org.apache.lucene/lucene-spatial3d/8.2.0 : org/apache/lucene/spatial3d/geom/Vector.java

Vector
http://lucene.apache.org/lucene-parent/lucene-spatial3d: Lucene Spatial shapes implemented using 3D planar geometry (The Apache Software Foundation)
Apache 2
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 * 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
 *
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 * 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
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package org.apache.lucene.spatial3d.geom;

A 3d vector in space, not necessarily
going through the origin.
@lucene.experimental /**
 * A 3d vector in space, not necessarily
 * going through the origin.
 *
 * @lucene.experimental
 */
public class Vector {
  Values that are all considered to be essentially zero have a magnitude
less than this.
/**
   * Values that are all considered to be essentially zero have a magnitude
   * less than this.
   */
  public static final double MINIMUM_RESOLUTION = 1.0e-12;
  Angular version of minimum resolution.
/**
   * Angular version of minimum resolution.
   */
  public static final double MINIMUM_ANGULAR_RESOLUTION = Math.PI * MINIMUM_RESOLUTION;
  For squared quantities, the bound is squared too.
/**
   * For squared quantities, the bound is squared too.
   */
  public static final double MINIMUM_RESOLUTION_SQUARED = MINIMUM_RESOLUTION * MINIMUM_RESOLUTION;
  For cubed quantities, cube the bound.
/**
   * For cubed quantities, cube the bound.
   */
  public static final double MINIMUM_RESOLUTION_CUBED = MINIMUM_RESOLUTION_SQUARED * MINIMUM_RESOLUTION;

  The x value /** The x value */
  public final double x;
  The y value /** The y value */
  public final double y;
  The z value /** The z value */
  public final double z;

  Gram-Schmidt convergence envelope is a bit smaller than we really need because we don't want the math to fail afterwards in
other places.
/**
    * Gram-Schmidt convergence envelope is a bit smaller than we really need because we don't want the math to fail afterwards in
    * other places.
    */
  private static final double MINIMUM_GRAM_SCHMIDT_ENVELOPE = MINIMUM_RESOLUTION * 0.5;
  
  Construct from (U.S.) x,y,z coordinates.
Params: x – is the x value.
y – is the y value.
z – is the z value./**
   * Construct from (U.S.) x,y,z coordinates.
   *@param x is the x value.
   *@param y is the y value.
   *@param z is the z value.
   */
  public Vector(double x, double y, double z) {
    this.x = x;
    this.y = y;
    this.z = z;
  }

  Construct a vector that is perpendicular to
two other (non-zero) vectors.  If the vectors are parallel,
IllegalArgumentException will be thrown.
Produces a normalized final vector.
Params: A – is the first vector
BX – is the X value of the second
BY – is the Y value of the second
BZ – is the Z value of the second/**
   * Construct a vector that is perpendicular to
   * two other (non-zero) vectors.  If the vectors are parallel,
   * IllegalArgumentException will be thrown.
   * Produces a normalized final vector.
   *
   * @param A is the first vector
   * @param BX is the X value of the second 
   * @param BY is the Y value of the second
   * @param BZ is the Z value of the second
   */
  public Vector(final Vector A, final double BX, final double BY, final double BZ) {
    // We're really looking at two vectors and computing a perpendicular one from that.
    this(A.x, A.y, A.z, BX, BY, BZ);
  }
  
  Construct a vector that is perpendicular to
two other (non-zero) vectors.  If the vectors are parallel,
IllegalArgumentException will be thrown.
Produces a normalized final vector.
Params: AX – is the X value of the first
AY – is the Y value of the first
AZ – is the Z value of the first
BX – is the X value of the second
BY – is the Y value of the second
BZ – is the Z value of the second/**
   * Construct a vector that is perpendicular to
   * two other (non-zero) vectors.  If the vectors are parallel,
   * IllegalArgumentException will be thrown.
   * Produces a normalized final vector.
   *
   * @param AX is the X value of the first 
   * @param AY is the Y value of the first
   * @param AZ is the Z value of the first
   * @param BX is the X value of the second 
   * @param BY is the Y value of the second
   * @param BZ is the Z value of the second
   */
  public Vector(final double AX, final double AY, final double AZ, final double BX, final double BY, final double BZ) {
    // We're really looking at two vectors and computing a perpendicular one from that.
    // We can think of this as having three points -- the origin, and two points that aren't the origin.
    // Normally, we can compute the perpendicular vector this way:
    // x = u2v3 - u3v2
    // y = u3v1 - u1v3
    // z = u1v2 - u2v1
    // Sometimes that produces a plane that does not contain the original three points, however, due to
    // numerical precision issues.  Then we continue making the answer more precise using the
    // Gram-Schmidt process: https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
    
