content: /*
  * Copyright (c) 1997 - 2016
  * Actelion Pharmaceuticals Ltd.
  * Gewerbestrasse 16
  * CH-4123 Allschwil, Switzerland
  *
  * All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions are met:
  *
  * 1. Redistributions of source code must retain the above copyright notice, this
  *    list of conditions and the following disclaimer.
  * 2. Redistributions in binary form must reproduce the above copyright notice,
  *    this list of conditions and the following disclaimer in the documentation
  *    and/or other materials provided with the distribution.
  * 3. Neither the name of the the copyright holder nor the
  *    names of its contributors may be used to endorse or promote products
  *    derived from this software without specific prior written permission.
  *
  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
  * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
  * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
  * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  *
  */
  
  package com.actelion.research.chem.forcefield.mmff;
  
  import java.lang.Math;
  import java.lang.Double;
  
  import com.actelion.research.chem.ExtendedMolecule;
  
  /**
   * The Vector3 class provides common vector operations used throughout the
   * MMFF codebase. This is not supposed to be a comprehensive vector
   * library;  instead, only those functions which were needed have been
   * implemented.
   */
  public class Vector3 {
      private final static double TOL = 0.01;
  
      public final double x;
      public final double y;
      public final double z;
  
      /**
       * Constructs a new vector with default coordinates.
       */
      public Vector3() {
          x = 0.0;
          y = 0.0;
          z = 0.0;
      }
  
      /**
       * Constructs a new vector with given x, y and z coordinates.
       *  @param x X coordinate.
       *  @param y Y coordinate.
       *  @param z Z coordinate.
       */
      public Vector3(double x, double y, double z) {
          this.x = x;
          this.y = y;
          this.z = z;
      }
  
      /**
       * Copy constructor, copies the x,y,z coordinates from another vector.
       */
      public Vector3(Vector3 that) {
          x = that.x;
          y = that.y;
          z = that.z;
      }
  
      /**
       * Constructs a new vector from the x, y, z coordinates of an atom in
       * a molecule.
       *  @param mol The molecule that the atom is in.
       *  @param atom The atom index.
       */
      public Vector3(MMFFMolecule mol, int atom) {
          this.x = mol.getAtomX(atom);
          this.y = mol.getAtomY(atom);
          this.z = mol.getAtomZ(atom);
      }
  
      /**
       * Constructs a new vector from the x, y, z coordinates of an atom in
       * a molecule.
       *  @param mol The molecule that the atom is in.
       *  @param atom The atom index.
       */
      public Vector3(ExtendedMolecule mol, int atom) {
          this.x = mol.getAtomX(atom);
          this.y = mol.getAtomY(atom);
          this.z = mol.getAtomZ(atom);
      }
  
      /**
       * Constructs a new vector from three consecutive doubles in a
       * positions array.
       *  @param pos The double array of position coordinates.
       *  @param offset Where in the array to fetch the values from.
       */
      public Vector3(double[] pos, int offset) {
          x = pos[3*offset    ];
          y = pos[3*offset + 1];
          z = pos[3*offset + 2];
      }
  
      /**
       * Constructs a new vector starting at atom1 position and ending at
       * atom2 position. The vector is constructed using point information
       * from a position array.
       */
      public Vector3(double[] pos, int atom1, int atom2) {
          this(new Vector3(pos, atom1).to(new Vector3(pos, atom2)));
      }
  
      /**
       * Constructs a vector that represents the line travelling from the
       * position of atom1 to the position of atom2. The resultant vector
       * points towards atom2 from atom1.
       *  @param mol The molecule that the atoms are in.
       *  @param atom1 The first atom and starting point of the line.
       *  @param atom2 The second atom and the end point of the line.
       */
      public Vector3(MMFFMolecule mol, int atom1, int atom2) {
          this(new Vector3(mol, atom1).to(new Vector3(mol, atom2)));
      }
  
      /**
       * Constructs a vector that represents the line travelling from the
       * position of atom1 to the position of atom2. The resultant vector
       * points towards atom2 from atom1.
       *  @param mol The molecule that the atoms are in.
       *  @param atom1 The first atom and starting point of the line.
       *  @param atom2 The second atom and the end point of the line.
       */
      public Vector3(ExtendedMolecule mol, int atom1, int atom2) {
          this(new Vector3(mol, atom1).to(new Vector3(mol, atom2)));
      }
  
