
-  @Override
-  public double computeDistance(final PlanetModel planetModel, final Plane plane, final GeoPoint point, final Membership... bounds) {
-    return plane.normalDistanceSquared(point, bounds);
-  }
-  
-  @Override
-  public double computeDistance(final PlanetModel planetModel, final Plane plane, final double x, final double y, final double z, final Membership... bounds) {
-    return plane.normalDistanceSquared(x,y,z, bounds);
-  }
-
-}
-
-

http://git-wip-us.apache.org/repos/asf/lucene-solr/blob/f7f81c32/lucene/spatial3d/src/java/org/apache/lucene/geo3d/Plane.java
----------------------------------------------------------------------
diff --git a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/Plane.java b/lucene/spatial3d/src/java/org/apache/lucene/geo3d/Plane.java
deleted file mode 100755
index 07d0c5b..0000000
--- a/lucene/spatial3d/src/java/org/apache/lucene/geo3d/Plane.java
+++ /dev/null
@@ -1,1657 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements.  See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License.  You may obtain a copy of the License at
- *
- *     http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-package org.apache.lucene.geo3d;
-
-/**
- * We know about three kinds of planes.  First kind: general plain through two points and origin
- * Second kind: horizontal plane at specified height.  Third kind: vertical plane with specified x and y value, through origin.
- *
- * @lucene.experimental
- */
-public class Plane extends Vector {
-  /** An array with no points in it */
-  protected final static GeoPoint[] NO_POINTS = new GeoPoint[0];
-  /** An array with no bounds in it */
-  protected final static Membership[] NO_BOUNDS = new Membership[0];
-  /** A vertical plane normal to the Y axis */
-  protected final static Plane normalYPlane = new Plane(0.0,1.0,0.0,0.0);
-  /** A vertical plane normal to the X axis */
-  protected final static Plane normalXPlane = new Plane(1.0,0.0,0.0,0.0);
-  /** A vertical plane normal to the Z axis */
-  protected final static Plane normalZPlane = new Plane(0.0,0.0,1.0,0.0);
-
-  /** Ax + By + Cz + D = 0 */
-  public final double D;
-
-  /**
-   * Construct a plane with all four coefficients defined.
-   *@param A is A
-   *@param B is B
-   *@param C is C
-   *@param D is D
-   */
-  public Plane(final double A, final double B, final double C, final double D) {
-    super(A, B, C);
-    this.D = D;
-  }
-
-  /**
-   * Construct a plane through two points and origin.
-   *
-   * @param A is the first point (origin based).
-   * @param B is the second point (origin based).
-   */
-  public Plane(final Vector A, final Vector B) {
-    super(A, B);
-    D = 0.0;
-  }
-
-  /**
-   * Construct a horizontal plane at a specified Z.
-   *
-   * @param planetModel is the planet model.
-   * @param sinLat is the sin(latitude).
-   */
-  public Plane(final PlanetModel planetModel, final double sinLat) {
-    super(0.0, 0.0, 1.0);
-    D = -sinLat * computeDesiredEllipsoidMagnitude(planetModel, sinLat);
-  }
-
-  /**
-   * Construct a vertical plane through a specified
-   * x, y and origin.
-   *
-   * @param x is the specified x value.
-   * @param y is the specified y value.
-   */
-  public Plane(final double x, final double y) {
-    super(y, -x, 0.0);
-    D = 0.0;
-  }
-
-  /**
-   * Construct a plane with a specific vector, and D offset
-   * from origin.
-   * @param v is the normal vector.
-   * @param D is the D offset from the origin.
-   */
-  public Plane(final Vector v, final double D) {
-    super(v.x, v.y, v.z);
-    this.D = D;
-  }
-
-  /** Construct the most accurate normalized plane through an x-y point and including the Z axis.
-   * If none of the points can determine the plane, return null.
-   * @param planePoints is a set of points to choose from.  The best one for constructing the most precise plane is picked.
-   * @return the plane
-   */
-  public static Plane constructNormalizedZPlane(final Vector... planePoints) {
-    // Pick the best one (with the greatest x-y distance)
-    double bestDistance = 0.0;
-    Vector bestPoint = null;
-    for (final Vector point : planePoints) {
-      final double pointDist = point.x * point.x + point.y * point.y;
-      if (pointDist > bestDistance) {
-        bestDistance = pointDist;
-        bestPoint = point;
-      }
-    }
-    return constructNormalizedZPlane(bestPoint.x, bestPoint.y);
-  }
-
-  /** Construct the most accurate normalized plane through an x-z point and including the Y axis.
-   * If none of the points can determine the plane, return null.
-   * @param planePoints is a set of points to choose from.  The best one for constructing the most precise plane is picked.
-   * @return the plane
-   */
-  public static Plane constructNormalizedYPlane(final Vector... planePoints) {
-    // Pick the best one (with the greatest x-z distance)
-    double bestDistance = 0.0;
-    Vector bestPoint = null;
-    for (final Vector point : planePoints) {
-      final double pointDist = point.x * point.x + point.z * point.z;
-      if (pointDist > bestDistance) {
-        bestDistance = pointDist;
-        bestPoint = point;
-      }
-    }
-    return constructNormalizedYPlane(bestPoint.x, bestPoint.z, 0.0);
-  }
-
-  /** Construct the most accurate normalized plane through an y-z point and including the X axis.
-   * If none of the points can determine the plane, return null.
-   * @param planePoints is a set of points to choose from.  The best one for constructing the most precise plane is picked.
-   * @return the plane
-   */
-  public static Plane constructNormalizedXPlane(final Vector... planePoints) {
-    // Pick the best one (with the greatest y-z distance)
-    double bestDistance = 0.0;
-    Vector bestPoint = null;
-    for (final Vector point : planePoints) {
-      final double pointDist = point.y * point.y + point.z * point.z;
-      if (pointDist > bestDistance) {
-        bestDistance = pointDist;
-        bestPoint = point;
-      }
-    }
-    return constructNormalizedXPlane(bestPoint.y, bestPoint.z, 0.0);
-  }
-
-  /** Construct a normalized plane through an x-y point and including the Z axis.
-   * If the x-y point is at (0,0), return null.
-   * @param x is the x value.
-   * @param y is the y value.
-   * @return a plane passing through the Z axis and (x,y,0).
-   */
-  public static Plane constructNormalizedZPlane(final double x, final double y) {
-    if (Math.abs(x) < MINIMUM_RESOLUTION && Math.abs(y) < MINIMUM_RESOLUTION)
-      return null;
-    final double denom = 1.0 / Math.sqrt(x*x + y*y);
-    return new Plane(y * denom, -x * denom, 0.0, 0.0);
-  }
-
-  /** Construct a normalized plane through an x-z point and parallel to the Y axis.
-   * If the x-z point is at (0,0), return null.
-   * @param x is the x value.
-   * @param z is the z value.
-   * @param DValue is the offset from the origin for the plane.
-   * @return a plane parallel to the Y axis and perpendicular to the x and z values given.
-   */
-  public static Plane constructNormalizedYPlane(final double x, final double z, final double DValue) {
-    if (Math.abs(x) < MINIMUM_RESOLUTION && Math.abs(z) < MINIMUM_RESOLUTION)
-      return null;
-    final double denom = 1.0 / Math.sqrt(x*x + z*z);
-    return new Plane(z * denom, 0.0, -x * denom, DValue);
-  }
-
-  /** Construct a normalized plane through a y-z point and parallel to the X axis.
-   * If the y-z point is at (0,0), return null.
-   * @param y is the y value.
-   * @param z is the z value.
-   * @param DValue is the offset from the origin for the plane.
-   * @return a plane parallel to the X axis and perpendicular to the y and z values given.
-   */
-  public static Plane constructNormalizedXPlane(final double y, final double z, final double DValue) {
-    if (Math.abs(y) < MINIMUM_RESOLUTION && Math.abs(z) < MINIMUM_RESOLUTION)
-      return null;
-    final double denom = 1.0 / Math.sqrt(y*y + z*z);
-    return new Plane(0.0, z * denom, -y * denom, DValue);
-  }
-  
-  /**
-   * Evaluate the plane equation for a given point, as represented
-   * by a vector.
-   *
-   * @param v is the vector.
-   * @return the result of the evaluation.
-   */
-  public double evaluate(final Vector v) {
-    return dotProduct(v) + D;
-  }
-
-  /**
-   * Evaluate the plane equation for a given point, as represented
-   * by a vector.
-   * @param x is the x value.
-   * @param y is the y value.
-   * @param z is the z value.
-   * @return the result of the evaluation.
-   */
-  public double evaluate(final double x, final double y, final double z) {
-    return dotProduct(x, y, z) + D;
-  }
-
-  /**
-   * Evaluate the plane equation for a given point, as represented
-   * by a vector.
-   *
-   * @param v is the vector.
-   * @return true if the result is on the plane.
-   */
-  public boolean evaluateIsZero(final Vector v) {
-    return Math.abs(evaluate(v)) < MINIMUM_RESOLUTION;
-  }
-
-  /**
-   * Evaluate the plane equation for a given point, as represented
-   * by a vector.
-   *
-   * @param x is the x value.
-   * @param y is the y value.
-   * @param z is the z value.
-   * @return true if the result is on the plane.
-   */
-  public boolean evaluateIsZero(final double x, final double y, final double z) {
-    return Math.abs(evaluate(x, y, z)) < MINIMUM_RESOLUTION;
-  }
-
-  /**
-   * Build a normalized plane, so that the vector is normalized.
-   *
-   * @return the normalized plane object, or null if the plane is indeterminate.
-   */
-  public Plane normalize() {
-    Vector normVect = super.normalize();
-    if (normVect == null)
-      return null;
-    return new Plane(normVect, this.D);
-  }
-
-  /** Compute arc distance from plane to a vector expressed with a {@link GeoPoint}.
-   *  @see #arcDistance(PlanetModel, double, double, double, Membership...) */
-  public double arcDistance(final PlanetModel planetModel, final GeoPoint v, final Membership... bounds) {
-    return arcDistance(planetModel, v.x, v.y, v.z, bounds);
-  }
-    
-  /**
-   * Compute arc distance from plane to a vector.
-   * @param planetModel is the planet model.
-   * @param x is the x vector value.
-   * @param y is the y vector value.
-   * @param z is the z vector value.
-   * @param bounds are the bounds which constrain the intersection point.
-   * @return the arc distance.
-   */
-  public double arcDistance(final PlanetModel planetModel, final double x, final double y, final double z, final Membership... bounds) {
-
-    if (evaluateIsZero(x,y,z)) {
-      if (meetsAllBounds(x,y,z, bounds))
-        return 0.0;
-      return Double.MAX_VALUE;
-    }
-    
-    // First, compute the perpendicular plane.
-    final Plane perpPlane = new Plane(this.y * z - this.z * y, this.z * x - this.x * z, this.x * y - this.y * x, 0.0);
-
-    // We need to compute the intersection of two planes on the geo surface: this one, and its perpendicular.
-    // Then, we need to choose which of the two points we want to compute the distance to.  We pick the
-    // shorter distance always.
