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* @module Utils
*/
import * as MC from "@lisn/globals/minification-constants";
import * as MH from "@lisn/globals/minification-helpers";
import { Point, Vector, AtLeastOne } from "@lisn/globals/types";
/**
* Round a number to the given decimal precision.
*
* @category Math
*/
export const roundNumTo = (value: number, numDecimal = 0) => {
const multiplicationFactor = MH.pow(10, numDecimal);
return MH.round(value * multiplicationFactor) / multiplicationFactor;
};
/**
* Returns true if the given value is a valid _finite_ number.
*
* @category Validation
*/
export const isValidNum = (value: unknown): value is number =>
MH.isNumber(value) && MC.NUMBER.isFinite(value);
/**
* Returns true if the given value is a valid _finite_ number or a numerical
* string.
*
* @category Validation
*/
export const isValidNumerical = (
value: unknown,
): value is number | `${number}` => !!toNum(value, false);
/**
* If the given value is a valid _finite_ number, it is returned, otherwise
* the default is returned.
*
* @category Math
*/
export const toNum = <D extends number | false | null = 0>(
value: unknown,
defaultValue: D | 0 = 0,
): number | D => {
const numValue = MH.isLiteralString(value) ? MH.parseFloat(value) : value;
// parseFloat will strip trailing non-numeric characters, so we check that
// the parsed number is equal to the string, if it was a string, using loose
// equality, in order to make sure the entire string was a number.
return isValidNum(numValue) && numValue == value ? numValue : defaultValue;
};
/**
* If the given value is a valid _finite integer_ number, it is returned,
* otherwise the default is returned.
*
* @category Math
*/
export const toInt = <D extends number | false | null = 0>(
value: unknown,
defaultValue: D | 0 = 0,
): number | D => {
let numValue = toNum(value, null);
numValue = numValue === null ? numValue : MH.floor(numValue);
// Ensure that the parsed int equaled the original by loose equality.
return isValidNum(numValue) && numValue == value ? numValue : defaultValue;
};
/**
* If the given value is a valid non-negative _finite_ number, it is returned,
* otherwise the default is returned.
*
* @category Math
*/
export const toNonNegNum = <D extends number | false | null = 0>(
value: unknown,
defaultValue: D | 0 = 0,
): number | D => {
const numValue = toNum(value, null);
return numValue !== null && numValue >= 0 ? numValue : defaultValue;
};
/**
* If the given value is a valid positive number, it is returned, otherwise the
* default is returned.
*
* @category Math
*/
export const toPosNum = <D extends number | false | null = 0>(
value: unknown,
defaultValue: D | 0 = 0,
): number | D => {
const numValue = toNum(value, null);
return numValue !== null && numValue > 0 ? numValue : defaultValue;
};
/**
* Returns the given number bound by min and/or max value.
*
* If the value is not a valid number, then `defaultValue` is returned if given
* (_including if it is null_), otherwise `limits.min` if given and not null,
* otherwise `limits.max` if given and not null, or finally 0.
*
* If the value is outside the bounds, then:
* - if `defaultValue` is given, `defaultValue` is returned (_including if it
* is null_)
* - otherwise, the min or the max value (whichever one is violated) is
* returned
*
* @category Math
*/
export const toNumWithBounds = <D extends number | false | null = number>(
value: unknown,
limits: AtLeastOne<{ min: number | null; max: number | null }>,
defaultValue?: D,
): number | D => {
const isDefaultGiven = defaultValue !== undefined;
const numValue = toNum(value, null);
const min = limits?.min ?? null;
const max = limits?.max ?? null;
let result: number | D;
if (!isValidNum(numValue)) {
result = isDefaultGiven ? defaultValue : (min ?? max ?? 0);
} else if (min !== null && numValue < min) {
result = isDefaultGiven ? defaultValue : min;
} else if (max !== null && numValue > max) {
result = isDefaultGiven ? defaultValue : max;
} else {
result = numValue;
}
return result;
};
/**
* Used as a custom calculator for {@link toRawNum}. The function should return
* the final numerical result.
*
* @since v1.3.0
*
* @category Math
*/
export type RawNumberCalculator = (props: {
/**
* The original value passed to {@link toRawNum}
*/
input: unknown;
/**
* Whether `+` or `-` prefix is present in {@link input}. At least one of
* {@link isAdditive} or {@link isPercent} is guaranteed to be true.
*/
isAdditive: boolean;
/**
* Whether `%` suffix is present in {@link input}. At least one of
* {@link isAdditive} or {@link isPercent} is guaranteed to be true.
*/
isPercent: boolean;
/**
* The actual numerical value of {@link input} after stripping the `%` suffix
* if any, but not the prefix (i.e. it will be negative if there was a `-`
* prefix)
*/
numerical: number;
}) => number;
/**
* Converts the given {@link RawOrRelativeNumber} to a raw number using the
* given reference or calculator function. If the final result is invalid, the
* default is returned.
