Angle

/*
 * 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.numbers.angle;

import java.util.function.DoubleSupplier;
import java.util.function.DoubleUnaryOperator;

/**
 * Represents the <a href="https://en.wikipedia.org/wiki/Angle">angle</a> concept.
 */
public abstract class Angle implements DoubleSupplier {
    /** 2&pi;. */
    public static final double TWO_PI = 2 * Math.PI;
    /** &pi;/2. */
    public static final double PI_OVER_TWO = 0.5 * Math.PI;
    /** Turns to degrees conversion factor. */
    private static final double TURN_TO_DEG = 360d;
    /** Radians to degrees conversion factor. */
    private static final double RAD_TO_DEG = 180.0 / Math.PI;
    /** Degrees to radians conversion factor. */
    private static final double DEG_TO_RAD = Math.PI / 180.0;

    /** Value (unit depends on concrete instance). */
    private final double value;

    /**
     * @param value Value in turns.
     */
    private Angle(final double value) {
        this.value = value;
    }

    /** @return the value. */
    @Override
    public double getAsDouble() {
        return value;
    }

    /** {@inheritDoc} */
    @Override
    public int hashCode() {
        return Double.hashCode(value);
    }

    /**
     * Test for equality with another object.
     * Objects are considered to be equal if their concrete types are
     * equal and their values are exactly the same (or both are {@code Double.NaN}).
     *
     * @param other Object to test for equality with this instance.
     * @return {@code true} if the objects are equal, {@code false} if
     * {@code other} is {@code null}, not of the same type as this instance,
     * or not equal to this instance.
     */
    @Override
    public boolean equals(final Object other) {
        return other != null &&
                getClass().equals(other.getClass()) &&
                Double.doubleToLongBits(value) == Double.doubleToLongBits(((Angle) other).value);
    }

    /**
     * @return the angle in <a href="https://en.wikipedia.org/wiki/Turn_%28geometry%29">turns</a>.
     */
    public abstract Turn toTurn();

    /**
     * @return the angle in <a href="https://en.wikipedia.org/wiki/Radian">radians</a>.
     */
    public abstract Rad toRad();

    /**
     * @return the angle in <a href="https://en.wikipedia.org/wiki/Degree_%28angle%29">degrees</a>.
     */
    public abstract Deg toDeg();

    /**
     * Unit: <a href="https://en.wikipedia.org/wiki/Turn_%28geometry%29">turns</a>.
     */
    public static final class Turn extends Angle {
        /** Zero. */
        public static final Turn ZERO = Turn.of(0d);
        /** Normalizing operator (result will be within the {@code [0, 1[} interval). */
        public static final DoubleUnaryOperator WITHIN_0_AND_1 = normalizer(0d);

        /**
         * @param angle (in turns).
         */
        private Turn(final double angle) {
            super(angle);
        }

        /**
         * @param angle (in turns).
         * @return a new intance.
         */
        public static Turn of(final double angle) {
            return new Turn(angle);
        }

        /** {@inheritDoc} */
        @Override
        public Turn toTurn() {
            return this;
        }

        /** {@inheritDoc} */
        @Override
        public Rad toRad() {
            return Rad.of(getAsDouble() * TWO_PI);
        }

        /** {@inheritDoc} */
        @Override
        public Deg toDeg() {
            return Deg.of(getAsDouble() * TURN_TO_DEG);
        }

        /**
         * Creates an operator for normalizing/reducing an angle.
         * The output will be within the {@code [lo, lo + 1[} interval.
         *
         * @param lo Lower bound of the normalized interval.
         * @return the normalization operator.
         */
        public static DoubleUnaryOperator normalizer(final double lo) {
            return new Normalizer(lo, 1d);
        }
    }

    /**
     * Unit: <a href="https://en.wikipedia.org/wiki/Radian">radians</a>.
     */
    public static final class Rad extends Angle {
        /** Zero. */
        public static final Rad ZERO = Rad.of(0d);
        /** &pi;. */
        public static final Rad PI = Rad.of(Math.PI);
        /** 2&pi;. */
        public static final Rad TWO_PI = Rad.of(Angle.TWO_PI);
        /** Normalizing operator (result will be within the <code>[0, 2&pi;[</code> interval). */
        public static final DoubleUnaryOperator WITHIN_0_AND_2PI = normalizer(0d);
        /** Normalizing operator (result will be within the <code>[-&pi;, &pi;[</code> interval). */
        public static final DoubleUnaryOperator WITHIN_MINUS_PI_AND_PI = normalizer(-Math.PI);