-    
-    final GeoPoint[] intersectionPoints = findIntersections(planetModel, perpPlane);
-    
-    // For each point, compute a linear distance, and take the minimum of them
-    double minDistance = Double.MAX_VALUE;
-    
-    for (final GeoPoint intersectionPoint : intersectionPoints) {
-      if (meetsAllBounds(intersectionPoint, bounds)) {
-        final double theDistance = intersectionPoint.arcDistance(x,y,z);
-        if (theDistance < minDistance) {
-          minDistance = theDistance;
-        }
-      }
-    }
-    return minDistance;
-
-  }
-
-  /**
-   * Compute normal distance from plane to a vector.
-   * @param v is the vector.
-   * @param bounds are the bounds which constrain the intersection point.
-   * @return the normal distance.
-   */
-  public double normalDistance(final Vector v, final Membership... bounds) {
-    return normalDistance(v.x, v.y, v.z, bounds);
-  }
-    
-  /**
-   * Compute normal distance from plane to a vector.
-   * @param x is the vector x.
-   * @param y is the vector y.
-   * @param z is the vector z.
-   * @param bounds are the bounds which constrain the intersection point.
-   * @return the normal distance.
-   */
-  public double normalDistance(final double x, final double y, final double z, final Membership... bounds) {
-
-    final double dist = evaluate(x,y,z);
-    final double perpX = x - dist * this.x;
-    final double perpY = y - dist * this.y;
-    final double perpZ = z - dist * this.z;
-
-    if (!meetsAllBounds(perpX, perpY, perpZ, bounds)) {
-      return Double.MAX_VALUE;
-    }
-    
-    return Math.abs(dist);
-  }
-  
-  /**
-   * Compute normal distance squared from plane to a vector.
-   * @param v is the vector.
-   * @param bounds are the bounds which constrain the intersection point.
-   * @return the normal distance squared.
-   */
-  public double normalDistanceSquared(final Vector v, final Membership... bounds) {
-    return normalDistanceSquared(v.x, v.y, v.z, bounds);
-  }
-  
-  /**
-   * Compute normal distance squared from plane to a vector.
-   * @param x is the vector x.
-   * @param y is the vector y.
-   * @param z is the vector z.
-   * @param bounds are the bounds which constrain the intersection point.
-   * @return the normal distance squared.
-   */
-  public double normalDistanceSquared(final double x, final double y, final double z, final Membership... bounds) {
-    final double normal = normalDistance(x,y,z,bounds);
-    if (normal == Double.MAX_VALUE)
-      return normal;
-    return normal * normal;
-  }
-
-  /**
-   * Compute linear distance from plane to a vector.  This is defined
-   * as the distance from the given point to the nearest intersection of 
-   * this plane with the planet surface.
-   * @param planetModel is the planet model.
-   * @param v is the point.
-   * @param bounds are the bounds which constrain the intersection point.
-   * @return the linear distance.
-   */
-  public double linearDistance(final PlanetModel planetModel, final GeoPoint v, final Membership... bounds) {
-    return linearDistance(planetModel, v.x, v.y, v.z, bounds);
-  }
-    
-  /**
-   * Compute linear distance from plane to a vector.  This is defined
-   * as the distance from the given point to the nearest intersection of 
-   * this plane with the planet surface.
-   * @param planetModel is the planet model.
-   * @param x is the vector x.
-   * @param y is the vector y.
-   * @param z is the vector z.
-   * @param bounds are the bounds which constrain the intersection point.
-   * @return the linear distance.
-   */
-  public double linearDistance(final PlanetModel planetModel, final double x, final double y, final double z, final Membership... bounds) {
-    if (evaluateIsZero(x,y,z)) {
-      if (meetsAllBounds(x,y,z, bounds))
-        return 0.0;
-      return Double.MAX_VALUE;
-    }
-    
-    // First, compute the perpendicular plane.
-    final Plane perpPlane = new Plane(this.y * z - this.z * y, this.z * x - this.x * z, this.x * y - this.y * x, 0.0);
-
-    // We need to compute the intersection of two planes on the geo surface: this one, and its perpendicular.
-    // Then, we need to choose which of the two points we want to compute the distance to.  We pick the
-    // shorter distance always.
-    
-    final GeoPoint[] intersectionPoints = findIntersections(planetModel, perpPlane);
-    
-    // For each point, compute a linear distance, and take the minimum of them
-    double minDistance = Double.MAX_VALUE;
-    
-    for (final GeoPoint intersectionPoint : intersectionPoints) {
-      if (meetsAllBounds(intersectionPoint, bounds)) {
-        final double theDistance = intersectionPoint.linearDistance(x,y,z);
-        if (theDistance < minDistance) {
-          minDistance = theDistance;
-        }
-      }
-    }
-    return minDistance;
-  }
-      
-  /**
-   * Compute linear distance squared from plane to a vector.  This is defined
-   * as the distance from the given point to the nearest intersection of 
-   * this plane with the planet surface.
-   * @param planetModel is the planet model.
-   * @param v is the point.
-   * @param bounds are the bounds which constrain the intersection point.
-   * @return the linear distance squared.
-   */
-  public double linearDistanceSquared(final PlanetModel planetModel, final GeoPoint v, final Membership... bounds) {
-    return linearDistanceSquared(planetModel, v.x, v.y, v.z, bounds);
-  }
-  
-  /**
-   * Compute linear distance squared from plane to a vector.  This is defined
-   * as the distance from the given point to the nearest intersection of 
-   * this plane with the planet surface.
-   * @param planetModel is the planet model.
-   * @param x is the vector x.
-   * @param y is the vector y.
-   * @param z is the vector z.
-   * @param bounds are the bounds which constrain the intersection point.
-   * @return the linear distance squared.
-   */
-  public double linearDistanceSquared(final PlanetModel planetModel, final double x, final double y, final double z, final Membership... bounds) {
-    final double linearDistance = linearDistance(planetModel, x, y, z, bounds);
-    return linearDistance * linearDistance;
-  }
-
-  /**
-   * Find points on the boundary of the intersection of a plane and the unit sphere,
-   * given a starting point, and ending point, and a list of proportions of the arc (e.g. 0.25, 0.5, 0.75).
-   * The angle between the starting point and ending point is assumed to be less than pi.
-   * @param start is the start point.
-   * @param end is the end point.
-   * @param proportions is an array of fractional proportions measured between start and end.
-   * @return an array of points corresponding to the proportions passed in.
-   */
-  public GeoPoint[] interpolate(final GeoPoint start, final GeoPoint end, final double[] proportions) {
-    // Steps:
-    // (1) Translate (x0,y0,z0) of endpoints into origin-centered place:
-    // x1 = x0 + D*A
-    // y1 = y0 + D*B
-    // z1 = z0 + D*C
-    // (2) Rotate counterclockwise in x-y:
-    // ra = -atan2(B,A)
-    // x2 = x1 cos ra - y1 sin ra
-    // y2 = x1 sin ra + y1 cos ra
-    // z2 = z1
-    // Faster:
-    // cos ra = A/sqrt(A^2+B^2+C^2)
-    // sin ra = -B/sqrt(A^2+B^2+C^2)
-    // cos (-ra) = A/sqrt(A^2+B^2+C^2)
-    // sin (-ra) = B/sqrt(A^2+B^2+C^2)
-    // (3) Rotate clockwise in x-z:
-    // ha = pi/2 - asin(C/sqrt(A^2+B^2+C^2))
-    // x3 = x2 cos ha - z2 sin ha
-    // y3 = y2
-    // z3 = x2 sin ha + z2 cos ha
-    // At this point, z3 should be zero.
-    // Faster:
-    // sin(ha) = cos(asin(C/sqrt(A^2+B^2+C^2))) = sqrt(1 - C^2/(A^2+B^2+C^2)) = sqrt(A^2+B^2)/sqrt(A^2+B^2+C^2)
-    // cos(ha) = sin(asin(C/sqrt(A^2+B^2+C^2))) = C/sqrt(A^2+B^2+C^2)
-    // (4) Compute interpolations by getting longitudes of original points
-    // la = atan2(y3,x3)
-    // (5) Rotate new points (xN0, yN0, zN0) counter-clockwise in x-z:
-    // ha = -(pi - asin(C/sqrt(A^2+B^2+C^2)))
-    // xN1 = xN0 cos ha - zN0 sin ha
-    // yN1 = yN0
-    // zN1 = xN0 sin ha + zN0 cos ha
-    // (6) Rotate new points clockwise in x-y:
-    // ra = atan2(B,A)
-    // xN2 = xN1 cos ra - yN1 sin ra
-    // yN2 = xN1 sin ra + yN1 cos ra
-    // zN2 = zN1
-    // (7) Translate new points:
-    // xN3 = xN2 - D*A
-    // yN3 = yN2 - D*B
-    // zN3 = zN2 - D*C
-
-    // First, calculate the angles and their sin/cos values
-    double A = x;
-    double B = y;
-    double C = z;
-
-    // Translation amounts
-    final double transX = -D * A;
-    final double transY = -D * B;
-    final double transZ = -D * C;
-
-    double cosRA;
-    double sinRA;
-    double cosHA;
-    double sinHA;
-
-    double magnitude = magnitude();
-    if (magnitude >= MINIMUM_RESOLUTION) {
-      final double denom = 1.0 / magnitude;
-      A *= denom;
-      B *= denom;
-      C *= denom;
-
-      // cos ra = A/sqrt(A^2+B^2+C^2)
-      // sin ra = -B/sqrt(A^2+B^2+C^2)
-      // cos (-ra) = A/sqrt(A^2+B^2+C^2)
-      // sin (-ra) = B/sqrt(A^2+B^2+C^2)
-      final double xyMagnitude = Math.sqrt(A * A + B * B);
-      if (xyMagnitude >= MINIMUM_RESOLUTION) {
-        final double xyDenom = 1.0 / xyMagnitude;
-        cosRA = A * xyDenom;
-        sinRA = -B * xyDenom;
-      } else {
-        cosRA = 1.0;
-        sinRA = 0.0;
-      }
-
-      // sin(ha) = cos(asin(C/sqrt(A^2+B^2+C^2))) = sqrt(1 - C^2/(A^2+B^2+C^2)) = sqrt(A^2+B^2)/sqrt(A^2+B^2+C^2)
-      // cos(ha) = sin(asin(C/sqrt(A^2+B^2+C^2))) = C/sqrt(A^2+B^2+C^2)
-      sinHA = xyMagnitude;
-      cosHA = C;
-    } else {
-      cosRA = 1.0;
-      sinRA = 0.0;
-      cosHA = 1.0;
-      sinHA = 0.0;
-    }
-
-    // Forward-translate the start and end points
-    final Vector modifiedStart = modify(start, transX, transY, transZ, sinRA, cosRA, sinHA, cosHA);
-    final Vector modifiedEnd = modify(end, transX, transY, transZ, sinRA, cosRA, sinHA, cosHA);
-    if (Math.abs(modifiedStart.z) >= MINIMUM_RESOLUTION)
-      throw new IllegalArgumentException("Start point was not on plane: " + modifiedStart.z);
-    if (Math.abs(modifiedEnd.z) >= MINIMUM_RESOLUTION)
-      throw new IllegalArgumentException("End point was not on plane: " + modifiedEnd.z);
-
-    // Compute the angular distance between start and end point
-    final double startAngle = Math.atan2(modifiedStart.y, modifiedStart.x);
-    final double endAngle = Math.atan2(modifiedEnd.y, modifiedEnd.x);
-
-    final double startMagnitude = Math.sqrt(modifiedStart.x * modifiedStart.x + modifiedStart.y * modifiedStart.y);
-    double delta;
-
-    double newEndAngle = endAngle;
-    while (newEndAngle < startAngle) {
-      newEndAngle += Math.PI * 2.0;
-    }
-
-    if (newEndAngle - startAngle <= Math.PI) {
-      delta = newEndAngle - startAngle;
-    } else {
-      double newStartAngle = startAngle;
-      while (newStartAngle < endAngle) {
-        newStartAngle += Math.PI * 2.0;
-      }
-      delta = newStartAngle - endAngle;
-    }
-
-    final GeoPoint[] returnValues = new GeoPoint[proportions.length];
-    for (int i = 0; i < returnValues.length; i++) {
-      final double newAngle = startAngle + proportions[i] * delta;
-      final double sinNewAngle = Math.sin(newAngle);
-      final double cosNewAngle = Math.cos(newAngle);
-      final Vector newVector = new Vector(cosNewAngle * startMagnitude, sinNewAngle * startMagnitude, 0.0);
-      returnValues[i] = reverseModify(newVector, transX, transY, transZ, sinRA, cosRA, sinHA, cosHA);
-    }
-
-    return returnValues;
-  }
-
-  /**
-   * Modify a point to produce a vector in translated/rotated space.