    // Compute the naive perpendicular
    final double thisX = AY * BZ - AZ * BY;
    final double thisY = AZ * BX - AX * BZ;
    final double thisZ = AX * BY - AY * BX;
    
    final double magnitude = magnitude(thisX, thisY, thisZ);
    if (magnitude == 0.0) {
      throw new IllegalArgumentException("Degenerate/parallel vector constructed");
    }
    final double inverseMagnitude = 1.0/magnitude;
    
    double normalizeX = thisX * inverseMagnitude;
    double normalizeY = thisY * inverseMagnitude;
    double normalizeZ = thisZ * inverseMagnitude;
    // For a plane to work, the dot product between the normal vector
    // and the points needs to be less than the minimum resolution.
    // This is sometimes not true for points that are very close. Therefore
    // we need to adjust
    int i = 0;
    while (true) {
      final double currentDotProdA = AX * normalizeX + AY * normalizeY + AZ * normalizeZ;
      final double currentDotProdB = BX * normalizeX + BY * normalizeY + BZ * normalizeZ;
      if (Math.abs(currentDotProdA) < MINIMUM_GRAM_SCHMIDT_ENVELOPE && Math.abs(currentDotProdB) < MINIMUM_GRAM_SCHMIDT_ENVELOPE) {
        break;
      }
      // Converge on the one that has largest dot product
      final double currentVectorX;
      final double currentVectorY;
      final double currentVectorZ;
      final double currentDotProd;
      if (Math.abs(currentDotProdA) > Math.abs(currentDotProdB)) {
        currentVectorX = AX;
        currentVectorY = AY;
        currentVectorZ = AZ;
        currentDotProd = currentDotProdA;
      } else {
        currentVectorX = BX;
        currentVectorY = BY;
        currentVectorZ = BZ;
        currentDotProd = currentDotProdB;
      }

      // Adjust
      normalizeX = normalizeX - currentDotProd * currentVectorX;
      normalizeY = normalizeY - currentDotProd * currentVectorY;
      normalizeZ = normalizeZ - currentDotProd * currentVectorZ;
      // Normalize
      final double correctedMagnitude = magnitude(normalizeX, normalizeY, normalizeZ);
      final double inverseCorrectedMagnitude = 1.0 / correctedMagnitude;
      normalizeX = normalizeX * inverseCorrectedMagnitude;
      normalizeY = normalizeY * inverseCorrectedMagnitude;
      normalizeZ = normalizeZ * inverseCorrectedMagnitude;
      //This is  probably not needed as the method seems to converge
      //quite quickly. But it is safer to have a way out.
      if (i++ > 10) {
        throw new IllegalArgumentException("Plane could not be constructed! Could not find a normal vector.");
      }
    }
    this.x = normalizeX;
    this.y = normalizeY;
    this.z = normalizeZ;
  }

  Construct a vector that is perpendicular to
two other (non-zero) vectors.  If the vectors are parallel,
IllegalArgumentException will be thrown.
Produces a normalized final vector.
Params: A – is the first vector
B – is the second/**
   * Construct a vector that is perpendicular to
   * two other (non-zero) vectors.  If the vectors are parallel,
   * IllegalArgumentException will be thrown.
   * Produces a normalized final vector.
   *
   * @param A is the first vector
   * @param B is the second
   */
  public Vector(final Vector A, final Vector B) {
    this(A, B.x, B.y, B.z);
  }

  Compute a magnitude of an x,y,z value.
/** Compute a magnitude of an x,y,z value.
   */
  public static double magnitude(final double x, final double y, final double z) {
    return Math.sqrt(x*x + y*y + z*z);
  }
  