        /**
         * @param angle (in radians).
         */
        private Rad(final double angle) {
            super(angle);
        }

        /**
         * @param angle (in radians).
         * @return a new intance.
         */
        public static Rad of(final double angle) {
            return new Rad(angle);
        }

        /** {@inheritDoc} */
        @Override
        public Turn toTurn() {
            return Turn.of(getAsDouble() / Angle.TWO_PI);
        }

        /** {@inheritDoc} */
        @Override
        public Rad toRad() {
            return this;
        }

        /** {@inheritDoc} */
        @Override
        public Deg toDeg() {
            return Deg.of(getAsDouble() * RAD_TO_DEG);
        }

        /**
         * Creates an operator for normalizing/reducing an angle.
         * The output will be within the <code> [lo, lo + 2&pi;[</code> interval.
         *
         * @param lo Lower bound of the normalized interval.
         * @return the normalization operator.
         */
        public static DoubleUnaryOperator normalizer(final double lo) {
            return new Normalizer(lo, Angle.TWO_PI);
        }
    }

    /**
     * Unit: <a href="https://en.wikipedia.org/wiki/Degree_%28angle%29">degrees</a>.
     */
    public static final class Deg extends Angle {
        /** Zero. */
        public static final Deg ZERO = Deg.of(0d);
        /** Normalizing operator (result will be within the {@code [0, 360[} interval). */
        public static final DoubleUnaryOperator WITHIN_0_AND_360 = normalizer(0d);

        /**
         * @param angle (in degrees).
         */
        private Deg(final double angle) {
            super(angle);
        }

        /**
         * @param angle (in degrees).
         * @return a new intance.
         */
        public static Deg of(final double angle) {
            return new Deg(angle);
        }

        /** {@inheritDoc} */
        @Override
        public Turn toTurn() {
            return Turn.of(getAsDouble() / TURN_TO_DEG);
        }

        /** {@inheritDoc} */
        @Override
        public Rad toRad() {
            return Rad.of(getAsDouble() * DEG_TO_RAD);
        }

        /** {@inheritDoc} */
        @Override
        public Deg toDeg() {
            return this;
        }

        /**
         * Creates an operator for normalizing/reducing an angle.
         * The output will be within the {@code [c, c + 360[} interval.
         *
         * @param lo Lower bound of the normalized interval.
         * @return the normalization operator.
         */
        public static DoubleUnaryOperator normalizer(final double lo) {
            return new Normalizer(lo, TURN_TO_DEG);
        }
    }

    /**
     * Normalizes an angle around a center value.
     */
    private static final class Normalizer implements DoubleUnaryOperator {
        /** Lower bound. */
        private final double lo;
        /** Upper bound. */
        private final double hi;
        /** Period. */
        private final double period;
        /** Normalizer. */
        private final Reduce reduce;

        /**
         * Note: It is assumed that both arguments have the same unit.
         *
         * @param lo Lower bound of the desired interval.
         * @param period Circonference of the circle.
         */
        Normalizer(final double lo,
                   final double period) {
            this.period = period;
            this.lo = lo;
            this.hi = lo + period;
            reduce = new Reduce(lo, period);
        }

        /**
         * @param a Angle.
         * @return {@code = a - k} where {@code k} is an integer that satisfies
         * {@code lo <= a - k < lo + period}.
         */
        @Override
        public double applyAsDouble(final double a) {
            if (lo <= a &&
                a < hi) {
                // Already within the main interval.
                return a;
            }

            final double normalized = reduce.applyAsDouble(a) + lo;
            return normalized < hi ?
                normalized :
                // If value is too small to be representable compared to the
                // floor expression above (i.e. value + x = x), then we may
                // end up with a number exactly equal to the upper bound.
                // In that case, subtract one period from the normalized value
                // so that the result is strictly less than the upper bound. (We also
                // want to ensure that we do not return anything less than the lower bound.)
                Math.max(lo, normalized - period);
        }
    }
}