prestonbane/src/engine/math/FastMath.java

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//      Magicbane Emulator Project © 2013 - 2022
//                www.magicbane.com

package engine.math;

import java.util.Calendar;
import java.util.concurrent.ThreadLocalRandom;

/**
 * <code>FastMath</code> provides 'fast' math approximations and float
 * equivalents of Math functions. These are all used as static values and
 * functions.
 *
 * @author Various
 */

final public class FastMath {

    /**
     * A "close to zero" double epsilon value for use
     */
    public static final double DBL_EPSILON = 2.220446049250313E-16d;
    /**
     * A "close to zero" float epsilon value for use
     */
    public static final float FLT_EPSILON = 1.1920928955078125E-7f;
    /**
     * A "close to zero" float epsilon value for use
     */
    public static final float ZERO_TOLERANCE = 0.0001f;
    public static final float ONE_THIRD = 1f / 3f;
    /**
     * The value PI as a float. (180 degrees)
     */
    public static final float PI = (float) Math.PI;
    /**
     * The value 2PI as a float. (360 degrees)
     */
    public static final float TWO_PI = 2.0f * PI;
    /**
     * The value 1/(2PI) as a float.
     */
    public static final float INV_TWO_PI = 1.0f / TWO_PI;
    /**
     * The value PI/2 as a float. (90 degrees)
     */
    public static final float HALF_PI = 0.5f * PI;

    /**
     * The value PI/4 as a float. (45 degrees)
     */
    public static final float QUARTER_PI = 0.25f * PI;

    /**
     * The value 1/PI as a float.
     */
    public static final float INV_PI = 1.0f / PI;
    /**
     * A value to multiply a degree value by, to convert it to radians.
     */
    public static final float DEG_TO_RAD = PI / 180.0f;
    /**
     * A value to multiply a radian value by, to convert it to degrees.
     */
    public static final float RAD_TO_DEG = 180.0f / PI;

    private FastMath() {
    }

    /**
     * Returns true if the number is a power of 2 (2,4,8,16...)
     * <p>
     * A good implementation found on the Java boards. note: a number is a power
     * of two if and only if it is the smallest number with that number of
     * significant bits. Therefore, if you subtract 1, you know that the new
     * number will have fewer bits, so ANDing the original number with anything
     * less than it will give 0.
     *
     * @param number The number to test.
     * @return True if it is a power of two.
     */
    public static boolean isPowerOfTwo(int number) {
        return (number > 0) && (number & (number - 1)) == 0;
    }

    public static int nearestPowerOfTwo(int number) {
        return (int) Math.pow(2, Math.ceil(Math.log(number) / Math.log(2)));
    }

    public static boolean between(float i, float minValueInclusive, float maxValueInclusive) {
        return (i >= minValueInclusive && i <= maxValueInclusive);
    }

    /**
     * Linear interpolation from startValue to endValue by the given percent.
     * Basically: ((1 - percent) * startValue) + (percent * endValue)
     *
     * @param percent    Percent value to use.
     * @param startValue Begining value. 0% of f
     * @param endValue   ending value. 100% of f
     * @return The interpolated value between startValue and endValue.
     */
    public static float LERP(float percent, float startValue, float endValue) {
        if (startValue == endValue)
            return startValue;
        return ((1 - percent) * startValue) + (percent * endValue);
    }

    /**
     * Returns the arc cosine of an angle given in radians.<br>
     * Special cases:
     * <ul>
     * <li>If fValue is smaller than -1, then the result is PI.
     * <li>If the argument is greater than 1, then the result is 0.
     * </ul>
     *
     * @param fValue The angle, in radians.
     * @return fValue's acos
     * @see java.lang.Math#acos(double)
     */
    public static float acos(float fValue) {
        if (-1.0f < fValue) {
            if (fValue < 1.0f)
                return (float) Math.acos(fValue);

            return 0.0f;
        }

        return PI;
    }

    /**
     * Returns the arc sine of an angle given in radians.<br>
     * Special cases:
     * <ul>
     * <li>If fValue is smaller than -1, then the result is -HALF_PI.
     * <li>If the argument is greater than 1, then the result is HALF_PI.
     * </ul>
     *
     * @param fValue The angle, in radians.
     * @return fValue's asin
     * @see java.lang.Math#asin(double)
     */
    public static float asin(float fValue) {
        if (-1.0f < fValue) {
            if (fValue < 1.0f)
                return (float) Math.asin(fValue);

            return HALF_PI;
        }

        return -HALF_PI;
    }

    /**
     * Returns the arc tangent of an angle given in radians.<br>
     *
     * @param fValue The angle, in radians.
     * @return fValue's asin
     * @see java.lang.Math#atan(double)
     */
    public static float atan(float fValue) {
        return (float) Math.atan(fValue);
    }