-   * @param start is the start point.
-   * @param transX is the translation x value.
-   * @param transY is the translation y value.
-   * @param transZ is the translation z value.
-   * @param sinRA is the sine of the ascension angle.
-   * @param cosRA is the cosine of the ascension angle.
-   * @param sinHA is the sine of the height angle.
-   * @param cosHA is the cosine of the height angle.
-   * @return the modified point.
-   */
-  protected static Vector modify(final GeoPoint start, final double transX, final double transY, final double transZ,
-                                 final double sinRA, final double cosRA, final double sinHA, final double cosHA) {
-    return start.translate(transX, transY, transZ).rotateXY(sinRA, cosRA).rotateXZ(sinHA, cosHA);
-  }
-
-  /**
-   * Reverse modify a point to produce a GeoPoint in normal space.
-   * @param point is the translated point.
-   * @param transX is the translation x value.
-   * @param transY is the translation y value.
-   * @param transZ is the translation z value.
-   * @param sinRA is the sine of the ascension angle.
-   * @param cosRA is the cosine of the ascension angle.
-   * @param sinHA is the sine of the height angle.
-   * @param cosHA is the cosine of the height angle.
-   * @return the original point.
-   */
-  protected static GeoPoint reverseModify(final Vector point, final double transX, final double transY, final double transZ,
-                                          final double sinRA, final double cosRA, final double sinHA, final double cosHA) {
-    final Vector result = point.rotateXZ(-sinHA, cosHA).rotateXY(-sinRA, cosRA).translate(-transX, -transY, -transZ);
-    return new GeoPoint(result.x, result.y, result.z);
-  }
-
-  /**
-   * Public version of findIntersections.
-   * @param planetModel is the planet model.
-   * @param q is the plane to intersect with.
-   * @param bounds are the bounds to consider to determine legal intersection points.
-   * @return the set of legal intersection points.
-   */
-  public GeoPoint[] findIntersections(final PlanetModel planetModel, final Plane q, final Membership... bounds) {
-    if (isNumericallyIdentical(q)) {
-      return null;
-    }
-    return findIntersections(planetModel, q, bounds, NO_BOUNDS);
-  }
-  
-  /**
-   * Find the intersection points between two planes, given a set of bounds.
-   *
-   * @param planetModel is the planet model to use in finding points.
-   * @param q          is the plane to intersect with.
-   * @param bounds     is the set of bounds.
-   * @param moreBounds is another set of bounds.
-   * @return the intersection point(s) on the unit sphere, if there are any.
-   */
-  protected GeoPoint[] findIntersections(final PlanetModel planetModel, final Plane q, final Membership[] bounds, final Membership[] moreBounds) {
-    //System.err.println("Looking for intersection between plane "+this+" and plane "+q+" within bounds");
-    // Unnormalized, unchecked...
-    final Vector lineVector = new Vector(y * q.z - z * q.y, z * q.x - x * q.z, x * q.y - y * q.x);
-    if (Math.abs(lineVector.x) < MINIMUM_RESOLUTION && Math.abs(lineVector.y) < MINIMUM_RESOLUTION && Math.abs(lineVector.z) < MINIMUM_RESOLUTION) {
-      // Degenerate case: parallel planes
-      //System.err.println(" planes are parallel - no intersection");
-      return NO_POINTS;
-    }
-
-    // The line will have the equation: A t + A0 = x, B t + B0 = y, C t + C0 = z.
-    // We have A, B, and C.  In order to come up with A0, B0, and C0, we need to find a point that is on both planes.
-    // To do this, we find the largest vector value (either x, y, or z), and look for a point that solves both plane equations
-    // simultaneous.  For example, let's say that the vector is (0.5,0.5,1), and the two plane equations are:
-    // 0.7 x + 0.3 y + 0.1 z + 0.0 = 0
-    // and
-    // 0.9 x - 0.1 y + 0.2 z + 4.0 = 0
-    // Then we'd pick z = 0, so the equations to solve for x and y would be:
-    // 0.7 x + 0.3y = 0.0
-    // 0.9 x - 0.1y = -4.0
-    // ... which can readily be solved using standard linear algebra.  Generally:
-    // Q0 x + R0 y = S0
-    // Q1 x + R1 y = S1
-    // ... can be solved by Cramer's rule:
-    // x = det(S0 R0 / S1 R1) / det(Q0 R0 / Q1 R1)
-    // y = det(Q0 S0 / Q1 S1) / det(Q0 R0 / Q1 R1)
-    // ... where det( a b / c d ) = ad - bc, so:
-    // x = (S0 * R1 - R0 * S1) / (Q0 * R1 - R0 * Q1)
-    // y = (Q0 * S1 - S0 * Q1) / (Q0 * R1 - R0 * Q1)
-    double x0;
-    double y0;
-    double z0;
-    // We try to maximize the determinant in the denominator
-    final double denomYZ = this.y * q.z - this.z * q.y;
-    final double denomXZ = this.x * q.z - this.z * q.x;
-    final double denomXY = this.x * q.y - this.y * q.x;
-    if (Math.abs(denomYZ) >= Math.abs(denomXZ) && Math.abs(denomYZ) >= Math.abs(denomXY)) {
-      // X is the biggest, so our point will have x0 = 0.0
-      if (Math.abs(denomYZ) < MINIMUM_RESOLUTION_SQUARED) {
-        //System.err.println(" Denominator is zero: no intersection");
-        return NO_POINTS;
-      }
-      final double denom = 1.0 / denomYZ;
-      x0 = 0.0;
-      y0 = (-this.D * q.z - this.z * -q.D) * denom;
-      z0 = (this.y * -q.D + this.D * q.y) * denom;
-    } else if (Math.abs(denomXZ) >= Math.abs(denomXY) && Math.abs(denomXZ) >= Math.abs(denomYZ)) {
-      // Y is the biggest, so y0 = 0.0
-      if (Math.abs(denomXZ) < MINIMUM_RESOLUTION_SQUARED) {
-        //System.err.println(" Denominator is zero: no intersection");
-        return NO_POINTS;
-      }
-      final double denom = 1.0 / denomXZ;
-      x0 = (-this.D * q.z - this.z * -q.D) * denom;
-      y0 = 0.0;
-      z0 = (this.x * -q.D + this.D * q.x) * denom;
-    } else {
-      // Z is the biggest, so Z0 = 0.0
-      if (Math.abs(denomXY) < MINIMUM_RESOLUTION_SQUARED) {
-        //System.err.println(" Denominator is zero: no intersection");
-        return NO_POINTS;
-      }
-      final double denom = 1.0 / denomXY;
-      x0 = (-this.D * q.y - this.y * -q.D) * denom;
-      y0 = (this.x * -q.D + this.D * q.x) * denom;
-      z0 = 0.0;
-    }
-
-    // Once an intersecting line is determined, the next step is to intersect that line with the ellipsoid, which
-    // will yield zero, one, or two points.
-    // The ellipsoid equation: 1,0 = x^2/a^2 + y^2/b^2 + z^2/c^2
-    // 1.0 = (At+A0)^2/a^2 + (Bt+B0)^2/b^2 + (Ct+C0)^2/c^2
-    // A^2 t^2 / a^2 + 2AA0t / a^2 + A0^2 / a^2 + B^2 t^2 / b^2 + 2BB0t / b^2 + B0^2 / b^2 + C^2 t^2 / c^2 + 2CC0t / c^2 + C0^2 / c^2  - 1,0 = 0.0
-    // [A^2 / a^2 + B^2 / b^2 + C^2 / c^2] t^2 + [2AA0 / a^2 + 2BB0 / b^2 + 2CC0 / c^2] t + [A0^2 / a^2 + B0^2 / b^2 + C0^2 / c^2 - 1,0] = 0.0
-    // Use the quadratic formula to determine t values and candidate point(s)
-    final double A = lineVector.x * lineVector.x * planetModel.inverseAbSquared +
-      lineVector.y * lineVector.y * planetModel.inverseAbSquared +
-      lineVector.z * lineVector.z * planetModel.inverseCSquared;
-    final double B = 2.0 * (lineVector.x * x0 * planetModel.inverseAbSquared + lineVector.y * y0 * planetModel.inverseAbSquared + lineVector.z * z0 * planetModel.inverseCSquared);
-    final double C = x0 * x0 * planetModel.inverseAbSquared + y0 * y0 * planetModel.inverseAbSquared + z0 * z0 * planetModel.inverseCSquared - 1.0;
-
-    final double BsquaredMinus = B * B - 4.0 * A * C;
-    if (Math.abs(BsquaredMinus) < MINIMUM_RESOLUTION_SQUARED) {
-      //System.err.println(" One point of intersection");
-      final double inverse2A = 1.0 / (2.0 * A);
-      // One solution only
-      final double t = -B * inverse2A;
-      GeoPoint point = new GeoPoint(lineVector.x * t + x0, lineVector.y * t + y0, lineVector.z * t + z0);
-      //System.err.println("  point: "+point);
-      //verifyPoint(planetModel, point, q);
-      if (point.isWithin(bounds, moreBounds))
-        return new GeoPoint[]{point};
-      return NO_POINTS;
-    } else if (BsquaredMinus > 0.0) {
-      //System.err.println(" Two points of intersection");
-      final double inverse2A = 1.0 / (2.0 * A);
-      // Two solutions
-      final double sqrtTerm = Math.sqrt(BsquaredMinus);
-      final double t1 = (-B + sqrtTerm) * inverse2A;
-      final double t2 = (-B - sqrtTerm) * inverse2A;
-      GeoPoint point1 = new GeoPoint(lineVector.x * t1 + x0, lineVector.y * t1 + y0, lineVector.z * t1 + z0);
-      GeoPoint point2 = new GeoPoint(lineVector.x * t2 + x0, lineVector.y * t2 + y0, lineVector.z * t2 + z0);
-      //verifyPoint(planetModel, point1, q);
-      //verifyPoint(planetModel, point2, q);
-      //System.err.println("  "+point1+" and "+point2);
-      if (point1.isWithin(bounds, moreBounds)) {
-        if (point2.isWithin(bounds, moreBounds))
-          return new GeoPoint[]{point1, point2};
-        return new GeoPoint[]{point1};
-      }
-      if (point2.isWithin(bounds, moreBounds))
-        return new GeoPoint[]{point2};
-      return NO_POINTS;
-    } else {
-      //System.err.println(" no solutions - no intersection");
-      return NO_POINTS;
-    }
-  }
-
-  /*
-  protected void verifyPoint(final PlanetModel planetModel, final GeoPoint point, final Plane q) {
-    if (!evaluateIsZero(point))
-      throw new RuntimeException("Intersection point not on original plane; point="+point+", plane="+this);
-    if (!q.evaluateIsZero(point))
-      throw new RuntimeException("Intersection point not on intersected plane; point="+point+", plane="+q);
-    if (Math.abs(point.x * point.x * planetModel.inverseASquared + point.y * point.y * planetModel.inverseBSquared + point.z * point.z * planetModel.inverseCSquared - 1.0) >= MINIMUM_RESOLUTION) 
-      throw new RuntimeException("Intersection point not on ellipsoid; point="+point);
-  }
-  */
-
-  /**
-   * Accumulate (x,y,z) bounds information for this plane, intersected with the unit sphere.