      /**
       * Checks for equality between two vectors. Vectors are considered
       * equal if each component value is equal to its corresponding
       * component value. Doubleing point values are considered equal if
       * their difference is below some tolerance value (set in TOL).
       *  @param obj The vector to compare this vector with.
       *  @return True if they are equal, false otherwise.
       */
      @Override
      public boolean equals(Object obj) {
          if (obj == this)
              return true;
  
          if (!(obj instanceof Vector3))
              return false;
  
          Vector3 that = (Vector3)obj;
  
          return Math.abs(x-that.x) < TOL
              && Math.abs(y-that.y) < TOL
              && Math.abs(z-that.z) < TOL;
      }
  
      /**
       * Returns the hashcode of this vector.
       *  @return The hashcode.
       */
      @Override
      public int hashCode() {
          return Double.hashCode(x) + Double.hashCode(y) + Double.hashCode(z);
      }
  
      /**
       * Writes the contents of this vector to the specified positions in a
       * positions array.
       *  @param pos The positions array to write to.
       *  @param offset Where in the array to write to.
       */
      public void write(double[] pos, int offset) {
          pos[3*offset    ] = x;
          pos[3*offset + 1] = y;
          pos[3*offset + 2] = z;
      }
  
      /**
       * Returns this vector negated (signs swapped).
       *  @return The negated vector.
       */
      public Vector3 negate() {
          return new Vector3(-x, -y, -z);
      }
  
      /**
       * Returns a vector that points from this vector to that vector. The
       * resultant vector will have a length equal to the distance between
       * the two vectors and will have a direction pointing towards that
       * vector.
       */
      public Vector3 to(Vector3 that) {
          return new Vector3(that.x-x, that.y-y, that.z-z);
      }
  
      /**
       * Returns the length (or magnitude) of this vector. This is the
       * euclidean distance from this vector to the origin (A vector at
       * x=0, y=0, z=0).
       *  @return The length.
       */
      public double length() {
          return Math.sqrt(x*x+y*y+z*z);
      }
  
      /**
       * Normalises a vector. If the vector to be normalised has length
       * zero, then the zero vector is returned.
       *  @return This vector normalised.
       */
      public Vector3 normalise() {
          if (length() > 0.0)
              return new Vector3(x/length(), y/length(), z/length());
          return new Vector3(0.0, 0.0, 0.0);
      }
  
      /**
       * Adds two vectors together by component.
       *  @param that The other vector.
       *  @return The component sum of the two vectors.
       */
      public Vector3 add(Vector3 that) {
          return new Vector3(x+that.x, y+that.y, z+that.z);
      }
  
      /**
       * Subtracts that vector from this vector by component.
       *  @param that The other vector.
       *  @return The component difference of the two vectors.
       */
      public Vector3 sub(Vector3 that) {
          return new Vector3(x-that.x, y-that.y, z-that.z);
      }
  
      /**
       * Computes the euclidean distance between two Vector3s.
       *  @param that The other Vector3 to calculate the distance to.
       *  @return The distance between the two vectors.
       */
      public double distance(Vector3 that) {
          return Math.sqrt(
                    (x-that.x)*(x-that.x)
                  + (y-that.y)*(y-that.y)
                  + (z-that.z)*(z-that.z) );
      }
  
      /**
       * Computes the vector dot product between this vector and that
       * vector.
       *  @param that The other vector.
       *  @return The dot product of the two vectors.
       */
      public double dot(Vector3 that) {
          return x*that.x + y*that.y + z*that.z;
      }
  
      /**
       * Computes the vector cross product between this vector and that
       * vector.
       *  @param that The other vector.
       *  @return The cross product of the two vectors.
       */
      public Vector3 cross(Vector3 that) {
          return new Vector3(y*that.z - z*that.y,
                  z*that.x - x*that.z,
                  x*that.y - y*that.x);
      }
  
      /**
       * Returns the angle between this vector and that vector.
       *  @param that The other vector.
       *  @return The angle between the two vectors in radians.
       */
      public double angle(Vector3 that) {
          return Math.acos(dot(that) / (length() * that.length()));
      }
  
      /**
       * Returns the cosine of the angle between this vector and that
       * vector.
       *  @param that The other vector.
       *  @return The cosine of the angle between the two vectors in
       *     radians.
       */
      public double cosAngle(Vector3 that) {
          return dot(that) / (length() * that.length());
      }
  
      /**
       * Returns a string form of this vector.
       *  @return The string form of the vector.
       */
      public String toString() {
          return "("+String.format("%.3f", x)+","+String.format("%.3f", y)+","
              +String.format("%.3f", z)+")";
      }
  }
  