/*
    * 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.commons.geometry.euclidean.threed.line;
  
  import java.text.MessageFormat;
  import java.util.Objects;
  
  import org.apache.commons.geometry.core.Embedding;
  import org.apache.commons.geometry.core.Transform;
  import org.apache.commons.geometry.euclidean.oned.AffineTransformMatrix1D;
  import org.apache.commons.geometry.euclidean.oned.Vector1D;
  import org.apache.commons.geometry.euclidean.threed.Vector3D;
  import org.apache.commons.numbers.core.Precision;
  
  /** Class representing a line in 3D space.
   *
   * <p>Instances of this class are guaranteed to be immutable.</p>
   * @see Lines3D
   */
  public final class Line3D implements Embedding<Vector3D, Vector1D> {
  
      /** Format string for creating line string representations. */
      static final String TO_STRING_FORMAT = "{0}[origin= {1}, direction= {2}]";
  
      /** Line point closest to the origin. */
      private final Vector3D origin;
  
      /** Line direction. */
      private final Vector3D direction;
  
      /** Precision context used to compare floating point numbers. */
      private final Precision.DoubleEquivalence precision;
  
      /** Simple constructor.
       * @param origin the origin of the line, meaning the point on the line closest to the origin of the
       *      3D space
       * @param direction the direction of the line
       * @param precision precision context used to compare floating point numbers
       */
      Line3D(final Vector3D origin, final Vector3D direction, final Precision.DoubleEquivalence precision) {
          this.origin = origin;
          this.direction = direction;
          this.precision = precision;
      }
  
      /** Get the line point closest to the origin.
       * @return line point closest to the origin
       */
      public Vector3D getOrigin() {
          return origin;
      }
  
      /** Get the normalized direction vector.
       * @return normalized direction vector
       */
      public Vector3D getDirection() {
          return direction;
      }
  
      /** Get the object used to determine floating point equality for this instance.
       * @return the floating point precision context for the instance
       */
      public Precision.DoubleEquivalence getPrecision() {
          return precision;
      }
  
      /** Return a line containing the same points as this instance but pointing
       * in the opposite direction.
       * @return an instance containing the same points but pointing in the opposite
       *      direction
       */
      public Line3D reverse() {
          return new Line3D(origin, direction.negate(), precision);
      }
  
      /** Transform this instance.
       * @param transform object used to transform the instance
       * @return a transformed instance
       */
      public Line3D transform(final Transform<Vector3D> transform) {
          final Vector3D p1 = transform.apply(origin);
          final Vector3D p2 = transform.apply(origin.add(direction));
  
          return Lines3D.fromPoints(p1, p2, precision);
      }
 
     /** Get an object containing the current line transformed by the argument along with a
      * 1D transform that can be applied to subspace points. The subspace transform transforms
      * subspace points such that their 3D location in the transformed line is the same as their
      * 3D location in the original line after the 3D transform is applied. For example, consider
      * the code below:
      * <pre>
      *      SubspaceTransform st = line.subspaceTransform(transform);
      *
      *      Vector1D subPt = Vector1D.of(1);
      *
      *      Vector3D a = transform.apply(line.toSpace(subPt)); // transform in 3D space
      *      Vector3D b = st.getLine().toSpace(st.getTransform().apply(subPt)); // transform in 1D space
      * </pre>
      * At the end of execution, the points {@code a} (which was transformed using the original
      * 3D transform) and {@code b} (which was transformed in 1D using the subspace transform)
      * are equivalent.
      *
      * @param transform the transform to apply to this instance
      * @return an object containing the transformed line along with a transform that can be applied
      *      to subspace points
      * @see #transform(Transform)
      */
     public SubspaceTransform subspaceTransform(final Transform<Vector3D> transform) {
         final Vector3D p1 = transform.apply(origin);
         final Vector3D p2 = transform.apply(origin.add(direction));
 
         final Line3D tLine = Lines3D.fromPoints(p1, p2, precision);
 
         final Vector1D tSubspaceOrigin = tLine.toSubspace(p1);
         final Vector1D tSubspaceDirection = tSubspaceOrigin.vectorTo(tLine.toSubspace(p2));
 
         final double translation = tSubspaceOrigin.getX();
         final double scale = tSubspaceDirection.getX();
 
         final AffineTransformMatrix1D subspaceTransform = AffineTransformMatrix1D.of(scale, translation);
 
         return new SubspaceTransform(tLine, subspaceTransform);
     }
 
     /** Get the abscissa of the given point on the line. The abscissa represents
      * the distance the projection of the point on the line is from the line's
      * origin point (the point on the line closest to the origin of the
      * 2D space). Abscissa values increase in the direction of the line. This method
      * is exactly equivalent to {@link #toSubspace(Vector3D)} except that this method
      * returns a double instead of a {@link Vector1D}.
      * @param pt point to compute the abscissa for
      * @return abscissa value of the point
      * @see #toSubspace(Vector3D)
      */
     public double abscissa(final Vector3D pt) {
         return pt.subtract(origin).dot(direction);
     }
 