-   * Updates min/max information, using max/min points found
-   * within the specified bounds.
-   *
-   * @param planetModel is the planet model to use in determining bounds.
-   * @param boundsInfo is the xyz info to update with additional bounding information.
-   * @param bounds     are the surfaces delineating what's inside the shape.
-   */
-  public void recordBounds(final PlanetModel planetModel, final XYZBounds boundsInfo, final Membership... bounds) {
-    // Basic plan is to do three intersections of the plane and the planet.
-    // For min/max x, we intersect a vertical plane such that y = 0.
-    // For min/max y, we intersect a vertical plane such that x = 0.
-    // For min/max z, we intersect a vertical plane that is chosen to go through the high point of the arc.
-    // For clarity, load local variables with good names
-    final double A = this.x;
-    final double B = this.y;
-    final double C = this.z;
-
-    // Do Z.  This can be done simply because it is symmetrical.
-    if (!boundsInfo.isSmallestMinZ(planetModel) || !boundsInfo.isLargestMaxZ(planetModel)) {
-      //System.err.println("    computing Z bound");
-      // Compute Z bounds for this arc
-      // With ellipsoids, we really have only one viable way to do this computation.
-      // Specifically, we compute an appropriate vertical plane, based on the current plane's x-y orientation, and
-      // then intersect it with this one and with the ellipsoid.  This gives us zero, one, or two points to use
-      // as bounds.
-      // There is one special case: horizontal circles.  These require TWO vertical planes: one for the x, and one for
-      // the y, and we use all four resulting points in the bounds computation.
-      if ((Math.abs(A) >= MINIMUM_RESOLUTION || Math.abs(B) >= MINIMUM_RESOLUTION)) {
-        // NOT a degenerate case
-        //System.err.println("    not degenerate");
-        final Plane normalizedZPlane = constructNormalizedZPlane(A,B);
-        final GeoPoint[] points = findIntersections(planetModel, normalizedZPlane, bounds, NO_BOUNDS);
-        for (final GeoPoint point : points) {
-          assert planetModel.pointOnSurface(point);
-          //System.err.println("      Point = "+point+"; this.evaluate(point)="+this.evaluate(point)+"; normalizedZPlane.evaluate(point)="+normalizedZPlane.evaluate(point));
-          addPoint(boundsInfo, bounds, point);
-        }
-      } else {
-        // Since a==b==0, any plane including the Z axis suffices.
-        //System.err.println("      Perpendicular to z");
-        final GeoPoint[] points = findIntersections(planetModel, normalYPlane, NO_BOUNDS, NO_BOUNDS);
-        boundsInfo.addZValue(points[0]);
-      }
-    }
-
-    // First, compute common subexpressions
-    final double k = 1.0 / ((x*x + y*y)*planetModel.ab*planetModel.ab + z*z*planetModel.c*planetModel.c);
-    final double abSquared = planetModel.ab * planetModel.ab;
-    final double cSquared = planetModel.c * planetModel.c;
-    final double ASquared = A * A;
-    final double BSquared = B * B;
-    final double CSquared = C * C;
-    
-    final double r = 2.0*D*k;
-    final double rSquared = r * r;
-    
-    if (!boundsInfo.isSmallestMinX(planetModel) || !boundsInfo.isLargestMaxX(planetModel)) {
-      // For min/max x, we need to use lagrange multipliers.
-      //
-      // For this, we need grad(F(x,y,z)) = (dF/dx, dF/dy, dF/dz).
-      //
-      // Minimize and maximize f(x,y,z) = x, with respect to g(x,y,z) = Ax + By + Cz - D and h(x,y,z) = x^2/ab^2 + y^2/ab^2 + z^2/c^2 - 1
-      //
-      // grad(f(x,y,z)) = (1,0,0)
-      // grad(g(x,y,z)) = (A,B,C)
-      // grad(h(x,y,z)) = (2x/ab^2,2y/ab^2,2z/c^2)
-      //
-      // Equations we need to simultaneously solve:
-      // 
-      // grad(f(x,y,z)) = l * grad(g(x,y,z)) + m * grad(h(x,y,z))
-      // g(x,y,z) = 0
-      // h(x,y,z) = 0
-      // 
-      // Equations:
-      // 1 = l*A + m*2x/ab^2
-      // 0 = l*B + m*2y/ab^2
-      // 0 = l*C + m*2z/c^2
-      // Ax + By + Cz + D = 0
-      // x^2/ab^2 + y^2/ab^2 + z^2/c^2 - 1 = 0
-      // 
-      // Solve for x,y,z in terms of (l, m):
-      // 
-      // x = ((1 - l*A) * ab^2 ) / (2 * m)
-      // y = (-l*B * ab^2) / ( 2 * m)
-      // z = (-l*C * c^2)/ (2 * m)
-      // 
-      // Two equations, two unknowns:
-      // 
-      // A * (((1 - l*A) * ab^2 ) / (2 * m)) + B * ((-l*B * ab^2) / ( 2 * m)) + C * ((-l*C * c^2)/ (2 * m)) + D = 0
-      // 
-      // and
-      // 
-      // (((1 - l*A) * ab^2 ) / (2 * m))^2/ab^2 + ((-l*B * ab^2) / ( 2 * m))^2/ab^2 + ((-l*C * c^2)/ (2 * m))^2/c^2 - 1 = 0
-      // 
-      // Simple: solve for l and m, then find x from it.
-      // 
-      // (a) Use first equation to find l in terms of m.
-      // 
-      // A * (((1 - l*A) * ab^2 ) / (2 * m)) + B * ((-l*B * ab^2) / ( 2 * m)) + C * ((-l*C * c^2)/ (2 * m)) + D = 0
-      // A * ((1 - l*A) * ab^2 ) + B * (-l*B * ab^2) + C * (-l*C * c^2) + D * 2 * m = 0
-      // A * ab^2 - l*A^2* ab^2 - B^2 * l * ab^2 - C^2 * l * c^2 + D * 2 * m = 0
-      // - l *(A^2* ab^2 + B^2 * ab^2 + C^2 * c^2) + (A * ab^2 + D * 2 * m) = 0
-      // l = (A * ab^2 + D * 2 * m) / (A^2* ab^2 + B^2 * ab^2 + C^2 * c^2)
-      // l = A * ab^2 / (A^2* ab^2 + B^2 * ab^2 + C^2 * c^2) + m * 2 * D / (A^2* ab^2 + B^2 * ab^2 + C^2 * c^2)
-      // 
-      // For convenience:
-      // 
-      // k = 1.0 / (A^2* ab^2 + B^2 * ab^2 + C^2 * c^2)
-      // 
-      // Then:
-      // 
-      // l = A * ab^2 * k + m * 2 * D * k
-      // l = k * (A*ab^2 + m*2*D)
-      //
-      // For further convenience:
-      //
-      // q = A*ab^2*k
-      // r = 2*D*k
-      //
-      // l = (r*m + q)
-      // l^2 = (r^2 * m^2 + 2*r*m*q + q^2)
-      // 
-      // (b) Simplify the second equation before substitution
-      // 
-      // (((1 - l*A) * ab^2 ) / (2 * m))^2/ab^2 + ((-l*B * ab^2) / ( 2 * m))^2/ab^2 + ((-l*C * c^2)/ (2 * m))^2/c^2 - 1 = 0
-      // ((1 - l*A) * ab^2 )^2/ab^2 + (-l*B * ab^2)^2/ab^2 + (-l*C * c^2)^2/c^2 = 4 * m^2
-      // (1 - l*A)^2 * ab^2 + (-l*B)^2 * ab^2 + (-l*C)^2 * c^2 = 4 * m^2
-      // (1 - 2*l*A + l^2*A^2) * ab^2 + l^2*B^2 * ab^2 + l^2*C^2 * c^2 = 4 * m^2
-      // ab^2 - 2*A*ab^2*l + A^2*ab^2*l^2 + B^2*ab^2*l^2 + C^2*c^2*l^2 - 4*m^2 = 0
-      // 
-      // (c) Substitute for l, l^2
-      //
-      // ab^2 - 2*A*ab^2*(r*m + q) + A^2*ab^2*(r^2 * m^2 + 2*r*m*q + q^2) + B^2*ab^2*(r^2 * m^2 + 2*r*m*q + q^2) + C^2*c^2*(r^2 * m^2 + 2*r*m*q + q^2) - 4*m^2 = 0
-      // ab^2 - 2*A*ab^2*r*m - 2*A*ab^2*q + A^2*ab^2*r^2*m^2 + 2*A^2*ab^2*r*q*m +
-      //        A^2*ab^2*q^2 + B^2*ab^2*r^2*m^2 + 2*B^2*ab^2*r*q*m + B^2*ab^2*q^2 + C^2*c^2*r^2*m^2 + 2*C^2*c^2*r*q*m + C^2*c^2*q^2 - 4*m^2 = 0
-      //
-      // (d) Group
-      //
-      // m^2 * [A^2*ab^2*r^2 + B^2*ab^2*r^2 + C^2*c^2*r^2 - 4] +
