MathUtil.kt

/*
 * Copyright 2013 Google Inc.
 *
 * Licensed 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 com.google.maps.android

import kotlin.math.PI
import kotlin.math.asin
import kotlin.math.atan
import kotlin.math.cos
import kotlin.math.exp
import kotlin.math.ln
import kotlin.math.sin
import kotlin.math.sqrt
import kotlin.math.tan

/**
 * Utility functions that are used my both PolyUtil and SphericalUtil.
 */
object MathUtil {
    /**
     * The earth's radius, in meters.
     * Mean radius as defined by IUGG.
     */
    const val EARTH_RADIUS: Double = 6371009.0

    /**
     * Constant by which to multiply an angular value in degrees to obtain an
     * angular value in radians.
     */
    private const val DEGREES_TO_RADIANS = PI / 180.0

    fun Double.toRadians() = this * DEGREES_TO_RADIANS

    /**
     * Constant by which to multiply an angular value in degrees to obtain an
     * angular value in radians.
     */
    private const val RADIANS_TO_DEGREES = 180.0 / PI

    fun Double.toDegrees() = this * RADIANS_TO_DEGREES

    /**
     * Restrict x to the range [low, high].
     */
    @JvmStatic
    fun clamp(x: Double, low: Double, high: Double): Double {
        return if (x < low) low else (if (x > high) high else x)
    }

    /**
     * Wraps the given value into the inclusive-exclusive interval between min and max.
     *
     * @param n   The value to wrap.
     * @param min The minimum.
     * @param max The maximum.
     */
    @JvmStatic
    fun wrap(n: Double, min: Double, max: Double): Double {
        return if ((n >= min && n < max)) n else (mod(n - min, max - min) + min)
    }

    /**
     * Returns the non-negative remainder of x / m.
     *
     * @param x The operand.
     * @param m The modulus.
     */
    @JvmStatic
    fun mod(x: Double, m: Double): Double {
        return ((x % m) + m) % m
    }

    /**
     * Returns mercator Y corresponding to latitude.
     * See http://en.wikipedia.org/wiki/Mercator_projection .
     */
    @JvmStatic
    fun mercator(lat: Double): Double {
        return ln(tan(lat * 0.5 + Math.PI / 4))
    }

    /**
     * Returns latitude from mercator Y.
     */
    @JvmStatic
    fun inverseMercator(y: Double): Double {
        return 2 * atan(exp(y)) - Math.PI / 2
    }

    /**
     * Returns haversine(angle-in-radians).
     * hav(x) == (1 - cos(x)) / 2 == sin(x / 2)^2.
     */
    @JvmStatic
    fun hav(x: Double): Double {
        val sinHalf = sin(x * 0.5)
        return sinHalf * sinHalf
    }

    /**
     * Computes inverse haversine. Has good numerical stability around 0.
     * arcHav(x) == acos(1 - 2 * x) == 2 * asin(sqrt(x)).
     * The argument must be in [0, 1], and the result is positive.
     */
    @JvmStatic
    fun arcHav(x: Double): Double {
        return 2 * asin(sqrt(x))
    }

    // Given h==hav(x), returns sin(abs(x)).
    @JvmStatic
    fun sinFromHav(h: Double): Double {
        return 2 * sqrt(h * (1 - h))
    }

    // Returns hav(asin(x)).
    @JvmStatic
    fun havFromSin(x: Double): Double {
        val x2 = x * x
        return x2 / (1 + sqrt(1 - x2)) * .5
    }

    // Returns sin(arcHav(x) + arcHav(y)).
    @JvmStatic
    fun sinSumFromHav(x: Double, y: Double): Double {
        val a = sqrt(x * (1 - x))
        val b = sqrt(y * (1 - y))
        return 2 * (a + b - 2 * (a * y + b * x))
    }

    /**
     * Returns hav() of distance from (lat1, lng1) to (lat2, lng2) on the unit sphere.
     */
    @JvmStatic
    fun havDistance(lat1: Double, lat2: Double, dLng: Double): Double {
        return hav(lat1 - lat2) + hav(dLng) * cos(lat1) * cos(lat2)
    }
}