Babylon.js/src/Math/math.scalar.ts

    /**
     * Scalar computation library
     */
    export class Scalar {

        /**
         * Two pi constants convenient for computation.
         */
        public static TwoPi: number = Math.PI * 2;

        /**
         * Boolean : true if the absolute difference between a and b is lower than epsilon (default = 1.401298E-45)
         * @param a number
         * @param b number
         * @param epsilon (default = 1.401298E-45)
         * @returns true if the absolute difference between a and b is lower than epsilon (default = 1.401298E-45)
         */
        public static WithinEpsilon(a: number, b: number, epsilon: number = 1.401298E-45): boolean {
            var num = a - b;
            return -epsilon <= num && num <= epsilon;
        }

        /**
         * Returns a string : the upper case translation of the number i to hexadecimal.
         * @param i number
         * @returns the upper case translation of the number i to hexadecimal.
         */
        public static ToHex(i: number): string {
            var str = i.toString(16);

            if (i <= 15) {
                return ("0" + str).toUpperCase();
            }

            return str.toUpperCase();
        }

        /**
         * Returns -1 if value is negative and +1 is value is positive.
         * @param value the value
         * @returns the value itself if it's equal to zero.
         */
        public static Sign(value: number): number {
            value = +value; // convert to a number

            if (value === 0 || isNaN(value)) {
                return value;
            }

            return value > 0 ? 1 : -1;
        }

        /**
         * Returns the value itself if it's between min and max.
         * Returns min if the value is lower than min.
         * Returns max if the value is greater than max.
         * @param value the value to clmap
         * @param min the min value to clamp to (default: 0)
         * @param max the max value to clamp to (default: 1)
         * @returns the clamped value
         */
        public static Clamp(value: number, min = 0, max = 1): number {
            return Math.min(max, Math.max(min, value));
        }

        /**
         * the log2 of value.
         * @param value the value to compute log2 of
         * @returns the log2 of value.
         */
        public static Log2(value: number): number {
            return Math.log(value) * Math.LOG2E;
        }

        /**
        * Loops the value, so that it is never larger than length and never smaller than 0.
        *
        * This is similar to the modulo operator but it works with floating point numbers.
        * For example, using 3.0 for t and 2.5 for length, the result would be 0.5.
        * With t = 5 and length = 2.5, the result would be 0.0.
        * Note, however, that the behaviour is not defined for negative numbers as it is for the modulo operator
        * @param value the value
        * @param length the length
        * @returns the looped value
        */
        public static Repeat(value: number, length: number): number {
            return value - Math.floor(value / length) * length;
        }

       /**
        * Normalize the value between 0.0 and 1.0 using min and max values
        * @param value value to normalize
        * @param min max to normalize between
        * @param max min to normalize between
        * @returns the normalized value
        */
        public static Normalize(value: number, min: number, max: number): number {
            return (value - min) / (max - min);
        }

        /**
        * Denormalize the value from 0.0 and 1.0 using min and max values
        * @param normalized value to denormalize
        * @param min max to denormalize between
        * @param max min to denormalize between
        * @returns the denormalized value
        */
        public static Denormalize(normalized: number, min: number, max: number): number {
            return (normalized * (max - min) + min);
        }

        /**
        * Calculates the shortest difference between two given angles given in degrees.
        * @param current current angle in degrees
        * @param target target angle in degrees
        * @returns the delta
        */
        public static DeltaAngle(current: number, target: number): number {
            var num: number = Scalar.Repeat(target - current, 360.0);
            if (num > 180.0) {
                num -= 360.0;
            }
            return num;
        }

        /**
        * PingPongs the value t, so that it is never larger than length and never smaller than 0.
        * @param tx value
        * @param length length
        * @returns The returned value will move back and forth between 0 and length
        */
        public static PingPong(tx: number, length: number): number {
            var t: number = Scalar.Repeat(tx, length * 2.0);
            return length - Math.abs(t - length);
        }

        /**
        * Interpolates between min and max with smoothing at the limits.
        *
        * This function interpolates between min and max in a similar way to Lerp. However, the interpolation will gradually speed up
        * from the start and slow down toward the end. This is useful for creating natural-looking animation, fading and other transitions.
        * @param from from
        * @param to to
        * @param tx value
        * @returns the smooth stepped value
        */
        public static SmoothStep(from: number, to: number, tx: number): number {
            var t: number = Scalar.Clamp(tx);
            t = -2.0 * t * t * t + 3.0 * t * t;
            return to * t + from * (1.0 - t);
        }

        /**
        * Moves a value current towards target.
        *
        * This is essentially the same as Mathf.Lerp but instead the function will ensure that the speed never exceeds maxDelta.
        * Negative values of maxDelta pushes the value away from target.
        * @param current current value
        * @param target target value
        * @param maxDelta max distance to move
        * @returns resulting value
        */
        public static MoveTowards(current: number, target: number, maxDelta: number): number {
            var result: number = 0;
            if (Math.abs(target - current) <= maxDelta) {
                result = target;
            } else {
                result = current + Scalar.Sign(target - current) * maxDelta;
            }
            return result;
        }