     /** Get one point from the line.
      * @param abscissa desired abscissa for the point
      * @return one point belonging to the line, at specified abscissa
      */
     public Vector3D pointAt(final double abscissa) {
         return Vector3D.Sum.of(origin)
                 .addScaled(abscissa, direction)
                 .get();
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector1D toSubspace(final Vector3D pt) {
         return Vector1D.of(abscissa(pt));
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector3D toSpace(final Vector1D pt) {
         return toSpace(pt.getX());
     }
 
     /** Get the 3 dimensional point at the given abscissa position
      * on the line.
      * @param abscissa location on the line
      * @return the 3 dimensional point at the given abscissa position
      *      on the line
      */
     public Vector3D toSpace(final double abscissa) {
         return pointAt(abscissa);
     }
 
     /** Check if the instance is similar to another line.
      * <p>Lines are considered similar if they contain the same
      * points. This does not mean they are equal since they can have
      * opposite directions.</p>
      * @param line line to which instance should be compared
      * @return true if the lines are similar
      */
     public boolean isSimilarTo(final Line3D line) {
         final double angle = direction.angle(line.direction);
         return (precision.eqZero(angle) || precision.eq(Math.abs(angle), Math.PI)) &&
                 contains(line.origin);
     }
 
     /** Check if the instance contains a point.
      * @param pt point to check
      * @return true if p belongs to the line
      */
     public boolean contains(final Vector3D pt) {
         return precision.eqZero(distance(pt));
     }
 
     /** Compute the distance between the instance and a point.
      * @param pt to check
      * @return distance between the instance and the point
      */
     public double distance(final Vector3D pt) {
         final Vector3D delta = pt.subtract(origin);
         final Vector3D orthogonal = delta.reject(direction);
 
         return orthogonal.norm();
     }
 
     /** Compute the shortest distance between the instance and another line.
      * @param line line to check against the instance
      * @return shortest distance between the instance and the line
      */
     public double distance(final Line3D line) {
 
         final Vector3D normal = direction.cross(line.direction);
         final double norm = normal.norm();
 
         if (precision.eqZero(norm)) {
             // the lines are parallel
             return distance(line.origin);
         }
 
         // signed separation of the two parallel planes that contains the lines
         final double offset = line.origin.subtract(origin).dot(normal) / norm;
 
         return Math.abs(offset);
     }
 
     /** Compute the point of the instance closest to another line.
      * @param line line to check against the instance
      * @return point of the instance closest to another line
      */
     public Vector3D closest(final Line3D line) {
 
         final double cos = direction.dot(line.direction);
         final double n = 1 - cos * cos;
 
         if (precision.eqZero(n)) {
             // the lines are parallel
             return origin;
         }
 
         final Vector3D delta = line.origin.subtract(origin);
         final double a = delta.dot(direction);
         final double b = delta.dot(line.direction);
 
         return Vector3D.Sum.of(origin)
                 .addScaled((a - (b * cos)) / n, direction)
                 .get();
     }
 
     /** Get the intersection point of the instance and another line.
      * @param line other line
      * @return intersection point of the instance and the other line
      * or null if there are no intersection points
      */
     public Vector3D intersection(final Line3D line) {
         final Vector3D closestPt = closest(line);
         return line.contains(closestPt) ? closestPt : null;
     }
 
     /** Return a new infinite line subset representing the entire line.
      * @return a new infinite line subset representing the entire line
      * @see Lines3D#span(Line3D)
      */
     public LineConvexSubset3D span() {
         return Lines3D.span(this);
     }
 
     /** Create a new line segment from the given 1D interval. The returned line
      * segment consists of all points between the two locations, regardless of the order the
      * arguments are given.
      * @param a first 1D location for the interval
      * @param b second 1D location for the interval
      * @return a new line segment on this line
      * @throws IllegalArgumentException if either of the locations is NaN or infinite
      * @see Lines3D#segmentFromLocations(Line3D, double, double)
      */
     public Segment3D segment(final double a, final double b) {
         return Lines3D.segmentFromLocations(this, a, b);
     }
 
     /** Create a new line segment from two points. The returned segment represents all points on this line
      * between the projected locations of {@code a} and {@code b}. The points may be given in any order.
      * @param a first point
      * @param b second point
      * @return a new line segment on this line
      * @throws IllegalArgumentException if either point contains NaN or infinite coordinate values
      * @see Lines3D#segmentFromPoints(Line3D, Vector3D, Vector3D)
      */
     public Segment3D segment(final Vector3D a, final Vector3D b) {
         return Lines3D.segmentFromPoints(this, a, b);
     }
 