-      // m * [- 2*A*ab^2*r + 2*A^2*ab^2*r*q + 2*B^2*ab^2*r*q + 2*C^2*c^2*r*q] +
-      // [ab^2 - 2*A*ab^2*q + A^2*ab^2*q^2 + B^2*ab^2*q^2 + C^2*c^2*q^2]  =  0
-      
-      //System.err.println("    computing X bound");
-      
-      // Useful subexpressions for this bound
-      final double q = A*abSquared*k;
-      final double qSquared = q * q;
-
-      // Quadratic equation
-      final double a = ASquared*abSquared*rSquared + BSquared*abSquared*rSquared + CSquared*cSquared*rSquared - 4.0;
-      final double b = - 2.0*A*abSquared*r + 2.0*ASquared*abSquared*r*q + 2.0*BSquared*abSquared*r*q + 2.0*CSquared*cSquared*r*q;
-      final double c = abSquared - 2.0*A*abSquared*q + ASquared*abSquared*qSquared + BSquared*abSquared*qSquared + CSquared*cSquared*qSquared;
-      
-      if (Math.abs(a) >= MINIMUM_RESOLUTION_SQUARED) {
-        final double sqrtTerm = b*b - 4.0*a*c;
-        if (Math.abs(sqrtTerm) < MINIMUM_RESOLUTION_SQUARED) {
-          // One solution
-          final double m = -b / (2.0 * a);
-          final double l = r * m + q;
-          // x = ((1 - l*A) * ab^2 ) / (2 * m)
-          // y = (-l*B * ab^2) / ( 2 * m)
-          // z = (-l*C * c^2)/ (2 * m)
-          final double denom0 = 0.5 / m;
-          final GeoPoint thePoint = new GeoPoint((1.0-l*A) * abSquared * denom0, -l*B * abSquared * denom0, -l*C * cSquared * denom0);
-          //Math is not quite accurate enough for this
-          //assert planetModel.pointOnSurface(thePoint): "Point: "+thePoint+"; Planetmodel="+planetModel+"; A="+A+" B="+B+" C="+C+" D="+D+" planetfcn="+
-          //  (thePoint.x*thePoint.x*planetModel.inverseAb*planetModel.inverseAb + thePoint.y*thePoint.y*planetModel.inverseAb*planetModel.inverseAb + thePoint.z*thePoint.z*planetModel.inverseC*planetModel.inverseC);
-          //assert evaluateIsZero(thePoint): "Evaluation of point: "+evaluate(thePoint);
-          addPoint(boundsInfo, bounds, thePoint);
-        } else if (sqrtTerm > 0.0) {
-          // Two solutions
-          final double sqrtResult = Math.sqrt(sqrtTerm);
-          final double commonDenom = 0.5/a;
-          final double m1 = (-b + sqrtResult) * commonDenom;
-          assert Math.abs(a * m1 * m1 + b * m1 + c) < MINIMUM_RESOLUTION;
-          final double m2 = (-b - sqrtResult) * commonDenom;
-          assert Math.abs(a * m2 * m2 + b * m2 + c) < MINIMUM_RESOLUTION;
-          final double l1 = r * m1 + q;
-          final double l2 = r * m2 + q;
-          // x = ((1 - l*A) * ab^2 ) / (2 * m)
-          // y = (-l*B * ab^2) / ( 2 * m)
-          // z = (-l*C * c^2)/ (2 * m)
-          final double denom1 = 0.5 / m1;
-          final double denom2 = 0.5 / m2;
-          final GeoPoint thePoint1 = new GeoPoint((1.0-l1*A) * abSquared * denom1, -l1*B * abSquared * denom1, -l1*C * cSquared * denom1);
-          final GeoPoint thePoint2 = new GeoPoint((1.0-l2*A) * abSquared * denom2, -l2*B * abSquared * denom2, -l2*C * cSquared * denom2);
-          //Math is not quite accurate enough for this
-          //assert planetModel.pointOnSurface(thePoint1): "Point1: "+thePoint1+"; Planetmodel="+planetModel+"; A="+A+" B="+B+" C="+C+" D="+D+" planetfcn="+
-          //  (thePoint1.x*thePoint1.x*planetModel.inverseAb*planetModel.inverseAb + thePoint1.y*thePoint1.y*planetModel.inverseAb*planetModel.inverseAb + thePoint1.z*thePoint1.z*planetModel.inverseC*planetModel.inverseC);
-          //assert planetModel.pointOnSurface(thePoint2): "Point1: "+thePoint2+"; Planetmodel="+planetModel+"; A="+A+" B="+B+" C="+C+" D="+D+" planetfcn="+
-          //  (thePoint2.x*thePoint2.x*planetModel.inverseAb*planetModel.inverseAb + thePoint2.y*thePoint2.y*planetModel.inverseAb*planetModel.inverseAb + thePoint2.z*thePoint2.z*planetModel.inverseC*planetModel.inverseC);
-          //assert evaluateIsZero(thePoint1): "Evaluation of point1: "+evaluate(thePoint1);
-          //assert evaluateIsZero(thePoint2): "Evaluation of point2: "+evaluate(thePoint2);
-          addPoint(boundsInfo, bounds, thePoint1);
-          addPoint(boundsInfo, bounds, thePoint2);
-        } else {
-          // No solutions
-        }
-      } else if (Math.abs(b) > MINIMUM_RESOLUTION_SQUARED) {
-        //System.err.println("Not x quadratic");
-        // a = 0, so m = - c / b
-        final double m = -c / b;
-        final double l = r * m + q;
-        // x = ((1 - l*A) * ab^2 ) / (2 * m)
-        // y = (-l*B * ab^2) / ( 2 * m)
-        // z = (-l*C * c^2)/ (2 * m)
-        final double denom0 = 0.5 / m;
-        final GeoPoint thePoint = new GeoPoint((1.0-l*A) * abSquared * denom0, -l*B * abSquared * denom0, -l*C * cSquared * denom0);
-        //Math is not quite accurate enough for this
-        //assert planetModel.pointOnSurface(thePoint): "Point: "+thePoint+"; Planetmodel="+planetModel+"; A="+A+" B="+B+" C="+C+" D="+D+" planetfcn="+
-        //  (thePoint.x*thePoint.x*planetModel.inverseAb*planetModel.inverseAb + thePoint.y*thePoint.y*planetModel.inverseAb*planetModel.inverseAb + thePoint.z*thePoint.z*planetModel.inverseC*planetModel.inverseC);
-        //assert evaluateIsZero(thePoint): "Evaluation of point: "+evaluate(thePoint);
-        addPoint(boundsInfo, bounds, thePoint);
-      } else {
-        // Something went very wrong; a = b = 0
-      }
-    }
-    
-    // Do Y
-    if (!boundsInfo.isSmallestMinY(planetModel) || !boundsInfo.isLargestMaxY(planetModel)) {
-      // For min/max x, we need to use lagrange multipliers.
-      //
-      // For this, we need grad(F(x,y,z)) = (dF/dx, dF/dy, dF/dz).
-      //
-      // Minimize and maximize f(x,y,z) = y, with respect to g(x,y,z) = Ax + By + Cz - D and h(x,y,z) = x^2/ab^2 + y^2/ab^2 + z^2/c^2 - 1
-      //
-      // grad(f(x,y,z)) = (0,1,0)
-      // grad(g(x,y,z)) = (A,B,C)
-      // grad(h(x,y,z)) = (2x/ab^2,2y/ab^2,2z/c^2)
-      //
-      // Equations we need to simultaneously solve:
-      // 
-      // grad(f(x,y,z)) = l * grad(g(x,y,z)) + m * grad(h(x,y,z))
-      // g(x,y,z) = 0
-      // h(x,y,z) = 0
-      // 
-      // Equations:
-      // 0 = l*A + m*2x/ab^2
-      // 1 = l*B + m*2y/ab^2
-      // 0 = l*C + m*2z/c^2
-      // Ax + By + Cz + D = 0
-      // x^2/ab^2 + y^2/ab^2 + z^2/c^2 - 1 = 0
-      // 
-      // Solve for x,y,z in terms of (l, m):
-      // 
-      // x = (-l*A * ab^2 ) / (2 * m)
-      // y = ((1 - l*B) * ab^2) / ( 2 * m)
-      // z = (-l*C * c^2)/ (2 * m)
-      // 
-      // Two equations, two unknowns:
-      // 
-      // A * ((-l*A * ab^2 ) / (2 * m)) + B * (((1 - l*B) * ab^2) / ( 2 * m)) + C * ((-l*C * c^2)/ (2 * m)) + D = 0
-      // 
-      // and
-      // 
-      // ((-l*A * ab^2 ) / (2 * m))^2/ab^2 + (((1 - l*B) * ab^2) / ( 2 * m))^2/ab^2 + ((-l*C * c^2)/ (2 * m))^2/c^2 - 1 = 0
-      // 
-      // Simple: solve for l and m, then find y from it.
-      // 
-      // (a) Use first equation to find l in terms of m.