        /**
        * Same as MoveTowards but makes sure the values interpolate correctly when they wrap around 360 degrees.
        *
        * Variables current and target are assumed to be in degrees. For optimization reasons, negative values of maxDelta
        *  are not supported and may cause oscillation. To push current away from a target angle, add 180 to that angle instead.
        * @param current current value
        * @param target target value
        * @param maxDelta max distance to move
        * @returns resulting angle
        */
        public static MoveTowardsAngle(current: number, target: number, maxDelta: number): number {
            var num: number = Scalar.DeltaAngle(current, target);
            var result: number = 0;
            if (-maxDelta < num && num < maxDelta) {
                result = target;
            } else {
                target = current + num;
                result = Scalar.MoveTowards(current, target, maxDelta);
            }
            return result;
        }

        /**
         * Creates a new scalar with values linearly interpolated of "amount" between the start scalar and the end scalar.
         * @param start start value
         * @param end target value
         * @param amount amount to lerp between
         * @returns the lerped value
         */
        public static Lerp(start: number, end: number, amount: number): number {
            return start + ((end - start) * amount);
        }

        /**
        * Same as Lerp but makes sure the values interpolate correctly when they wrap around 360 degrees.
        * The parameter t is clamped to the range [0, 1]. Variables a and b are assumed to be in degrees.
        * @param start start value
        * @param end target value
        * @param amount amount to lerp between
        * @returns the lerped value
        */
        public static LerpAngle(start: number, end: number, amount: number): number {
            var num: number = Scalar.Repeat(end - start, 360.0);
            if (num > 180.0) {
                num -= 360.0;
            }
            return start + num * Scalar.Clamp(amount);
        }

        /**
        * Calculates the linear parameter t that produces the interpolant value within the range [a, b].
        * @param a start value
        * @param b target value
        * @param value value between a and b
        * @returns the inverseLerp value
        */
        public static InverseLerp(a: number, b: number, value: number): number {
            var result: number = 0;
            if (a != b) {
                result = Scalar.Clamp((value - a) / (b - a));
            } else {
                result = 0.0;
            }
            return result;
        }

        /**
         * Returns a new scalar located for "amount" (float) on the Hermite spline defined by the scalars "value1", "value3", "tangent1", "tangent2".
         * @see http://mathworld.wolfram.com/HermitePolynomial.html
         * @param value1 spline value
         * @param tangent1 spline value
         * @param value2 spline value
         * @param tangent2 spline value
         * @param amount input value
         * @returns hermite result
         */
        public static Hermite(value1: number, tangent1: number, value2: number, tangent2: number, amount: number): number {
            var squared = amount * amount;
            var cubed = amount * squared;
            var part1 = ((2.0 * cubed) - (3.0 * squared)) + 1.0;
            var part2 = (-2.0 * cubed) + (3.0 * squared);
            var part3 = (cubed - (2.0 * squared)) + amount;
            var part4 = cubed - squared;

            return (((value1 * part1) + (value2 * part2)) + (tangent1 * part3)) + (tangent2 * part4);
        }

        /**
        * Returns a random float number between and min and max values
        * @param min min value of random
        * @param max max value of random
        * @returns random value
        */
        public static RandomRange(min: number, max: number): number {
            if (min === max) { return min; }
            return ((Math.random() * (max - min)) + min);
        }

        /**
        * This function returns percentage of a number in a given range.
        *
        * RangeToPercent(40,20,60) will return 0.5 (50%)
        * RangeToPercent(34,0,100) will return 0.34 (34%)
        * @param number to convert to percentage
        * @param min min range
        * @param max max range
        * @returns the percentage
        */
        public static RangeToPercent(number: number, min: number, max: number): number {
            return ((number - min) / (max - min));
        }

        /**
        * This function returns number that corresponds to the percentage in a given range.
        *
        * PercentToRange(0.34,0,100) will return 34.
        * @param percent to convert to number
        * @param min min range
        * @param max max range
        * @returns the number
        */
        public static PercentToRange(percent: number, min: number, max: number): number {
            return ((max - min) * percent + min);
        }

        /**
         * Returns the angle converted to equivalent value between -Math.PI and Math.PI radians.
         * @param angle The angle to normalize in radian.
         * @return The converted angle.
         */
        public static NormalizeRadians(angle: number): number {
            // More precise but slower version kept for reference.
            // angle = angle % Tools.TwoPi;
            // angle = (angle + Tools.TwoPi) % Tools.TwoPi;

            //if (angle > Math.PI) {
            //	angle -= Tools.TwoPi;
            //}

            angle -= (Scalar.TwoPi * Math.floor((angle + Math.PI) / Scalar.TwoPi));

            return angle;
        }
    }