    /**
     * A direct call to Math.atan2.
     *
     * @param fY
     * @param fX
     * @return Math.atan2(fY, fX)
     * @see java.lang.Math#atan2(double, double)
     */
    public static float atan2(float fY, float fX) {
        return (float) Math.atan2(fY, fX);
    }

    /**
     * Rounds a fValue up. A call to Math.ceil
     *
     * @param fValue The value.
     * @return The fValue rounded up
     * @see java.lang.Math#ceil(double)
     */
    public static float ceil(float fValue) {
        return (float) Math.ceil(fValue);
    }

    /**
     * Fast Trig functions for x86. This forces the trig functiosn to stay
     * within the safe area on the x86 processor (-45 degrees to +45 degrees)
     * The results may be very slightly off from what the Math and StrictMath
     * trig functions give due to rounding in the angle reduction but it will be
     * very very close.
     */
    public static float reduceSinAngle(float radians) {
        radians %= TWO_PI; // put us in -2PI to +2PI space
        if (Math.abs(radians) > PI) { // put us in -PI to +PI space
            radians -= (TWO_PI);
        }
        if (Math.abs(radians) > HALF_PI) {// put us in -PI/2 to +PI/2 space
            radians = PI - radians;
        }

        return radians;
    }

    /**
     * Returns sine of a value.
     *
     * @param fValue The value to sine, in radians.
     * @return The sine of fValue.
     * @see java.lang.Math#sin(double)
     */
    public static float sin(float fValue) {
        fValue = reduceSinAngle(fValue); // limits angle to between -PI/2 and
        // +PI/2
        if (Math.abs(fValue) <= Math.PI / 4) {
            return (float) Math.sin(fValue);
        }

        return (float) Math.cos(Math.PI / 2 - fValue);
    }

    /**
     * Returns cos of a value.
     *
     * @param fValue The value to cosine, in radians.
     * @return The cosine of fValue.
     * @see java.lang.Math#cos(double)
     */
    public static float cos(float fValue) {
        return sin(fValue + HALF_PI);
    }

    /**
     * Returns E^fValue
     *
     * @param fValue Value to raise to a power.
     * @return The value E^fValue
     * @see java.lang.Math#exp(double)
     */
    public static float exp(float fValue) {
        return (float) Math.exp(fValue);
    }

    /**
     * Returns Absolute value of a float.
     *
     * @param fValue The value to abs.
     * @return The abs of the value.
     * @see java.lang.Math#abs(float)
     */
    public static float abs(float fValue) {
        if (fValue < 0)
            return -fValue;
        return fValue;
    }

    /**
     * Returns a number rounded down.
     *
     * @param fValue The value to round
     * @return The given number rounded down
     * @see java.lang.Math#floor(double)
     */
    public static float floor(float fValue) {
        return (float) Math.floor(fValue);
    }

    /**
     * Returns 1/sqrt(fValue)
     *
     * @param fValue The value to process.
     * @return 1/sqrt(fValue)
     * @see java.lang.Math#sqrt(double)
     */
    public static float invSqrt(float fValue) {
        return (float) (1.0f / Math.sqrt(fValue));
    }

    /**
     * Returns the log base E of a value.
     *
     * @param fValue The value to Logger.getInstance().
     * @return The log of fValue base E
     * @see java.lang.Math#log(double)
     */
    public static float log(float fValue) {
        return (float) Math.log(fValue);
    }

    /**
     * Returns the logarithm of value with given base, calculated as
     * log(value)/log(base), so that pow(base, return)==value (contributed by
     * vear)
     *
     * @param value The value to Logger.getInstance().
     * @param base  Base of logarithm.
     * @return The logarithm of value with given base
     */
    public static float log(float value, float base) {
        return (float) (Math.log(value) / Math.log(base));
    }

    /**
     * Returns a number raised to an exponent power. fBase^fExponent
     *
     * @param fBase     The base value (IE 2)
     * @param fExponent The exponent value (IE 3)
     * @return base raised to exponent (IE 8)
     * @see java.lang.Math#pow(double, double)
     */
    public static float pow(float fBase, float fExponent) {
        return (float) Math.pow(fBase, fExponent);
    }

    /**
     * Returns the value squared. fValue ^ 2
     *
     * @param fValue The vaule to square.
     * @return The square of the given value.
     */
    public static float sqr(float fValue) {
        return fValue * fValue;
    }

    public static double sqr(double fValue) {
        return fValue * fValue;
    }

    /**
     * Returns the square root of a given value.
     *
     * @param fValue The value to sqrt.
     * @return The square root of the given value.
     * @see java.lang.Math#sqrt(double)
     */
    public static float sqrt(float fValue) {
        return (float) Math.sqrt(fValue);
    }