  Compute a normalized unit vector based on the current vector.
Returns: the normalized vector, or null if the current vector has
a magnitude of zero./**
   * Compute a normalized unit vector based on the current vector.
   *
   * @return the normalized vector, or null if the current vector has
   * a magnitude of zero.
   */
  public Vector normalize() {
    double denom = magnitude();
    if (denom < MINIMUM_RESOLUTION)
      // Degenerate, can't normalize
      return null;
    double normFactor = 1.0 / denom;
    return new Vector(x * normFactor, y * normFactor, z * normFactor);
  }

  Evaluate the cross product of two vectors against a point.
If the dot product of the resultant vector resolves to "zero", then
return true.
Params: A – is the first vector to use for the cross product.
B – is the second vector to use for the cross product.
point – is the point to evaluate.
Returns: true if we get a zero dot product./**
    * Evaluate the cross product of two vectors against a point.
    * If the dot product of the resultant vector resolves to "zero", then
    * return true.
    * @param A is the first vector to use for the cross product.
    * @param B is the second vector to use for the cross product.
    * @param point is the point to evaluate.
    * @return true if we get a zero dot product.
    */
  public static boolean crossProductEvaluateIsZero(final Vector A, final Vector B, final Vector point) {
    // Include Gram-Schmidt in-line so we avoid creating objects unnecessarily
    // Compute the naive perpendicular
    final double thisX = A.y * B.z - A.z * B.y;
    final double thisY = A.z * B.x - A.x * B.z;
    final double thisZ = A.x * B.y - A.y * B.x;
    
    final double magnitude = magnitude(thisX, thisY, thisZ);
    if (magnitude == 0.0) {
      return true;
    }
    
    final double inverseMagnitude = 1.0/magnitude;
    
    double normalizeX = thisX * inverseMagnitude;
    double normalizeY = thisY * inverseMagnitude;
    double normalizeZ = thisZ * inverseMagnitude;
    // For a plane to work, the dot product between the normal vector
    // and the points needs to be less than the minimum resolution.
    // This is sometimes not true for points that are very close. Therefore
    // we need to adjust
    int i = 0;
    while (true) {
      final double currentDotProdA = A.x * normalizeX + A.y * normalizeY + A.z * normalizeZ;
      final double currentDotProdB = B.x * normalizeX + B.y * normalizeY + B.z * normalizeZ;
      if (Math.abs(currentDotProdA) < MINIMUM_GRAM_SCHMIDT_ENVELOPE && Math.abs(currentDotProdB) < MINIMUM_GRAM_SCHMIDT_ENVELOPE) {
        break;
      }
      // Converge on the one that has largest dot product
      final double currentVectorX;
      final double currentVectorY;
      final double currentVectorZ;
      final double currentDotProd;
      if (Math.abs(currentDotProdA) > Math.abs(currentDotProdB)) {
        currentVectorX = A.x;
        currentVectorY = A.y;
        currentVectorZ = A.z;
        currentDotProd = currentDotProdA;
      } else {
        currentVectorX = B.x;
        currentVectorY = B.y;
        currentVectorZ = B.z;
        currentDotProd = currentDotProdB;
      }

      // Adjust
      normalizeX = normalizeX - currentDotProd * currentVectorX;
      normalizeY = normalizeY - currentDotProd * currentVectorY;
      normalizeZ = normalizeZ - currentDotProd * currentVectorZ;
      // Normalize
      final double correctedMagnitude = magnitude(normalizeX, normalizeY, normalizeZ);
      final double inverseCorrectedMagnitude = 1.0 / correctedMagnitude;
      normalizeX = normalizeX * inverseCorrectedMagnitude;
      normalizeY = normalizeY * inverseCorrectedMagnitude;
      normalizeZ = normalizeZ * inverseCorrectedMagnitude;
      //This is  probably not needed as the method seems to converge
      //quite quickly. But it is safer to have a way out.
      if (i++ > 10) {
        throw new IllegalArgumentException("Plane could not be constructed! Could not find a normal vector.");
      }
    }
    return Math.abs(normalizeX * point.x + normalizeY * point.y + normalizeZ * point.z) < MINIMUM_RESOLUTION;
  }

