/*
    * 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.twod;
  
  import java.text.MessageFormat;
  import java.util.Objects;
  
  import org.apache.commons.geometry.core.Transform;
  import org.apache.commons.geometry.core.partitioning.AbstractHyperplane;
  import org.apache.commons.geometry.core.partitioning.EmbeddingHyperplane;
  import org.apache.commons.geometry.core.partitioning.Hyperplane;
  import org.apache.commons.geometry.euclidean.internal.Vectors;
  import org.apache.commons.geometry.euclidean.oned.AffineTransformMatrix1D;
  import org.apache.commons.geometry.euclidean.oned.Vector1D;
  import org.apache.commons.numbers.angle.Angle;
  import org.apache.commons.numbers.core.Precision;
  
  /** This class represents an oriented line in the 2D plane.
  
   * <p>An oriented line can be defined either by extending a line
   * segment between two points past these points, by specifying a
   * point and a direction, or by specifying a point and an angle
   * relative to the x-axis.</p>
  
   * <p>Since the line oriented, the two half planes on its sides are
   * unambiguously identified as the left half plane and the right half
   * plane. This can be used to identify the interior and the exterior
   * in a simple way when a line is used to define a portion of a polygon
   * boundary.</p>
  
   * <p>A line can also be used to completely define a reference frame
   * in the plane. It is sufficient to select one specific point in the
   * line (the orthogonal projection of the original reference frame on
   * the line) and to use the unit vector in the line direction (see
   * {@link #getDirection()} and the orthogonal vector oriented from the
   * left half plane to the right half plane (see {@link #getOffsetDirection()}.
   * We define two coordinates by the process, the <em>abscissa</em> along
   * the line, and the <em>offset</em> across the line. All points of the
   * plane are uniquely identified by these two coordinates. The line is
   * the set of points at zero offset, the left half plane is the set of
   * points with negative offsets and the right half plane is the set of
   * points with positive offsets.</p>
   * @see Lines
   */
  public final class Line extends AbstractHyperplane<Vector2D>
      implements EmbeddingHyperplane<Vector2D, Vector1D> {
  
      /** Format string for creating line string representations. */
      static final String TO_STRING_FORMAT = "{0}[origin= {1}, direction= {2}]";
  
      /** The direction of the line as a normalized vector. */
      private final Vector2D.Unit direction;
  
      /** The distance between the origin and the line. */
      private final double originOffset;
  
      /** Simple constructor.
       * @param direction The direction of the line.
       * @param originOffset The signed distance between the line and the origin.
       * @param precision Precision context used to compare floating point numbers.
       */
      Line(final Vector2D.Unit direction, final double originOffset, final Precision.DoubleEquivalence precision) {
          super(precision);
  
          this.direction = direction;
          this.originOffset = originOffset;
      }
  
      /** Get the angle of the line in radians with respect to the abscissa (+x) axis. The
       * returned angle is in the range {@code [0, 2pi)}.
       * @return the angle of the line with respect to the abscissa (+x) axis in the range
       *      {@code [0, 2pi)}
       */
      public double getAngle() {
          final double angle = Math.atan2(direction.getY(), direction.getX());
          return Angle.Rad.WITHIN_0_AND_2PI.applyAsDouble(angle);
      }
  
      /** Get the direction of the line.
       * @return the direction of the line
       */
      public Vector2D.Unit getDirection() {
          return direction;
      }
  
     /** Get the offset direction of the line. This vector is perpendicular to the
      * line and points in the direction of positive offset values, meaning that
      * it points from the left side of the line to the right when one is looking
      * along the line direction.
      * @return the offset direction of the line.
      */
     public Vector2D getOffsetDirection() {
         return Vector2D.of(direction.getY(), -direction.getX());
     }
 
     /** Get the line origin point. This is the projection of the 2D origin
      * onto the line and also serves as the origin for the 1D embedded subspace.
      * @return the origin point of the line
      */
     public Vector2D getOrigin() {
         return toSpace(Vector1D.ZERO);
     }
 
     /** Get the signed distance from the origin of the 2D space to the
      * closest point on the line.
      * @return the signed distance from the origin to the line
      */
     public double getOriginOffset() {
         return originOffset;
     }
 
     /** {@inheritDoc} */
     @Override
     public Line reverse() {
         return new Line(direction.negate(), -originOffset, getPrecision());
     }
 
     /** {@inheritDoc} */
     @Override
     public Line transform(final Transform<Vector2D> transform) {
         final Vector2D origin = getOrigin();
 
         final Vector2D tOrigin = transform.apply(origin);
         final Vector2D tOriginPlusDir = transform.apply(origin.add(getDirection()));
 
         return Lines.fromPoints(tOrigin, tOriginPlusDir, getPrecision());
     }
 
     /** 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 2D location in the transformed line is the same as their
      * 2D location in the original line after the 2D transform is applied. For example, consider
      * the code below:
      * <pre>
      *      SubspaceTransform st = line.subspaceTransform(transform);
      *
      *      Vector1D subPt = Vector1D.of(1);
      *
      *      Vector2D a = transform.apply(line.toSpace(subPt)); // transform in 2D space
      *      Vector2D 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
      * 2D 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<Vector2D> transform) {
         final Vector2D origin = getOrigin();
 
         final Vector2D p1 = transform.apply(origin);
         final Vector2D p2 = transform.apply(origin.add(direction));
 
         final Line tLine = Lines.fromPoints(p1, p2, getPrecision());
 