    /**
     * Returns the tangent of a value. If USE_FAST_TRIG is enabled, an
     * approximate value is returned. Otherwise, a direct value is used.
     *
     * @param fValue The value to tangent, in radians.
     * @return The tangent of fValue.
     * @see java.lang.Math#tan(double)
     */
    public static float tan(float fValue) {
        return (float) Math.tan(fValue);
    }

    /**
     * Returns 1 if the number is positive, -1 if the number is negative, and 0
     * otherwise
     *
     * @param iValue The integer to examine.
     * @return The integer's sign.
     */
    public static int sign(int iValue) {
        if (iValue > 0)
            return 1;

        if (iValue < 0)
            return -1;

        return 0;
    }

    /**
     * Returns 1 if the number is positive, -1 if the number is negative, and 0
     * otherwise
     *
     * @param fValue The float to examine.
     * @return The float's sign.
     */
    public static float sign(float fValue) {
        return Math.signum(fValue);
    }

    /**
     * Given 3 points in a 2d plane, this function computes if the points going
     * from A-B-C are moving counter clock wise.
     *
     * @param p0 Point 0.
     * @param p1 Point 1.
     * @param p2 Point 2.
     * @return 1 If they are CCW, -1 if they are not CCW, 0 if p2 is between p0
     * and p1.
     */
    public static int counterClockwise(Vector2f p0, Vector2f p1, Vector2f p2) {
        float dx1, dx2, dy1, dy2;
        dx1 = p1.x - p0.x;
        dy1 = p1.y - p0.y;
        dx2 = p2.x - p0.x;
        dy2 = p2.y - p0.y;
        if (dx1 * dy2 > dy1 * dx2)
            return 1;
        if (dx1 * dy2 < dy1 * dx2)
            return -1;
        if ((dx1 * dx2 < 0) || (dy1 * dy2 < 0))
            return -1;
        if ((dx1 * dx1 + dy1 * dy1) < (dx2 * dx2 + dy2 * dy2))
            return 1;
        return 0;
    }

    /**
     * Test if a point is inside a triangle. 1 if the point is on the ccw side,
     * -1 if the point is on the cw side, and 0 if it is on neither.
     *
     * @param t0 First point of the triangle.
     * @param t1 Second point of the triangle.
     * @param t2 Third point of the triangle.
     * @param p  The point to test.
     * @return Value 1 or -1 if inside triangle, 0 otherwise.
     */
    public static int pointInsideTriangle(Vector2f t0, Vector2f t1,
                                          Vector2f t2, Vector2f p) {
        int val1 = counterClockwise(t0, t1, p);
        if (val1 == 0)
            return 1;
        int val2 = counterClockwise(t1, t2, p);
        if (val2 == 0)
            return 1;
        if (val2 != val1)
            return 0;
        int val3 = counterClockwise(t2, t0, p);
        if (val3 == 0)
            return 1;
        if (val3 != val1)
            return 0;
        return val3;
    }

    /**
     * Returns the determinant of a 4x4 matrix.
     */
    public static float determinant(double m00, double m01, double m02,
                                    double m03, double m10, double m11, double m12, double m13,
                                    double m20, double m21, double m22, double m23, double m30,
                                    double m31, double m32, double m33) {

        double det01 = m20 * m31 - m21 * m30;
        double det02 = m20 * m32 - m22 * m30;
        double det03 = m20 * m33 - m23 * m30;
        double det12 = m21 * m32 - m22 * m31;
        double det13 = m21 * m33 - m23 * m31;
        double det23 = m22 * m33 - m23 * m32;
        return (float) (m00 * (m11 * det23 - m12 * det13 + m13 * det12) - m01
                * (m10 * det23 - m12 * det03 + m13 * det02) + m02
                * (m10 * det13 - m11 * det03 + m13 * det01) - m03
                * (m10 * det12 - m11 * det02 + m12 * det01));
    }

    /**
     * Converts a point from Spherical coordinates to Cartesian (using positive
     * Y as up) and stores the results in the store var.
     */
    public static Vector3f sphericalToCartesian(Vector3f sphereCoords,
                                                Vector3f store) {
        store.y = sphereCoords.x * FastMath.sin(sphereCoords.z);
        float a = sphereCoords.x * FastMath.cos(sphereCoords.z);
        store.x = a * FastMath.cos(sphereCoords.y);
        store.z = a * FastMath.sin(sphereCoords.y);

        return store;
    }

    /**
     * Converts a point from Cartesian coordinates (using positive Y as up) to
     * Spherical and stores the results in the store var. (Radius, Azimuth,
     * Polar)
     */
    public static Vector3f cartesianToSpherical(Vector3f cartCoords,
                                                Vector3f store) {
        if (cartCoords.x == 0)
            cartCoords.x = FastMath.FLT_EPSILON;
        store.x = FastMath
                .sqrt((cartCoords.x * cartCoords.x)
                        + (cartCoords.y * cartCoords.y)
                        + (cartCoords.z * cartCoords.z));
        store.y = FastMath.atan(cartCoords.z / cartCoords.x);
        if (cartCoords.x < 0)
            store.y += FastMath.PI;
        store.z = FastMath.asin(cartCoords.y / store.x);
        return store;
    }