  Do a dot product.
Params: v – is the vector to multiply.
Returns: the result./**
   * Do a dot product.
   *
   * @param v is the vector to multiply.
   * @return the result.
   */
  public double dotProduct(final Vector v) {
    return this.x * v.x + this.y * v.y + this.z * v.z;
  }

  Do a dot product.
Params: x – is the x value of the vector to multiply.
y – is the y value of the vector to multiply.
z – is the z value of the vector to multiply.
Returns: the result./**
   * Do a dot product.
   *
   * @param x is the x value of the vector to multiply.
   * @param y is the y value of the vector to multiply.
   * @param z is the z value of the vector to multiply.
   * @return the result.
   */
  public double dotProduct(final double x, final double y, final double z) {
    return this.x * x + this.y * y + this.z * z;
  }

  Determine if this vector, taken from the origin,
describes a point within a set of planes.
Params: bounds –     is the first part of the set of planes.
moreBounds – is the second part of the set of planes.
Returns: true if the point is within the bounds./**
   * Determine if this vector, taken from the origin,
   * describes a point within a set of planes.
   *
   * @param bounds     is the first part of the set of planes.
   * @param moreBounds is the second part of the set of planes.
   * @return true if the point is within the bounds.
   */
  public boolean isWithin(final Membership[] bounds, final Membership... moreBounds) {
    // Return true if the point described is within all provided bounds
    //System.err.println("  checking if "+this+" is within bounds");
    for (final Membership bound : bounds) {
      if (bound != null && !bound.isWithin(this)) {
        //System.err.println("    NOT within "+bound);
        return false;
      }
    }
    for (final Membership bound : moreBounds) {
      if (bound != null && !bound.isWithin(this)) {
        //System.err.println("    NOT within "+bound);
        return false;
      }
    }
    //System.err.println("    is within");
    return true;
  }

  Translate vector.
/**
   * Translate vector.
   */
  public Vector translate(final double xOffset, final double yOffset, final double zOffset) {
    return new Vector(x - xOffset, y - yOffset, z - zOffset);
  }

  Rotate vector counter-clockwise in x-y by an angle.
/**
   * Rotate vector counter-clockwise in x-y by an angle.
   */
  public Vector rotateXY(final double angle) {
    return rotateXY(Math.sin(angle), Math.cos(angle));
  }

  Rotate vector counter-clockwise in x-y by an angle, expressed as sin and cos.
/**
   * Rotate vector counter-clockwise in x-y by an angle, expressed as sin and cos.
   */
  public Vector rotateXY(final double sinAngle, final double cosAngle) {
    return new Vector(x * cosAngle - y * sinAngle, x * sinAngle + y * cosAngle, z);
  }

  Rotate vector counter-clockwise in x-z by an angle.
/**
   * Rotate vector counter-clockwise in x-z by an angle.
   */
  public Vector rotateXZ(final double angle) {
    return rotateXZ(Math.sin(angle), Math.cos(angle));
  }

  Rotate vector counter-clockwise in x-z by an angle, expressed as sin and cos.
/**
   * Rotate vector counter-clockwise in x-z by an angle, expressed as sin and cos.
   */
  public Vector rotateXZ(final double sinAngle, final double cosAngle) {
    return new Vector(x * cosAngle - z * sinAngle, y, x * sinAngle + z * cosAngle);
  }

  Rotate vector counter-clockwise in z-y by an angle.
/**
   * Rotate vector counter-clockwise in z-y by an angle.
   */
  public Vector rotateZY(final double angle) {
    return rotateZY(Math.sin(angle), Math.cos(angle));
  }

  Rotate vector counter-clockwise in z-y by an angle, expressed as sin and cos.
/**
   * Rotate vector counter-clockwise in z-y by an angle, expressed as sin and cos.
   */
  public Vector rotateZY(final double sinAngle, final double cosAngle) {
    return new Vector(x, z * sinAngle + y * cosAngle, z * cosAngle - y * sinAngle);
  }