-      // 
-      // A * ((-l*A * ab^2 ) / (2 * m)) + B * (((1 - l*B) * ab^2) / ( 2 * m)) + C * ((-l*C * c^2)/ (2 * m)) + D = 0
-      // A * (-l*A * ab^2 ) + B * ((1-l*B) * ab^2) + C * (-l*C * c^2) + D * 2 * m = 0
-      // -A^2*l*ab^2 + B*ab^2 - l*B^2*ab^2 - C^2*l*c^2 + D*2*m = 0
-      // - l *(A^2* ab^2 + B^2 * ab^2 + C^2 * c^2) + (B * ab^2 + D * 2 * m) = 0
-      // l = (B * ab^2 + D * 2 * m) / (A^2* ab^2 + B^2 * ab^2 + C^2 * c^2)
-      // l = B * ab^2 / (A^2* ab^2 + B^2 * ab^2 + C^2 * c^2) + m * 2 * D / (A^2* ab^2 + B^2 * ab^2 + C^2 * c^2)
-      // 
-      // For convenience:
-      // 
-      // k = 1.0 / (A^2* ab^2 + B^2 * ab^2 + C^2 * c^2)
-      // 
-      // Then:
-      // 
-      // l = B * ab^2 * k + m * 2 * D * k
-      // l = k * (B*ab^2 + m*2*D)
-      //
-      // For further convenience:
-      //
-      // q = B*ab^2*k
-      // r = 2*D*k
-      //
-      // l = (r*m + q)
-      // l^2 = (r^2 * m^2 + 2*r*m*q + q^2)
-      // 
-      // (b) Simplify the second equation before substitution
-      // 
-      // ((-l*A * ab^2 ) / (2 * m))^2/ab^2 + (((1 - l*B) * ab^2) / ( 2 * m))^2/ab^2 + ((-l*C * c^2)/ (2 * m))^2/c^2 - 1 = 0
-      // (-l*A * ab^2 )^2/ab^2 + ((1 - l*B) * ab^2)^2/ab^2 + (-l*C * c^2)^2/c^2 = 4 * m^2
-      // (-l*A)^2 * ab^2 + (1 - l*B)^2 * ab^2 + (-l*C)^2 * c^2 = 4 * m^2
-      // l^2*A^2 * ab^2 + (1 - 2*l*B + l^2*B^2) * ab^2 + l^2*C^2 * c^2 = 4 * m^2
-      // A^2*ab^2*l^2 + ab^2 - 2*B*ab^2*l + B^2*ab^2*l^2 + C^2*c^2*l^2 - 4*m^2 = 0
-      // 
-      // (c) Substitute for l, l^2
-      //
-      // A^2*ab^2*(r^2 * m^2 + 2*r*m*q + q^2) + ab^2 - 2*B*ab^2*(r*m + q) + B^2*ab^2*(r^2 * m^2 + 2*r*m*q + q^2) + C^2*c^2*(r^2 * m^2 + 2*r*m*q + q^2) - 4*m^2 = 0
-      // A^2*ab^2*r^2*m^2 + 2*A^2*ab^2*r*q*m + A^2*ab^2*q^2 + ab^2 - 2*B*ab^2*r*m - 2*B*ab^2*q + B^2*ab^2*r^2*m^2 +
-      //    2*B^2*ab^2*r*q*m + B^2*ab^2*q^2 + C^2*c^2*r^2*m^2 + 2*C^2*c^2*r*q*m + C^2*c^2*q^2 - 4*m^2 = 0
-      //
-      // (d) Group
-      //
-      // m^2 * [A^2*ab^2*r^2 + B^2*ab^2*r^2 + C^2*c^2*r^2 - 4] +
-      // m * [2*A^2*ab^2*r*q - 2*B*ab^2*r + 2*B^2*ab^2*r*q + 2*C^2*c^2*r*q] +
-      // [A^2*ab^2*q^2 + ab^2 - 2*B*ab^2*q + B^2*ab^2*q^2 + C^2*c^2*q^2]  =  0
-
-      //System.err.println("    computing Y bound");
-      
-      // Useful subexpressions for this bound
-      final double q = B*abSquared*k;
-      final double qSquared = q * q;
-
-      // Quadratic equation
-      final double a = ASquared*abSquared*rSquared + BSquared*abSquared*rSquared + CSquared*cSquared*rSquared - 4.0;
-      final double b = 2.0*ASquared*abSquared*r*q - 2.0*B*abSquared*r + 2.0*BSquared*abSquared*r*q + 2.0*CSquared*cSquared*r*q;
-      final double c = ASquared*abSquared*qSquared + abSquared - 2.0*B*abSquared*q + BSquared*abSquared*qSquared + CSquared*cSquared*qSquared;
-
-      if (Math.abs(a) >= MINIMUM_RESOLUTION_SQUARED) {
-        final double sqrtTerm = b*b - 4.0*a*c;
-        if (Math.abs(sqrtTerm) < MINIMUM_RESOLUTION_SQUARED) {
-          // One solution
-          final double m = -b / (2.0 * a);
-          final double l = r * m + q;
-          // x = (-l*A * ab^2 ) / (2 * m)
-          // y = ((1.0-l*B) * ab^2) / ( 2 * m)
-          // z = (-l*C * c^2)/ (2 * m)
-          final double denom0 = 0.5 / m;
-          final GeoPoint thePoint = new GeoPoint(-l*A * abSquared * denom0, (1.0-l*B) * abSquared * denom0, -l*C * cSquared * denom0);
-          //Math is not quite accurate enough for this
-          //assert planetModel.pointOnSurface(thePoint): "Point: "+thePoint+"; Planetmodel="+planetModel+"; A="+A+" B="+B+" C="+C+" D="+D+" planetfcn="+
-          //  (thePoint1.x*thePoint.x*planetModel.inverseAb*planetModel.inverseAb + thePoint.y*thePoint.y*planetModel.inverseAb*planetModel.inverseAb + thePoint.z*thePoint.z*planetModel.inverseC*planetModel.inverseC);
-          //assert evaluateIsZero(thePoint): "Evaluation of point: "+evaluate(thePoint);
-          addPoint(boundsInfo, bounds, thePoint);
-        } else if (sqrtTerm > 0.0) {
-          // Two solutions
-          final double sqrtResult = Math.sqrt(sqrtTerm);
-          final double commonDenom = 0.5/a;
-          final double m1 = (-b + sqrtResult) * commonDenom;
-          assert Math.abs(a * m1 * m1 + b * m1 + c) < MINIMUM_RESOLUTION;
-          final double m2 = (-b - sqrtResult) * commonDenom;
-          assert Math.abs(a * m2 * m2 + b * m2 + c) < MINIMUM_RESOLUTION;
-          final double l1 = r * m1 + q;
-          final double l2 = r * m2 + q;
-          // x = (-l*A * ab^2 ) / (2 * m)
-          // y = ((1.0-l*B) * ab^2) / ( 2 * m)
-          // z = (-l*C * c^2)/ (2 * m)
-          final double denom1 = 0.5 / m1;
-          final double denom2 = 0.5 / m2;
-          final GeoPoint thePoint1 = new GeoPoint(-l1*A * abSquared * denom1, (1.0-l1*B) * abSquared * denom1, -l1*C * cSquared * denom1);
-          final GeoPoint thePoint2 = new GeoPoint(-l2*A * abSquared * denom2, (1.0-l2*B) * abSquared * denom2, -l2*C * cSquared * denom2);
-          //Math is not quite accurate enough for this
-          //assert planetModel.pointOnSurface(thePoint1): "Point1: "+thePoint1+"; Planetmodel="+planetModel+"; A="+A+" B="+B+" C="+C+" D="+D+" planetfcn="+
-          //  (thePoint1.x*thePoint1.x*planetModel.inverseAb*planetModel.inverseAb + thePoint1.y*thePoint1.y*planetModel.inverseAb*planetModel.inverseAb + thePoint1.z*thePoint1.z*planetModel.inverseC*planetModel.inverseC);
-          //assert planetModel.pointOnSurface(thePoint2): "Point2: "+thePoint2+"; Planetmodel="+planetModel+"; A="+A+" B="+B+" C="+C+" D="+D+" planetfcn="+
-          //  (thePoint2.x*thePoint2.x*planetModel.inverseAb*planetModel.inverseAb + thePoint2.y*thePoint2.y*planetModel.inverseAb*planetModel.inverseAb + thePoint2.z*thePoint2.z*planetModel.inverseC*planetModel.inverseC);
-          //assert evaluateIsZero(thePoint1): "Evaluation of point1: "+evaluate(thePoint1);
-          //assert evaluateIsZero(thePoint2): "Evaluation of point2: "+evaluate(thePoint2);
-          addPoint(boundsInfo, bounds, thePoint1);
-          addPoint(boundsInfo, bounds, thePoint2);
-        } else {
-          // No solutions
-        }
-      } else if (Math.abs(b) > MINIMUM_RESOLUTION_SQUARED) {
-        // a = 0, so m = - c / b
-        final double m = -c / b;
-        final double l = r * m + q;
-        // x = ( -l*A * ab^2 ) / (2 * m)
-        // y = ((1-l*B) * ab^2) / ( 2 * m)
-        // z = (-l*C * c^2)/ (2 * m)
-        final double denom0 = 0.5 / m;
-        final GeoPoint thePoint = new GeoPoint(-l*A * abSquared * denom0, (1.0-l*B) * abSquared * denom0, -l*C * cSquared * denom0);
-        //Math is not quite accurate enough for this
-        //assert planetModel.pointOnSurface(thePoint): "Point: "+thePoint+"; Planetmodel="+planetModel+"; A="+A+" B="+B+" C="+C+" D="+D+" planetfcn="+
-        //  (thePoint.x*thePoint.x*planetModel.inverseAb*planetModel.inverseAb + thePoint.y*thePoint.y*planetModel.inverseAb*planetModel.inverseAb + thePoint.z*thePoint.z*planetModel.inverseC*planetModel.inverseC);
-        //assert evaluateIsZero(thePoint): "Evaluation of point: "+evaluate(thePoint);
-        addPoint(boundsInfo, bounds, thePoint);
-      } else {
-        // Something went very wrong; a = b = 0
-      }
-    }
-  }
-  
-  /**
-   * Accumulate bounds information for this plane, intersected with the unit sphere.
-   * Updates both latitude and longitude information, using max/min points found
-   * within the specified bounds.
-   *
-   * @param planetModel is the planet model to use in determining bounds.
-   * @param boundsInfo is the lat/lon info to update with additional bounding information.
-   * @param bounds     are the surfaces delineating what's inside the shape.
-   */
-  public void recordBounds(final PlanetModel planetModel, final LatLonBounds boundsInfo, final Membership... bounds) {
-    // For clarity, load local variables with good names
-    final double A = this.x;
-    final double B = this.y;
-    final double C = this.z;
-
-    // Now compute latitude min/max points
-    if (!boundsInfo.checkNoTopLatitudeBound() || !boundsInfo.checkNoBottomLatitudeBound()) {
-      //System.err.println("Looking at latitude for plane "+this);
-      // With ellipsoids, we really have only one viable way to do this computation.
-      // Specifically, we compute an appropriate vertical plane, based on the current plane's x-y orientation, and
-      // then intersect it with this one and with the ellipsoid.  This gives us zero, one, or two points to use
-      // as bounds.
-      // There is one special case: horizontal circles.  These require TWO vertical planes: one for the x, and one for
-      // the y, and we use all four resulting points in the bounds computation.
-      if ((Math.abs(A) >= MINIMUM_RESOLUTION || Math.abs(B) >= MINIMUM_RESOLUTION)) {
-        // NOT a horizontal circle!
-        //System.err.println(" Not a horizontal circle");
-        final Plane verticalPlane = constructNormalizedZPlane(A,B);
-        final GeoPoint[] points = findIntersections(planetModel, verticalPlane, bounds, NO_BOUNDS);
-        for (final GeoPoint point : points) {
-          addPoint(boundsInfo, bounds, point);
-        }
-      } else {
-        // Horizontal circle.  Since a==b, any vertical plane suffices.
-        final GeoPoint[] points = findIntersections(planetModel, normalXPlane, NO_BOUNDS, NO_BOUNDS);
-        boundsInfo.addZValue(points[0]);
-      }
-      //System.err.println("Done latitude bounds");
-    }
-
-    // First, figure out our longitude bounds, unless we no longer need to consider that
-    if (!boundsInfo.checkNoLongitudeBound()) {
-      //System.err.println("Computing longitude bounds for "+this);
-      //System.out.println("A = "+A+" B = "+B+" C = "+C+" D = "+D);
-      // Compute longitude bounds
-
-      double a;
-      double b;
-      double c;
-
-      if (Math.abs(C) < MINIMUM_RESOLUTION) {
-        // Degenerate; the equation describes a line
-        //System.out.println("It's a zero-width ellipse");
-        // Ax + By + D = 0
-        if (Math.abs(D) >= MINIMUM_RESOLUTION) {
-          if (Math.abs(A) > Math.abs(B)) {
-            // Use equation suitable for A != 0
-            // We need to find the endpoints of the zero-width ellipse.