         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);
     }
 
     /** {@inheritDoc} */
     @Override
     public LineConvexSubset span() {
         return Lines.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 Lines#segmentFromLocations(Line, double, double)
      */
     public Segment segment(final double a, final double b) {
         return Lines.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 Lines#segmentFromPoints(Line, Vector2D, Vector2D)
      */
     public Segment segment(final Vector2D a, final Vector2D b) {
         return Lines.segmentFromPoints(this, a, b);
     }
 
     /** Create a new convex line 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 Lines#reverseRayFromPoint(Line, Vector2D)
      */
     public ReverseRay reverseRayTo(final Vector2D endPoint) {
         return Lines.reverseRayFromPoint(this, endPoint);
     }
 
     /** Create a new convex line 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 Lines#reverseRayFromLocation(Line, double)
      */
     public ReverseRay reverseRayTo(final double endLocation) {
         return Lines.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 Lines#rayFromPoint(Line, Vector2D)
      */
     public Ray rayFrom(final Vector2D startPoint) {
         return Lines.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 Lines#rayFromLocation(Line, double)
      */
     public Ray rayFrom(final double startLocation) {
         return Lines.rayFromLocation(this, startLocation);
     }
 
     /** 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(Vector2D)} except that this method
      * returns a double instead of a {@link Vector1D}.
      * @param point point to compute the abscissa for
      * @return abscissa value of the point
      * @see #toSubspace(Vector2D)
      */
     public double abscissa(final Vector2D point) {
         return direction.dot(point);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector1D toSubspace(final Vector2D point) {
         return Vector1D.of(abscissa(point));
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D toSpace(final Vector1D point) {
         return toSpace(point.getX());
     }
 
     /** Convert the given abscissa value (1D location on the line)
      * into a 2D point.
      * @param abscissa value to convert
      * @return 2D point corresponding to the line abscissa value
      */
     public Vector2D toSpace(final double abscissa) {
         // The 2D coordinate is equal to the projection of the
         // 2D origin onto the line plus the direction multiplied
         // by the abscissa. We can combine everything into a single
         // step below given that the origin location is equal to
         // (-direction.y * originOffset, direction.x * originOffset).
         return Vector2D.of(
                     Vectors.linearCombination(abscissa, direction.getX(), -originOffset, direction.getY()),
                     Vectors.linearCombination(abscissa, direction.getY(), originOffset, direction.getX())
                 );
     }
 
     /** Get the intersection point of the instance and another line.
      * @param other other line
      * @return intersection point of the instance and the other line
      *      or null if there is no unique intersection point (ie, the lines
      *      are parallel or coincident)
      */
     public Vector2D intersection(final Line other) {
         final double area = this.direction.signedArea(other.direction);
         if (getPrecision().eqZero(area)) {
             // lines are parallel
             return null;
         }
 
         final double x = Vectors.linearCombination(
                 other.direction.getX(), originOffset,
                 -direction.getX(), other.originOffset) / area;
 
         final double y = Vectors.linearCombination(
                 other.direction.getY(), originOffset,
                 -direction.getY(), other.originOffset) / area;
 
         return Vector2D.of(x, y);
     }
 
     /** Compute the angle in radians between this instance's direction and the direction
      * of the given line. The return value is in the range {@code [-pi, +pi)}. This method
      * always returns a value, even for parallel or coincident lines.
      * @param other other line
      * @return the angle required to rotate this line to point in the direction of
      *      the given line
      */
     public double angle(final Line other) {
         final double thisAngle = Math.atan2(direction.getY(), direction.getX());
         final double otherAngle = Math.atan2(other.direction.getY(), other.direction.getX());
 
         return Angle.Rad.WITHIN_MINUS_PI_AND_PI.applyAsDouble(otherAngle - thisAngle);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D project(final Vector2D point) {
         return toSpace(toSubspace(point));
     }
 
     /** {@inheritDoc} */
     @Override
     public double offset(final Vector2D point) {
         return originOffset - direction.signedArea(point);
     }
 