  Compute the square of a straight-line distance to a point described by the
vector taken from the origin.
Monotonically increasing for arc distances up to PI.
Params: v – is the vector to compute a distance to.
Returns: the square of the linear distance./**
   * Compute the square of a straight-line distance to a point described by the
   * vector taken from the origin.
   * Monotonically increasing for arc distances up to PI.
   *
   * @param v is the vector to compute a distance to.
   * @return the square of the linear distance.
   */
  public double linearDistanceSquared(final Vector v) {
    double deltaX = this.x - v.x;
    double deltaY = this.y - v.y;
    double deltaZ = this.z - v.z;
    return deltaX * deltaX + deltaY * deltaY + deltaZ * deltaZ;
  }

  Compute the square of a straight-line distance to a point described by the
vector taken from the origin.
Monotonically increasing for arc distances up to PI.
Params: x – is the x part of the vector to compute a distance to.
y – is the y part of the vector to compute a distance to.
z – is the z part of the vector to compute a distance to.
Returns: the square of the linear distance./**
   * Compute the square of a straight-line distance to a point described by the
   * vector taken from the origin.
   * Monotonically increasing for arc distances up to PI.
   *
   * @param x is the x part of the vector to compute a distance to.
   * @param y is the y part of the vector to compute a distance to.
   * @param z is the z part of the vector to compute a distance to.
   * @return the square of the linear distance.
   */
  public double linearDistanceSquared(final double x, final double y, final double z) {
    double deltaX = this.x - x;
    double deltaY = this.y - y;
    double deltaZ = this.z - z;
    return deltaX * deltaX + deltaY * deltaY + deltaZ * deltaZ;
  }

  Compute the straight-line distance to a point described by the
vector taken from the origin.
Monotonically increasing for arc distances up to PI.
Params: v – is the vector to compute a distance to.
Returns: the linear distance./**
   * Compute the straight-line distance to a point described by the
   * vector taken from the origin.
   * Monotonically increasing for arc distances up to PI.
   *
   * @param v is the vector to compute a distance to.
   * @return the linear distance.
   */
  public double linearDistance(final Vector v) {
    return Math.sqrt(linearDistanceSquared(v));
  }

  Compute the straight-line distance to a point described by the
vector taken from the origin.
Monotonically increasing for arc distances up to PI.
Params: x – is the x part of the vector to compute a distance to.
y – is the y part of the vector to compute a distance to.
z – is the z part of the vector to compute a distance to.
Returns: the linear distance./**
   * Compute the straight-line distance to a point described by the
   * vector taken from the origin.
   * Monotonically increasing for arc distances up to PI.
   *
   * @param x is the x part of the vector to compute a distance to.
   * @param y is the y part of the vector to compute a distance to.
   * @param z is the z part of the vector to compute a distance to.
   * @return the linear distance.
   */
  public double linearDistance(final double x, final double y, final double z) {
    return Math.sqrt(linearDistanceSquared(x, y, z));
  }

  Compute the square of the normal distance to a vector described by a
vector taken from the origin.
Monotonically increasing for arc distances up to PI/2.
Params: v – is the vector to compute a distance to.
Returns: the square of the normal distance./**
   * Compute the square of the normal distance to a vector described by a
   * vector taken from the origin.
   * Monotonically increasing for arc distances up to PI/2.
   *
   * @param v is the vector to compute a distance to.
   * @return the square of the normal distance.
   */
  public double normalDistanceSquared(final Vector v) {
    double t = dotProduct(v);
    double deltaX = this.x * t - v.x;
    double deltaY = this.y * t - v.y;
    double deltaZ = this.z * t - v.z;
    return deltaX * deltaX + deltaY * deltaY + deltaZ * deltaZ;
  }

  Compute the square of the normal distance to a vector described by a
vector taken from the origin.
Monotonically increasing for arc distances up to PI/2.
Params: x – is the x part of the vector to compute a distance to.
y – is the y part of the vector to compute a distance to.
z – is the z part of the vector to compute a distance to.
Returns: the square of the normal distance./**
   * Compute the square of the normal distance to a vector described by a
   * vector taken from the origin.
   * Monotonically increasing for arc distances up to PI/2.
   *
   * @param x is the x part of the vector to compute a distance to.
   * @param y is the y part of the vector to compute a distance to.
   * @param z is the z part of the vector to compute a distance to.
   * @return the square of the normal distance.
   */
  public double normalDistanceSquared(final double x, final double y, final double z) {
    double t = dotProduct(x, y, z);
    double deltaX = this.x * t - x;
    double deltaY = this.y * t - y;
    double deltaZ = this.z * t - z;
    return deltaX * deltaX + deltaY * deltaY + deltaZ * deltaZ;
  }