-            // Geometrically, we have a line segment in x-y space.  We need to locate the endpoints
-            // of that line.  But luckily, we know some things: specifically, since it is a
-            // degenerate situation in projection, the C value had to have been 0.  That
-            // means that our line's endpoints will coincide with the projected ellipse.  All we
-            // need to do then is to find the intersection of the projected ellipse and the line
-            // equation:
-            //
-            // A x + B y + D = 0
-            //
-            // Since A != 0:
-            // x = (-By - D)/A
-            //
-            // The projected ellipse:
-            // x^2/a^2 + y^2/b^2 - 1 = 0
-            // Substitute:
-            // [(-By-D)/A]^2/a^2 + y^2/b^2 -1 = 0
-            // Multiply through by A^2:
-            // [-By - D]^2/a^2 + A^2*y^2/b^2 - A^2 = 0
-            // Multiply out:
-            // B^2*y^2/a^2 + 2BDy/a^2 + D^2/a^2 + A^2*y^2/b^2 - A^2 = 0
-            // Group:
-            // y^2 * [B^2/a^2 + A^2/b^2] + y [2BD/a^2] + [D^2/a^2-A^2] = 0
-
-            a = B * B * planetModel.inverseAbSquared + A * A * planetModel.inverseAbSquared;
-            b = 2.0 * B * D * planetModel.inverseAbSquared;
-            c = D * D * planetModel.inverseAbSquared - A * A;
-
-            double sqrtClause = b * b - 4.0 * a * c;
-
-            if (Math.abs(sqrtClause) < MINIMUM_RESOLUTION_SQUARED) {
-              double y0 = -b / (2.0 * a);
-              double x0 = (-D - B * y0) / A;
-              double z0 = 0.0;
-              addPoint(boundsInfo, bounds, new GeoPoint(x0, y0, z0));
-            } else if (sqrtClause > 0.0) {
-              double sqrtResult = Math.sqrt(sqrtClause);
-              double denom = 1.0 / (2.0 * a);
-              double Hdenom = 1.0 / A;
-
-              double y0a = (-b + sqrtResult) * denom;
-              double y0b = (-b - sqrtResult) * denom;
-
-              double x0a = (-D - B * y0a) * Hdenom;
-              double x0b = (-D - B * y0b) * Hdenom;
-
-              double z0a = 0.0;
-              double z0b = 0.0;
-
-              addPoint(boundsInfo, bounds, new GeoPoint(x0a, y0a, z0a));
-              addPoint(boundsInfo, bounds, new GeoPoint(x0b, y0b, z0b));
-            }
-
-          } else {
-            // Use equation suitable for B != 0
-            // Since I != 0, we rewrite:
-            // y = (-Ax - D)/B
-            a = B * B * planetModel.inverseAbSquared + A * A * planetModel.inverseAbSquared;
-            b = 2.0 * A * D * planetModel.inverseAbSquared;
-            c = D * D * planetModel.inverseAbSquared - B * B;
-
-            double sqrtClause = b * b - 4.0 * a * c;
-
-            if (Math.abs(sqrtClause) < MINIMUM_RESOLUTION_SQUARED) {
-              double x0 = -b / (2.0 * a);
-              double y0 = (-D - A * x0) / B;
-              double z0 = 0.0;
-              addPoint(boundsInfo, bounds, new GeoPoint(x0, y0, z0));
-            } else if (sqrtClause > 0.0) {
-              double sqrtResult = Math.sqrt(sqrtClause);
-              double denom = 1.0 / (2.0 * a);
-              double Idenom = 1.0 / B;
-
-              double x0a = (-b + sqrtResult) * denom;
-              double x0b = (-b - sqrtResult) * denom;
-              double y0a = (-D - A * x0a) * Idenom;
-              double y0b = (-D - A * x0b) * Idenom;
-              double z0a = 0.0;
-              double z0b = 0.0;
-
-              addPoint(boundsInfo, bounds, new GeoPoint(x0a, y0a, z0a));
-              addPoint(boundsInfo, bounds, new GeoPoint(x0b, y0b, z0b));
-            }
-          }
-        }
-
-      } else {
-        //System.err.println("General longitude bounds...");
-
-        // NOTE WELL: The x,y,z values generated here are NOT on the unit sphere.
-        // They are for lat/lon calculation purposes only.  x-y is meant to be used for longitude determination,
-        // and z for latitude, and that's all the values are good for.
-
-        // (1) Intersect the plane and the ellipsoid, and project the results into the x-y plane:
-        // From plane:
-        // z = (-Ax - By - D) / C
-        // From ellipsoid:
-        // x^2/a^2 + y^2/b^2 + [(-Ax - By - D) / C]^2/c^2 = 1
-        // Simplify/expand:
-        // C^2*x^2/a^2 + C^2*y^2/b^2 + (-Ax - By - D)^2/c^2 = C^2
-        //
-        // x^2 * C^2/a^2 + y^2 * C^2/b^2 + x^2 * A^2/c^2 + ABxy/c^2 + ADx/c^2 + ABxy/c^2 + y^2 * B^2/c^2 + BDy/c^2 + ADx/c^2 + BDy/c^2 + D^2/c^2 = C^2
-        // Group:
-        // [A^2/c^2 + C^2/a^2] x^2 + [B^2/c^2 + C^2/b^2] y^2 + [2AB/c^2]xy + [2AD/c^2]x + [2BD/c^2]y + [D^2/c^2-C^2] = 0
-        // For convenience, introduce post-projection coefficient variables to make life easier.
-        // E x^2 + F y^2 + G xy + H x + I y + J = 0
-        double E = A * A * planetModel.inverseCSquared + C * C * planetModel.inverseAbSquared;
-        double F = B * B * planetModel.inverseCSquared + C * C * planetModel.inverseAbSquared;
-        double G = 2.0 * A * B * planetModel.inverseCSquared;
-        double H = 2.0 * A * D * planetModel.inverseCSquared;
-        double I = 2.0 * B * D * planetModel.inverseCSquared;
-        double J = D * D * planetModel.inverseCSquared - C * C;
-
-        //System.err.println("E = " + E + " F = " + F + " G = " + G + " H = "+ H + " I = " + I + " J = " + J);
-
-        // Check if the origin is within, by substituting x = 0, y = 0 and seeing if less than zero
-        if (Math.abs(J) >= MINIMUM_RESOLUTION && J > 0.0) {
-          // The derivative of the curve above is:
-          // 2Exdx + 2Fydy + G(xdy+ydx) + Hdx + Idy = 0
-          // (2Ex + Gy + H)dx + (2Fy + Gx + I)dy = 0
-          // dy/dx = - (2Ex + Gy + H) / (2Fy + Gx + I)
-          //
-          // The equation of a line going through the origin with the slope dy/dx is:
-          // y = dy/dx x
-          // y = - (2Ex + Gy + H) / (2Fy + Gx + I)  x
-          // Rearrange:
-          // (2Fy + Gx + I) y + (2Ex + Gy + H) x = 0
-          // 2Fy^2 + Gxy + Iy + 2Ex^2 + Gxy + Hx = 0
-          // 2Ex^2 + 2Fy^2 + 2Gxy + Hx + Iy = 0
-          //
-          // Multiply the original equation by 2:
-          // 2E x^2 + 2F y^2 + 2G xy + 2H x + 2I y + 2J = 0
-          // Subtract one from the other, to remove the high-order terms:
-          // Hx + Iy + 2J = 0
-          // Now, we can substitute either x = or y = into the derivative equation, or into the original equation.
-          // But we will need to base this on which coefficient is non-zero
-
-          if (Math.abs(H) > Math.abs(I)) {
-            //System.err.println(" Using the y quadratic");
-            // x = (-2J - Iy)/H
-
-            // Plug into the original equation:
-            // E [(-2J - Iy)/H]^2 + F y^2 + G [(-2J - Iy)/H]y + H [(-2J - Iy)/H] + I y + J = 0
-            // E [(-2J - Iy)/H]^2 + F y^2 + G [(-2J - Iy)/H]y - J = 0
-            // Same equation as derivative equation, except for a factor of 2!  So it doesn't matter which we pick.
-
-            // Plug into derivative equation:
-            // 2E[(-2J - Iy)/H]^2 + 2Fy^2 + 2G[(-2J - Iy)/H]y + H[(-2J - Iy)/H] + Iy = 0
-            // 2E[(-2J - Iy)/H]^2 + 2Fy^2 + 2G[(-2J - Iy)/H]y - 2J = 0
-            // E[(-2J - Iy)/H]^2 + Fy^2 + G[(-2J - Iy)/H]y - J = 0
-
-            // Multiply by H^2 to make manipulation easier
-            // E[(-2J - Iy)]^2 + F*H^2*y^2 + GH[(-2J - Iy)]y - J*H^2 = 0
-            // Do the square
-            // E[4J^2 + 4IJy + I^2*y^2] + F*H^2*y^2 + GH(-2Jy - I*y^2) - J*H^2 = 0
-
-            // Multiply it out
-            // 4E*J^2 + 4EIJy + E*I^2*y^2 + H^2*Fy^2 - 2GHJy - GH*I*y^2 - J*H^2 = 0
-            // Group:
-            // y^2 [E*I^2 - GH*I + F*H^2] + y [4EIJ - 2GHJ] + [4E*J^2 - J*H^2] = 0
-
-            a = E * I * I - G * H * I + F * H * H;
-            b = 4.0 * E * I * J - 2.0 * G * H * J;
-            c = 4.0 * E * J * J - J * H * H;
-
-            //System.out.println("a="+a+" b="+b+" c="+c);
-            double sqrtClause = b * b - 4.0 * a * c;
-            //System.out.println("sqrtClause="+sqrtClause);
-
-            if (Math.abs(sqrtClause) < MINIMUM_RESOLUTION_CUBED) {
-              //System.err.println(" One solution");
-              double y0 = -b / (2.0 * a);
-              double x0 = (-2.0 * J - I * y0) / H;
-              double z0 = (-A * x0 - B * y0 - D) / C;
-
-              addPoint(boundsInfo, bounds, new GeoPoint(x0, y0, z0));
-            } else if (sqrtClause > 0.0) {
-              //System.err.println(" Two solutions");
-              double sqrtResult = Math.sqrt(sqrtClause);
-              double denom = 1.0 / (2.0 * a);
-              double Hdenom = 1.0 / H;
-              double Cdenom = 1.0 / C;
-
-              double y0a = (-b + sqrtResult) * denom;
-              double y0b = (-b - sqrtResult) * denom;
-              double x0a = (-2.0 * J - I * y0a) * Hdenom;
-              double x0b = (-2.0 * J - I * y0b) * Hdenom;
-              double z0a = (-A * x0a - B * y0a - D) * Cdenom;
-              double z0b = (-A * x0b - B * y0b - D) * Cdenom;
-
-              addPoint(boundsInfo, bounds, new GeoPoint(x0a, y0a, z0a));
-              addPoint(boundsInfo, bounds, new GeoPoint(x0b, y0b, z0b));
-            }
-
-          } else {
-            //System.err.println(" Using the x quadratic");
-            // y = (-2J - Hx)/I
-
-            // Plug into the original equation:
-            // E x^2 + F [(-2J - Hx)/I]^2 + G x[(-2J - Hx)/I] - J = 0
-
-            // Multiply by I^2 to make manipulation easier
-            // E * I^2 * x^2 + F [(-2J - Hx)]^2 + GIx[(-2J - Hx)] - J * I^2 = 0
-            // Do the square
-            // E * I^2 * x^2 + F [ 4J^2 + 4JHx + H^2*x^2] + GI[(-2Jx - H*x^2)] - J * I^2 = 0
-
-            // Multiply it out
-            // E * I^2 * x^2 + 4FJ^2 + 4FJHx + F*H^2*x^2 - 2GIJx - HGI*x^2 - J * I^2 = 0
-            // Group:
-            // x^2 [E*I^2 - GHI + F*H^2] + x [4FJH - 2GIJ] + [4FJ^2 - J*I^2] = 0
-
-            // E x^2 + F y^2 + G xy + H x + I y + J = 0
-
-            a = E * I * I - G * H * I + F * H * H;
-            b = 4.0 * F * H * J - 2.0 * G * I * J;
-            c = 4.0 * F * J * J - J * I * I;
-
-            //System.out.println("a="+a+" b="+b+" c="+c);
-            double sqrtClause = b * b - 4.0 * a * c;
-            //System.out.println("sqrtClause="+sqrtClause);
-            if (Math.abs(sqrtClause) < MINIMUM_RESOLUTION_CUBED) {
-              //System.err.println(" One solution; sqrt clause was "+sqrtClause);
-              double x0 = -b / (2.0 * a);
-              double y0 = (-2.0 * J - H * x0) / I;
-              double z0 = (-A * x0 - B * y0 - D) / C;
-              // Verify that x&y fulfill the equation
-              // 2Ex^2 + 2Fy^2 + 2Gxy + Hx + Iy = 0
-              addPoint(boundsInfo, bounds, new GeoPoint(x0, y0, z0));
-            } else if (sqrtClause > 0.0) {
-              //System.err.println(" Two solutions");
-              double sqrtResult = Math.sqrt(sqrtClause);
-              double denom = 1.0 / (2.0 * a);
-              double Idenom = 1.0 / I;
-              double Cdenom = 1.0 / C;
-
-              double x0a = (-b + sqrtResult) * denom;
-              double x0b = (-b - sqrtResult) * denom;
-              double y0a = (-2.0 * J - H * x0a) * Idenom;
-              double y0b = (-2.0 * J - H * x0b) * Idenom;
-              double z0a = (-A * x0a - B * y0a - D) * Cdenom;
-              double z0b = (-A * x0b - B * y0b - D) * Cdenom;
-
-              addPoint(boundsInfo, bounds, new GeoPoint(x0a, y0a, z0a));
-              addPoint(boundsInfo, bounds, new GeoPoint(x0b, y0b, z0b));
-            }
-          }
-        }
-      }
-    }
-
-  }
-
-  /** Add a point to boundsInfo if within a specifically bounded area.