*
* The default calculation process, if `input` is relative and if
* `referenceOrCalculator` is only a number is as follows:
* - If `input` is percentage, it is multiplied with the reference value.
* Afterwards, if `input` also has a `+` or `-` prefix, the resulting
* percentage is added to the reference. I.e:
* - `"30%"` results in `0.3 * reference`
* - `"+30%"` results in `1.3 * reference`
* - `"-30%"` results in `0.7 * reference`
* - Otherwise, if `input` only has a `+` or `-` prefix it is added or
* subtracted from the reference.
*
* @param input If it's a pure number or a positive numerical string without
* `+` prefix, it is treated as the raw value to use and no
* reference or further calculation is used. Otherwise the raw
* value is calculated using `referenceOrCalculator`
* @param referenceOrCalculator
* If given as a number, it will be the reference value used
* with the default calculation process (see above).
* Otherwise, if given as a function, then it is used as the
* calculator and its return value is used as the final result.
*
* @since v1.3.0
*
* @example
* If you want to use the default calculator function, but specify a custom
* reference value based on the type of input, you could call {@link toRawNum}
* recursively like so:
*
* ```javascript
* const calculator = ({input, isAdditive, isPercent, numerical}) => {
* return toRawNum(input, isAdditive && isPercent ? referenceA : referenceB);
* }
*
* toRawNum(input, calculator);
* ```
*
* @category Math
*/
export const toRawNum = <D extends number | false | null = 0>(
input: unknown,
referenceOrCalculator: number | RawNumberCalculator,
defaultValue?: D,
) => {
let numerical = NaN,
isAdditive = false,
isPercent = false;
if (MH.isNumber(input)) {
numerical = input;
} else if (MH.isString(input)) {
const opA = input.slice(0, 1);
const opB = input.slice(-1);
isAdditive = opA === "+" || opA === "-";
isPercent = opB === "%";
numerical = toNum(isPercent ? input.slice(0, -1) : input, NaN);
}
let result = numerical;
if (isAdditive || isPercent) {
const calculator: RawNumberCalculator = MH.isFunction(referenceOrCalculator)
? referenceOrCalculator
: ({ isAdditive, isPercent, numerical }) => {
const reference = referenceOrCalculator;
if (isPercent) {
return (reference * numerical) / 100 + (isAdditive ? reference : 0);
}
return reference + numerical;
};
result = calculator({ input, isAdditive, isPercent, numerical });
}
return toNum(result, defaultValue);
};
/**
* Returns the largest absolute value among the given ones.
*
* The result is always positive.
*
* @category Math
*/
export const maxAbs = (...values: number[]) =>
MH.max(...values.map((v) => MH.abs(v)));
/**
* Returns the smallest absolute value among the given ones.
*
* The result is always positive.
*
* @category Math
*/
export const minAbs = (...values: number[]) =>
MH.min(...values.map((v) => MH.abs(v)));
/**
* Returns the value with the largest absolute value among the given ones.
*
* The result can be negative.
*
* @category Math
*/
export const havingMaxAbs = (...values: number[]): number =>
MH.lengthOf(values)
? values.sort((a, b) => MH.abs(b) - MH.abs(a))[0]
: -MC.INFINITY;
/**
* Returns the value with the smallest absolute value among the given ones.
*
* The result can be negative.
*
* @category Math
*/
export const havingMinAbs = (...values: number[]) =>
MH.lengthOf(values)
? values.sort((a, b) => MH.abs(a) - MH.abs(b))[0]
: MC.INFINITY;
/**
* Returns the sum of the given values.
*
* @since v1.3.0
*
* @category Math
*/
export const sum = (...values: number[]) =>
values.reduce((total, current) => total + current, 0);
/**
* Returns the angle (in radians) that the vector defined by the given x, y
* makes with the positive horizontal axis.
*
* The angle returned is in the range -PI to PI, not including -PI.
*
* @category Math
*/
export const hAngle = (x: number, y: number) =>
normalizeAngle(MC.MATH.atan2(y, x)); // ensure that -PI is transformed to +PI
/**
* Normalizes the given angle (in radians) so that it's in the range -PI to PI,
* not including -PI.
*
* @category Math
*/
export const normalizeAngle = (a: number) => {
// ensure it's positive in the range 0 to 2 PI
while (a < 0 || a > MC.PI * 2) {
a += (a < 0 ? 1 : -1) * MC.PI * 2;
}
// then, if > PI, offset by - 2PI
return a > MC.PI ? a - MC.PI * 2 : a;
};
/**
* Normalizes a vector defined by the given x, y and z coordinates to length 1.