  Compute the normal (perpendicular) distance to a vector described by a
vector taken from the origin.
Monotonically increasing for arc distances up to PI/2.
Params: v – is the vector to compute a distance to.
Returns: the normal distance./**
   * Compute the normal (perpendicular) distance to a vector described by a
   * vector taken from the origin.
   * Monotonically increasing for arc distances up to PI/2.
   *
   * @param v is the vector to compute a distance to.
   * @return the normal distance.
   */
  public double normalDistance(final Vector v) {
    return Math.sqrt(normalDistanceSquared(v));
  }

  Compute the normal (perpendicular) distance to a vector described by a
vector taken from the origin.
Monotonically increasing for arc distances up to PI/2.
Params: x – is the x part of the vector to compute a distance to.
y – is the y part of the vector to compute a distance to.
z – is the z part of the vector to compute a distance to.
Returns: the normal distance./**
   * Compute the normal (perpendicular) distance to a vector described by a
   * vector taken from the origin.
   * Monotonically increasing for arc distances up to PI/2.
   *
   * @param x is the x part of the vector to compute a distance to.
   * @param y is the y part of the vector to compute a distance to.
   * @param z is the z part of the vector to compute a distance to.
   * @return the normal distance.
   */
  public double normalDistance(final double x, final double y, final double z) {
    return Math.sqrt(normalDistanceSquared(x, y, z));
  }

  Compute the magnitude of this vector.
Returns: the magnitude./**
   * Compute the magnitude of this vector.
   *
   * @return the magnitude.
   */
  public double magnitude() {
    return magnitude(x,y,z);
  }

  Compute whether two vectors are numerically identical.
Params: otherX – is the other vector X.
otherY – is the other vector Y.
otherZ – is the other vector Z.
Returns: true if they are numerically identical./**
   * Compute whether two vectors are numerically identical.
   * @param otherX is the other vector X.
   * @param otherY is the other vector Y.
   * @param otherZ is the other vector Z.
   * @return true if they are numerically identical.
   */
  public boolean isNumericallyIdentical(final double otherX, final double otherY, final double otherZ) {
    final double deltaX = x - otherX;
    final double deltaY = y - otherY;
    final double deltaZ = z - otherZ;
    return deltaX * deltaX + deltaY * deltaY + deltaZ * deltaZ < MINIMUM_RESOLUTION_SQUARED;
  }

  Compute whether two vectors are numerically identical.
Params: other – is the other vector.
Returns: true if they are numerically identical./**
   * Compute whether two vectors are numerically identical.
   * @param other is the other vector.
   * @return true if they are numerically identical.
   */
  public boolean isNumericallyIdentical(final Vector other) {
    final double deltaX = x - other.x;
    final double deltaY = y - other.y;
    final double deltaZ = z - other.z;
    return deltaX * deltaX + deltaY * deltaY + deltaZ * deltaZ < MINIMUM_RESOLUTION_SQUARED;
  }

  Compute whether two vectors are parallel.
Params: otherX – is the other vector X.
otherY – is the other vector Y.
otherZ – is the other vector Z.
Returns: true if they are parallel./**
   * Compute whether two vectors are parallel.
   * @param otherX is the other vector X.
   * @param otherY is the other vector Y.
   * @param otherZ is the other vector Z.
   * @return true if they are parallel.
   */
  public boolean isParallel(final double otherX, final double otherY, final double otherZ) {
    final double thisX = y * otherZ - z * otherY;
    final double thisY = z * otherX - x * otherZ;
    final double thisZ = x * otherY - y * otherX;
    return thisX * thisX + thisY * thisY + thisZ * thisZ < MINIMUM_RESOLUTION_SQUARED;
  }

