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    1   /*
    2    * Licensed to the Apache Software Foundation (ASF) under one or more
    3    * contributor license agreements.  See the NOTICE file distributed with
    4    * this work for additional information regarding copyright ownership.
    5    * The ASF licenses this file to You under the Apache License, Version 2.0
    6    * (the "License"); you may not use this file except in compliance with
    7    * the License.  You may obtain a copy of the License at
    8    *
    9    *      http://www.apache.org/licenses/LICENSE-2.0
    10   *
    11   * Unless required by applicable law or agreed to in writing, software
    12   * distributed under the License is distributed on an "AS IS" BASIS,
    13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    14   * See the License for the specific language governing permissions and
    15   * limitations under the License.
    16   */
    17  package org.apache.commons.geometry.euclidean.twod.rotation;
    18
    19  import org.apache.commons.geometry.euclidean.EuclideanTransform;
    20  import org.apache.commons.geometry.euclidean.internal.Vectors;
    21  import org.apache.commons.geometry.euclidean.twod.AffineTransformMatrix2D;
    22  import org.apache.commons.geometry.euclidean.twod.Vector2D;
    23
    24  /** Class representing a rotation in 2 dimensional Euclidean space. Positive
    25   * rotations are in a <em>counter-clockwise</em> direction.
    26   */
    27  public final class Rotation2D implements EuclideanTransform<Vector2D> {
    28
    29      /** Instance representing a rotation of zero radians. */
    30      private static final Rotation2D IDENTITY = new Rotation2D(0);
    31
    32      /** The angle of the rotation in radians. */
    33      private final double angle;
    34
    35      /** The cosine of the angle of rotation, cached to avoid repeated computation. */
    36      private final double cosAngle;
    37
    38      /** The sine of the angle of rotation, cached to avoid repeated computation. */
    39      private final double sinAngle;
    40
    41      /** Create a new instance representing the given angle.
    42       * @param angle the angle of rotation, in radians
    43       */
    44      private Rotation2D(final double angle) {
    45          this.angle = angle;
    46          this.cosAngle = Math.cos(angle);
    47          this.sinAngle = Math.sin(angle);
    48      }
    49
    50      /** Get the angle of rotation in radians.
    51       * @return the angle of rotation in radians
    52       */
    53      public double getAngle() {
    54          return angle;
    55      }
    56
    57      /** {@inheritDoc} */
    58      @Override
    59      public Rotation2D inverse() {
    60          return new Rotation2D(-angle);
    61      }
    62
    63      /** {@inheritDoc}
    64       *
    65       * <p>This method simply returns true since rotations always preserve the orientation
    66       * of the space.</p>
    67       */
    68      @Override
    69      public boolean preservesOrientation() {
    70          return true;
    71      }
    72
    73      /** {@inheritDoc} */
    74      @Override
    75      public Vector2D apply(final Vector2D pt) {
    76          final double x = pt.getX();
    77          final double y = pt.getY();
    78
    79          return Vector2D.of(
    80                      (x * cosAngle) - (y * sinAngle),
    81                      (x * sinAngle) + (y * cosAngle)
    82                  );
    83      }
    84
    85      /** {@inheritDoc}
    86       *
    87       * <p>This method simply calls {@code apply(vec)} since rotations treat
    88       * points and vectors similarly.</p>
    89       * */
    90      @Override
    91      public Vector2D applyVector(final Vector2D vec) {
    92          return apply(vec);
    93      }
    94
    95      /** Return an {@link AffineTransformMatrix2D} representing the same rotation
    96       * as this instance.
    97       * @return a transform matrix representing the same rotation
    98       */
    99      public AffineTransformMatrix2D toMatrix() {
    100         return AffineTransformMatrix2D.of(
    101                     cosAngle, -sinAngle, 0.0,
    102                     sinAngle, cosAngle, 0.0
    103                 );
    104     }
    105
    106     /** {@inheritDoc} */
    107     @Override
    108     public int hashCode() {
    109         return Double.hashCode(angle);
    110     }
    111
    112     /** {@inheritDoc} */
    113     @Override
    114     public boolean equals(final Object obj) {
    115         if (this == obj) {
    116             return true;
    117         }
    118         if (!(obj instanceof Rotation2D)) {
    119             return false;
    120         }
    121
    122         final Rotation2D other = (Rotation2D) obj;
    123
    124         return Double.compare(this.angle, other.angle) == 0;
    125     }
    126
    127     /** {@inheritDoc} */
    128     @Override
    129     public String toString() {
    130         final StringBuilder sb = new StringBuilder();
    131         sb.append(this.getClass().getSimpleName())
    132             .append("[angle=")
    133             .append(angle)
    134             .append(']');
    135
    136         return sb.toString();
    137     }
    138
    139     /** Create a new instance with the given angle of rotation.
    140      * @param angle the angle of rotation in radians
    141      * @return a new instance with the given angle of rotation
    142      */
    143     public static Rotation2D of(final double angle) {
    144         return new Rotation2D(angle);
    145     }
    146
    147     /** Return an instance representing the identity rotation, ie a rotation
    148      * of zero radians.
    149      * @return an instance representing a rotation of zero radians
    150      */
    151     public static Rotation2D identity() {
    152         return IDENTITY;
    153     }
    154
    155     /** Create a rotation instance that rotates the vector {@code u} to point in the direction of
    156      * vector {@code v}.
    157      * @param u input vector
    158      * @param v target vector
    159      * @return a rotation instance that rotates {@code u} to point in the direction of {@code v}
    160      * @throws IllegalArgumentException if either vector cannot be normalized
    161      */
    162     public static Rotation2D createVectorRotation(final Vector2D u, final Vector2D v) {
    163         // make sure that the vectors are real-valued and of non-zero length; we don't
    164         // actually need to use the norm value; we just need to check its properties
    165         Vectors.checkedNorm(u);
    166         Vectors.checkedNorm(v);
    167
    168         final double uAzimuth = Math.atan2(u.getY(), u.getX());
    169         final double vAzimuth = Math.atan2(v.getY(), v.getX());
    170
    171         return of(vAzimuth - uAzimuth);
    172     }
    173 }