-   * @param boundsInfo is the object to be modified.
-   * @param bounds is the area that the point must be within.
-   * @param point is the point.
-   */
-  protected static void addPoint(final Bounds boundsInfo, final Membership[] bounds, final GeoPoint point) {
-    // Make sure the discovered point is within the bounds
-    for (Membership bound : bounds) {
-      if (!bound.isWithin(point))
-        return;
-    }
-    // Add the point
-    boundsInfo.addPoint(point);
-  }
-
-  /** Add a point to boundsInfo if within a specifically bounded area.
-   * @param boundsInfo is the object to be modified.
-   * @param bounds is the area that the point must be within.
-   * @param x is the x value.
-   * @param y is the y value.
-   * @param z is the z value.
-   */
-  /*
-  protected static void addPoint(final Bounds boundsInfo, final Membership[] bounds, final double x, final double y, final double z) {
-    //System.err.println(" Want to add point x="+x+" y="+y+" z="+z);
-    // Make sure the discovered point is within the bounds
-    for (Membership bound : bounds) {
-      if (!bound.isWithin(x, y, z))
-        return;
-    }
-    // Add the point
-    //System.err.println("  point added");
-    //System.out.println("Adding point x="+x+" y="+y+" z="+z);
-    boundsInfo.addPoint(x, y, z);
-  }
-  */
-
-  /**
-   * Determine whether the plane intersects another plane within the
-   * bounds provided.
-   *
-   * @param planetModel is the planet model to use in determining intersection.
-   * @param q                 is the other plane.
-   * @param notablePoints     are points to look at to disambiguate cases when the two planes are identical.
-   * @param moreNotablePoints are additional points to look at to disambiguate cases when the two planes are identical.
-   * @param bounds            is one part of the bounds.
-   * @param moreBounds        are more bounds.
-   * @return true if there's an intersection.
-   */
-  public boolean intersects(final PlanetModel planetModel, final Plane q, final GeoPoint[] notablePoints, final GeoPoint[] moreNotablePoints, final Membership[] bounds, final Membership... moreBounds) {
-    //System.err.println("Does plane "+this+" intersect with plane "+q);
-    // If the two planes are identical, then the math will find no points of intersection.
-    // So a special case of this is to check for plane equality.  But that is not enough, because
-    // what we really need at that point is to determine whether overlap occurs between the two parts of the intersection
-    // of plane and circle.  That is, are there *any* points on the plane that are within the bounds described?
-    if (isNumericallyIdentical(q)) {
-      //System.err.println(" Identical plane");
-      // The only way to efficiently figure this out will be to have a list of trial points available to evaluate.
-      // We look for any point that fulfills all the bounds.
-      for (GeoPoint p : notablePoints) {
-        if (meetsAllBounds(p, bounds, moreBounds)) {
-          //System.err.println("  found a notable point in bounds, so intersects");
-          return true;
-        }
-      }
-      for (GeoPoint p : moreNotablePoints) {
-        if (meetsAllBounds(p, bounds, moreBounds)) {
-          //System.err.println("  found a notable point in bounds, so intersects");
-          return true;
-        }
-      }
-      //System.err.println("  no notable points inside found; no intersection");
-      return false;
-    }
-    return findIntersections(planetModel, q, bounds, moreBounds).length > 0;
-  }
-
-  /**
-   * Returns true if this plane and the other plane are identical within the margin of error.
-   * @param p is the plane to compare against.
-   * @return true if the planes are numerically identical.
-   */
-  protected boolean isNumericallyIdentical(final Plane p) {
-    // We can get the correlation by just doing a parallel plane check.  If that passes, then compute a point on the plane
-    // (using D) and see if it also on the other plane.
-    if (Math.abs(this.y * p.z - this.z * p.y) >= MINIMUM_RESOLUTION)
-      return false;
-    if (Math.abs(this.z * p.x - this.x * p.z) >= MINIMUM_RESOLUTION)
-      return false;
-    if (Math.abs(this.x * p.y - this.y * p.x) >= MINIMUM_RESOLUTION)
-      return false;
-
-    // Now, see whether the parallel planes are in fact on top of one another.
-    // The math:
-    // We need a single point that fulfills:
-    // Ax + By + Cz + D = 0
-    // Pick:
-    // x0 = -(A * D) / (A^2 + B^2 + C^2)
-    // y0 = -(B * D) / (A^2 + B^2 + C^2)
-    // z0 = -(C * D) / (A^2 + B^2 + C^2)
-    // Check:
-    // A (x0) + B (y0) + C (z0) + D =? 0
-    // A (-(A * D) / (A^2 + B^2 + C^2)) + B (-(B * D) / (A^2 + B^2 + C^2)) + C (-(C * D) / (A^2 + B^2 + C^2)) + D ?= 0
-    // -D [ A^2 / (A^2 + B^2 + C^2) + B^2 / (A^2 + B^2 + C^2) + C^2 / (A^2 + B^2 + C^2)] + D ?= 0
-    // Yes.
-    final double denom = 1.0 / (p.x * p.x + p.y * p.y + p.z * p.z);
-    return evaluateIsZero(-p.x * p.D * denom, -p.y * p.D * denom, -p.z * p.D * denom);
-  }
-
-  /**
-   * Check if a vector meets the provided bounds.
-   * @param p is the vector.
-   * @param bounds are the bounds.
-   * @return true if the vector describes a point within the bounds.
-   */
-  protected static boolean meetsAllBounds(final Vector p, final Membership[] bounds) {
-    return meetsAllBounds(p.x, p.y, p.z, bounds);
-  }
-
-  /**
-   * Check if a vector meets the provided bounds.
-   * @param x is the x value.
-   * @param y is the y value.
-   * @param z is the z value.
-   * @param bounds are the bounds.
-   * @return true if the vector describes a point within the bounds.
-   */
-  protected static boolean meetsAllBounds(final double x, final double y, final double z, final Membership[] bounds) {
-    for (final Membership bound : bounds) {
-      if (!bound.isWithin(x,y,z))
-        return false;
-    }
-    return true;
-  }
-
-  /**
-   * Check if a vector meets the provided bounds.
-   * @param p is the vector.
-   * @param bounds are the bounds.
-   * @param moreBounds are an additional set of bounds.
-   * @return true if the vector describes a point within the bounds.
-   */
-  protected static boolean meetsAllBounds(final Vector p, final Membership[] bounds, final Membership[] moreBounds) {
-    return meetsAllBounds(p.x, p.y, p.z, bounds, moreBounds);
-  }
-
-  /**
-   * Check if a vector meets the provided bounds.
-   * @param x is the x value.
-   * @param y is the y value.
-   * @param z is the z value.
-   * @param bounds are the bounds.
-   * @param moreBounds are an additional set of bounds.
-   * @return true if the vector describes a point within the bounds.
-   */
-  protected static boolean meetsAllBounds(final double x, final double y, final double z, final Membership[] bounds,
-                                          final Membership[] moreBounds) {
-    return meetsAllBounds(x,y,z, bounds) && meetsAllBounds(x,y,z, moreBounds);
-  }
-
-  /**
-   * Find a sample point on the intersection between two planes and the world.
-   * @param planetModel is the planet model.
-   * @param q is the second plane to consider.
-   * @return a sample point that is on the intersection between the two planes and the world.
-   */
-  public GeoPoint getSampleIntersectionPoint(final PlanetModel planetModel, final Plane q) {
-    final GeoPoint[] intersections = findIntersections(planetModel, q, NO_BOUNDS, NO_BOUNDS);
-    if (intersections.length == 0)
-      return null;
-    return intersections[0];
-  }
-
-  @Override
-  public String toString() {
-    return "[A=" + x + ", B=" + y + "; C=" + z + "; D=" + D + "]";
-  }
-
-  @Override
-  public boolean equals(Object o) {
-    if (!super.equals(o))
-      return false;
-    if (!(o instanceof Plane))
-      return false;
-    Plane other = (Plane) o;
-    return other.D == D;
-  }
-
-  @Override
-  public int hashCode() {
-    int result = super.hashCode();
-    long temp;
-    temp = Double.doubleToLongBits(D);
-    result = 31 * result + (int) (temp ^ (temp >>> 32));
-    return result;
-  }
-}


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