    /**
     * Converts a point from Spherical coordinates to Cartesian (using positive
     * Z as up) and stores the results in the store var.
     */
    public static Vector3f sphericalToCartesianZ(Vector3f sphereCoords,
                                                 Vector3f store) {
        store.z = sphereCoords.x * FastMath.sin(sphereCoords.z);
        float a = sphereCoords.x * FastMath.cos(sphereCoords.z);
        store.x = a * FastMath.cos(sphereCoords.y);
        store.y = a * FastMath.sin(sphereCoords.y);

        return store;
    }

    /**
     * Converts a point from Cartesian coordinates (using positive Z as up) to
     * Spherical and stores the results in the store var. (Radius, Azimuth,
     * Polar)
     */
    public static Vector3f cartesianZToSpherical(Vector3f cartCoords,
                                                 Vector3f store) {
        if (cartCoords.x == 0)
            cartCoords.x = FastMath.FLT_EPSILON;
        store.x = FastMath
                .sqrt((cartCoords.x * cartCoords.x)
                        + (cartCoords.y * cartCoords.y)
                        + (cartCoords.z * cartCoords.z));
        store.z = FastMath.atan(cartCoords.z / cartCoords.x);
        if (cartCoords.x < 0)
            store.z += FastMath.PI;
        store.y = FastMath.asin(cartCoords.y / store.x);
        return store;
    }

    /**
     * Takes an value and expresses it in terms of min to max.
     *
     * @param val - the angle to normalize (in radians)
     * @return the normalized angle (also in radians)
     */
    public static float normalize(float val, float min, float max) {
        if (Float.isInfinite(val) || Float.isNaN(val))
            return 0f;
        float range = max - min;
        while (val > max)
            val -= range;
        while (val < min)
            val += range;
        return val;
    }

    /**
     * @param x the value whose sign is to be adjusted.
     * @param y the value whose sign is to be used.
     * @return x with its sign changed to match the sign of y.
     */
    public static float copysign(float x, float y) {
        if (y >= 0 && x <= -0)
            return -x;
        else if (y < 0 && x >= 0)
            return -x;
        else
            return x;
    }

    /**
     * Take a float input and clamp it between min and max.
     *
     * @param input
     * @param min
     * @param max
     * @return clamped input
     */
    public static float clamp(float input, float min, float max) {
        return (input < min) ? min : (input > max) ? max : input;
    }


    /**
     * Return a random 2D vector
     * this needs checked
     */
    public static Vector3fImmutable randomVector2D() {
        float x = ((ThreadLocalRandom.current().nextFloat() * 2) - 1);
        float z = ((ThreadLocalRandom.current().nextFloat() * 2) - 1);
        Vector3fImmutable ret = new Vector3fImmutable(x, 0, z);
        return ret.normalize();
    }

    /**
     * Turns a String into an Integer hash that the client will recognize.
     *
     * @param s The String to hash
     * @return the Integer hash
     */
    public static int hash(String s) {
        int out = 0, pad = 0;
        for (char c : s.toCharArray()) {
            if (c == ' ' || c == '\\') {
                pad += 5;
                continue;
            }
            if (c > 0x40 && c < 0x60)
                out ^= _rotl((byte) 0x60, pad);
            out ^= _rotl((byte) (c & 0xDF), pad);
            pad += 5;
        }
        return out;
    }

    /**
     * Utility function for making hashes
     */
    private static int _rotl(int value, int shift) {
        if ((shift &= 31) == 0)
            return value;
        return (value << shift) | (value >> (32 - shift));
    }

    /**
     * Gets number of seconds until next hours
     */

    public static int secondsUntilNextHour() {
        Calendar cal = Calendar.getInstance();
        int minute = cal.get(Calendar.MINUTE);
        int second = cal.get(Calendar.SECOND);
        return 3600 - (minute * 60) - second;
    }

    public static float area(float x1, float y1, float x2, float y2, float x3, float y3) {
        return (float) Math.abs((x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0); //Change to *.5?
    }

    public static float GetDegrees(float yRot) {
        double radian = Math.asin(yRot);
        float degrees = (float) Math.toDegrees(radian);

        degrees *= 2;
        return degrees;
    }

    public static float degreesToW(float degrees) {
        return (float) Math.abs(Math.cos(Math.toRadians(degrees) / 2));
    }

    public static float degreesToYRotation(float degrees) {
        return (float) Math.sin(Math.toRadians(degrees) / 2);
    }
}