     /** Create a new line convex subset that starts at infinity and continues along
      * the line up to the projection of the given end point.
      * @param endPoint point defining the end point of the line subset; the end point
      *      is equal to the projection of this point onto the line
      * @return a new, half-open line subset that ends at the given point
      * @throws IllegalArgumentException if any coordinate in {@code endPoint} is NaN or infinite
      * @see Lines3D#reverseRayFromPoint(Line3D, Vector3D)
      */
     public ReverseRay3D reverseRayTo(final Vector3D endPoint) {
         return Lines3D.reverseRayFromPoint(this, endPoint);
     }
 
     /** Create a new line convex subset that starts at infinity and continues along
      * the line up to the given 1D location.
      * @param endLocation the 1D location of the end of the half-line
      * @return a new, half-open line subset that ends at the given 1D location
      * @throws IllegalArgumentException if {@code endLocation} is NaN or infinite
      * @see Lines3D#reverseRayFromLocation(Line3D, double)
      */
     public ReverseRay3D reverseRayTo(final double endLocation) {
         return Lines3D.reverseRayFromLocation(this, endLocation);
     }
 
     /** Create a new ray instance that starts at the projection of the given point
      * and continues in the direction of the line to infinity.
      * @param startPoint point defining the start point of the ray; the start point
      *      is equal to the projection of this point onto the line
      * @return a ray starting at the projected point and extending along this line
      *      to infinity
      * @throws IllegalArgumentException if any coordinate in {@code startPoint} is NaN or infinite
      * @see Lines3D#rayFromPoint(Line3D, Vector3D)
      */
     public Ray3D rayFrom(final Vector3D startPoint) {
         return Lines3D.rayFromPoint(this, startPoint);
     }
 
     /** Create a new ray instance that starts at the given 1D location and continues in
      * the direction of the line to infinity.
      * @param startLocation 1D location defining the start point of the ray
      * @return a ray starting at the given 1D location and extending along this line
      *      to infinity
      * @throws IllegalArgumentException if {@code startLocation} is NaN or infinite
      * @see Lines3D#rayFromLocation(Line3D, double)
      */
     public Ray3D rayFrom(final double startLocation) {
         return Lines3D.rayFromLocation(this, startLocation);
     }
 
     /** Return true if this instance should be considered equivalent to the argument, using the
      * given precision context for comparison. Instances are considered equivalent if they have
      * equivalent {@code origin}s and {@code direction}s.
      * @param other the point to compare with
      * @param ctx precision context to use for the comparison
      * @return true if this instance should be considered equivalent to the argument
      * @see Vector3D#eq(Vector3D, Precision.DoubleEquivalence)
      */
     public boolean eq(final Line3D other, final Precision.DoubleEquivalence ctx) {
         return getOrigin().eq(other.getOrigin(), ctx) &&
                 getDirection().eq(other.getDirection(), ctx);
     }
 
     /** {@inheritDoc} */
     @Override
     public int hashCode() {
         return Objects.hash(origin, direction, precision);
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean equals(final Object obj) {
         if (this == obj) {
             return true;
         }
         if (!(obj instanceof Line3D)) {
             return false;
         }
         final Line3D other = (Line3D) obj;
         return this.origin.equals(other.origin) &&
                 this.direction.equals(other.direction) &&
                 this.precision.equals(other.precision);
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString() {
         return MessageFormat.format(TO_STRING_FORMAT,
                 getClass().getSimpleName(),
                 getOrigin(),
                 getDirection());
     }
 
     /** Class containing a transformed line instance along with a subspace (1D) transform. The subspace
      * transform produces the equivalent of the 3D transform in 1D.
      */
     public static final class SubspaceTransform {
         /** The transformed line. */
         private final Line3D line;
 
         /** The subspace transform instance. */
         private final AffineTransformMatrix1D transform;
 
         /** Simple constructor.
          * @param line the transformed line
          * @param transform 1D transform that can be applied to subspace points
          */
         public SubspaceTransform(final Line3D line, final AffineTransformMatrix1D transform) {
             this.line = line;
             this.transform = transform;
         }
 
         /** Get the transformed line instance.
          * @return the transformed line instance
          */
         public Line3D getLine() {
             return line;
         }
 
         /** Get the 1D transform that can be applied to subspace points. This transform can be used
          * to perform the equivalent of the 3D transform in 1D space.
          * @return the subspace transform instance
          */
         public AffineTransformMatrix1D getTransform() {
             return transform;
         }
     }
 }