     /** Get the offset (oriented distance) of the given line relative to this instance.
      * Since an infinite number of distances can be calculated between points on two
      * different lines, this method returns the value closest to zero. For intersecting
      * lines, this will simply be zero. For parallel lines, this will be the
      * perpendicular distance between the two lines, as a signed value.
      *
      * <p>The sign of the returned offset indicates the side of the line that the
      * argument lies on. The offset is positive if the line lies on the right side
      * of the instance and negative if the line lies on the left side
      * of the instance.</p>
      * @param line line to check
      * @return offset of the line
      * @see #distance(Line)
      */
     public double offset(final Line line) {
         if (isParallel(line)) {
             // since the lines are parallel, the offset between
             // them is simply the difference between their origin offsets,
             // with the second offset negated if the lines point if opposite
             // directions
             final double dot = direction.dot(line.direction);
             return originOffset - (Math.signum(dot) * line.originOffset);
         }
 
         // the lines are not parallel, which means they intersect at some point
         return 0.0;
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean similarOrientation(final Hyperplane<Vector2D> other) {
         final Line otherLine = (Line) other;
         return direction.dot(otherLine.direction) >= 0.0;
     }
 
     /** Get one point from the plane, relative to the coordinate system
      * of the line. Note that the direction of increasing offsets points
      * to the <em>right</em> of the line. This means that if one pictures
      * the line (abscissa) direction as equivalent to the +x-axis, the offset
      * direction will point along the -y axis.
      * @param abscissa desired abscissa (distance along the line) for the point
      * @param offset desired offset (distance perpendicular to the line) for the point
      * @return one point in the plane, with given abscissa and offset
      *      relative to the line
      */
     public Vector2D pointAt(final double abscissa, final double offset) {
         final double pointOffset = offset - originOffset;
         return Vector2D.of(Vectors.linearCombination(abscissa, direction.getX(),  pointOffset, direction.getY()),
                             Vectors.linearCombination(abscissa, direction.getY(), -pointOffset, direction.getX()));
     }
 
     /** Check if the line contains a point.
      * @param p point to check
      * @return true if p belongs to the line
      */
     @Override
     public boolean contains(final Vector2D p) {
         return getPrecision().eqZero(offset(p));
     }
 
     /** Check if this instance completely contains the other line.
      * This will be true if the two instances represent the same line,
      * with perhaps different directions.
      * @param line line to check
      * @return true if this instance contains all points in the given line
      */
     public boolean contains(final Line line) {
         return isParallel(line) && getPrecision().eqZero(offset(line));
     }
 
     /** Compute the distance between the instance and a point.
      * <p>This is a shortcut for invoking Math.abs(getOffset(p)),
      * and provides consistency with what is in the
      * org.apache.commons.geometry.euclidean.threed.Line class.</p>
      *
      * @param p to check
      * @return distance between the instance and the point
      */
     public double distance(final Vector2D p) {
         return Math.abs(offset(p));
     }
 
     /** Compute the shortest distance between this instance and
      * the given line. This value will simply be zero for intersecting
      * lines.
      * @param line line to compute the closest distance to
      * @return the shortest distance between this instance and the
      *      given line
      * @see #offset(Line)
      */
     public double distance(final Line line) {
         return Math.abs(offset(line));
     }
 
     /** Check if the instance is parallel to another line.
      * @param line other line to check
      * @return true if the instance is parallel to the other line
      *  (they can have either the same or opposite orientations)
      */
     public boolean isParallel(final Line line) {
         final double area = direction.signedArea(line.direction);
         return getPrecision().eqZero(area);
     }
 
     /** 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} points and make similar angles with the x-axis.
      * @param other the point to compare with
      * @param precision precision context to use for the comparison
      * @return true if this instance should be considered equivalent to the argument
      * @see Vector2D#eq(Vector2D, Precision.DoubleEquivalence)
      */
     public boolean eq(final Line other, final Precision.DoubleEquivalence precision) {
         return getOrigin().eq(other.getOrigin(), precision) &&
                 precision.eq(getAngle(), other.getAngle());
     }
 
     /** {@inheritDoc} */
     @Override
     public int hashCode() {
         final int prime = 167;
 
         int result = 1;
         result = (prime * result) + Objects.hashCode(direction);
         result = (prime * result) + Double.hashCode(originOffset);
         result = (prime * result) + Objects.hashCode(getPrecision());
 
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean equals(final Object obj) {
         if (this == obj) {
             return true;
         } else if (!(obj instanceof Line)) {
             return false;
         }
 
         final Line other = (Line) obj;
 
         return Objects.equals(this.direction, other.direction) &&
                 Double.compare(this.originOffset, other.originOffset) == 0 &&
                 Objects.equals(this.getPrecision(), other.getPrecision());
     }
 
     /** {@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 2D transform in 1D.
      */
     public static final class SubspaceTransform {
         /** The transformed line. */
         private final Line 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 Line line, final AffineTransformMatrix1D transform) {
             this.line = line;
             this.transform = transform;
         }
 
         /** Get the transformed line instance.
          * @return the transformed line instance
          */
         public Line 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 2D transform in 1D space.
          * @return the subspace transform instance
          */
         public AffineTransformMatrix1D getTransform() {
             return transform;
         }
     }
 }