  Compute whether two vectors are numerically identical.
Params: other – is the other vector.
Returns: true if they are parallel./**
   * Compute whether two vectors are numerically identical.
   * @param other is the other vector.
   * @return true if they are parallel.
   */
  public boolean isParallel(final Vector other) {
    final double thisX = y * other.z - z * other.y;
    final double thisY = z * other.x - x * other.z;
    final double thisZ = x * other.y - y * other.x;
    return thisX * thisX + thisY * thisY + thisZ * thisZ < MINIMUM_RESOLUTION_SQUARED;
  }

  Compute the desired magnitude of a unit vector projected to a given
planet model.
Params: planetModel – is the planet model.
x – is the unit vector x value.
y – is the unit vector y value.
z – is the unit vector z value.
Returns: a magnitude value for that (x,y,z) that projects the vector onto the specified ellipsoid./** Compute the desired magnitude of a unit vector projected to a given
   * planet model.
   * @param planetModel is the planet model.
   * @param x is the unit vector x value.
   * @param y is the unit vector y value.
   * @param z is the unit vector z value.
   * @return a magnitude value for that (x,y,z) that projects the vector onto the specified ellipsoid.
   */
  static double computeDesiredEllipsoidMagnitude(final PlanetModel planetModel, final double x, final double y, final double z) {
    return 1.0 / Math.sqrt(x*x*planetModel.inverseAbSquared + y*y*planetModel.inverseAbSquared + z*z*planetModel.inverseCSquared);
  }

  Compute the desired magnitude of a unit vector projected to a given
planet model.  The unit vector is specified only by a z value.
Params: planetModel – is the planet model.
z – is the unit vector z value.
Returns: a magnitude value for that z value that projects the vector onto the specified ellipsoid./** Compute the desired magnitude of a unit vector projected to a given
   * planet model.  The unit vector is specified only by a z value.
   * @param planetModel is the planet model.
   * @param z is the unit vector z value.
   * @return a magnitude value for that z value that projects the vector onto the specified ellipsoid.
   */
  static double computeDesiredEllipsoidMagnitude(final PlanetModel planetModel, final double z) {
    return 1.0 / Math.sqrt((1.0-z*z)*planetModel.inverseAbSquared + z*z*planetModel.inverseCSquared);
  }

  @Override
  public boolean equals(Object o) {
    if (!(o instanceof Vector))
      return false;
    Vector other = (Vector) o;
    return (other.x == x && other.y == y && other.z == z);
  }

  @Override
  public int hashCode() {
    int result;
    long temp;
    temp = Double.doubleToLongBits(x);
    result = (int) (temp ^ (temp >>> 32));
    temp = Double.doubleToLongBits(y);
    result = 31 * result + (int) (temp ^ (temp >>> 32));
    temp = Double.doubleToLongBits(z);
    result = 31 * result + (int) (temp ^ (temp >>> 32));
    return result;
  }

  @Override
  public String toString() {
    return "[X=" + x + ", Y=" + y + ", Z=" + z + "]";
  }
}
Params:	A – is the first vector to use for the cross product. B – is the second vector to use for the cross product. point – is the point to evaluate.
Returns:	true if we get a zero dot product.
Params:	x – is the x value of the vector to multiply. y – is the y value of the vector to multiply. z – is the z value of the vector to multiply.
Returns:	the result.
Params:	bounds – is the first part of the set of planes. moreBounds – is the second part of the set of planes.
Returns:	true if the point is within the bounds.
Params:	v – is the vector to compute a distance to.
Returns:	the square of the linear distance.
Params:	x – is the x part of the vector to compute a distance to. y – is the y part of the vector to compute a distance to. z – is the z part of the vector to compute a distance to.
Returns:	the square of the linear distance.
Params:	otherX – is the other vector X. otherY – is the other vector Y. otherZ – is the other vector Z.
Returns:	true if they are numerically identical.
Params:	other – is the other vector.
Returns:	true if they are numerically identical.
Params:	planetModel – is the planet model. x – is the unit vector x value. y – is the unit vector y value. z – is the unit vector z value.
Returns:	a magnitude value for that (x,y,z) that projects the vector onto the specified ellipsoid.
Params:	planetModel – is the planet model. z – is the unit vector z value.
Returns:	a magnitude value for that z value that projects the vector onto the specified ellipsoid.
/

org.apache.lucene/ lucene-spatial3d/ 8.2.0/ org/apache/lucene/spatial3d/geom/Vector.java