*
* @since v1.3.0
*
* @category Math
*/
export const normalizeAxis = (x: number, y: number, z = 0) => {
const len = MH.sqrt(x * x + y * y + z * z);
return len > 0 ? [x / len, y / len, z / len] : [0, 0, 0];
};
/**
* Converts the given angle in degrees to radians.
*
* @category Math
*/
export const degToRad = (a: number) => (a * MC.PI) / 180;
/**
* Converts the given angle in radians to degrees.
*
* @category Math
*/
export const radToDeg = (a: number) => (a * 180) / MC.PI;
/**
* Returns true if the given vectors point in the same direction.
*
* @param angleDiffThreshold
* Sets the threshold in degrees when comparing the angles of
* two vectors. E.g. for 5 degrees threshold, directions
* whose vectors are within 5 degrees of each other are
* considered parallel.
* It doesn't make sense for this value to be < 0 or >= 90
* degrees. If it is, it's forced to be positive (absolute)
* and <= 89.99.
*
* @category Math
*/
export const areParallel = (vA: Vector, vB: Vector, angleDiffThreshold = 0) => {
const angleA = hAngle(vA[0], vA[1]);
const angleB = hAngle(vB[0], vB[1]);
angleDiffThreshold = MH.min(89.99, MH.abs(angleDiffThreshold));
return (
MH.abs(normalizeAngle(angleA - angleB)) <= degToRad(angleDiffThreshold)
);
};
/**
* Returns true if the given vectors point in the opposite direction.
*
* @param angleDiffThreshold
* Sets the threshold in degrees when comparing the angles of
* two vectors. E.g. for 5 degrees threshold, directions
* whose vectors are within 175-185 degrees of each other are
* considered antiparallel.
* It doesn't make sense for this value to be < 0 or >= 90
* degrees. If it is, it's forced to be positive (absolute)
* and <= 89.99.
*
* @category Math
*/
export const areAntiParallel = (
vA: Vector,
vB: Vector,
angleDiffThreshold = 0,
) => areParallel(vA, [-vB[0], -vB[1]], angleDiffThreshold);
/**
* Returns the distance between two points on the screen.
*
* @category Math
*/
export const distanceBetween = (ptA: Point, ptB: Point) =>
MH.sqrt(MH.pow(ptA[0] - ptB[0], 2) + MH.pow(ptA[1] - ptB[1], 2));
/**
* Returns the two roots of the quadratic equation with coefficients
* `a`, `b` & `c`, i.e. `a * x^2 + b * x + c = 0`
*
* The roots may be `NaN` if the quadratic has no real solutions.
*
* @category Math
*/
export const quadraticRoots = (a: number, b: number, c: number) => {
const z = MH.sqrt(b * b - 4 * a * c);
return [(-b + z) / (2 * a), (-b - z) / (2 * a)];
};
/**
* Returns the value that an "easing" quadratic function would have at the
* given x.
*
* @see https://easings.net/#easeInOutQuad
*
* @param x Must be between 0 and 1.
*
* @returns The current y-axis value between 0 and 1.
*
* @category Math
*/
export const easeInOutQuad = (x: number) =>
x < 0.5 ? 2 * x * x : 1 - MH.pow(-2 * x + 2, 2) / 2;
/**
* @since v1.3.0
*
* @category Math
*/
export type CriticallyDampedSettings = {
lTarget: number;
dt: number;
lag: number;
l?: number;
v?: number;
precision?: number;
};
/**
* @since v1.3.0
*
* @category Math
*/
export type CriticallyDampedState = {
l: number;
v: number;
dlFr: number;
};
/**
* Returns the new position and velocity for a critically damped user-driven
* spring state toward a current target position.
*
* @param [settings.lTarget] Target final position.
* @param [settings.dt] Time step in milliseconds since the last call.
* Must be small for the returned values to be
* meaningful.
* @param [settings.lag] Lag in milliseconds (how long it should take
* for it to reach the final position). Must be
* positive.
* @param [settings.l = 0] Current position (starting or one returned by
* previous call).
* @param [settings.v = 0] Current velocity (returned by previous call).
* @param [settings.precision = 2] Number of decimal places to round position to
* in order to determine when it's "done".
*
* @returns Updated
* - `l`: position
* - `v`: velocity
* - `dlFr`: fractional change in position since the last call
*
* @since v1.2.0 (Fractional change in position in return value was added in v1.3.0)
*
* @category Math
*/
export const criticallyDamped = (
settings: CriticallyDampedSettings,
): CriticallyDampedState => {
const { lTarget, precision = 2 } = settings;
const lag = toNumWithBounds(settings.lag, { min: 1 }) / 1000; // to seconds
// Since the position only approaches asymptotically the target it never truly
// reaches it exactly we need an approximation to calculate w0. N determines
// how far away from the target position we are after `lag` milliseconds.
const N = 7;
const w0 = N / lag;
let { l = 0, v = 0, dt } = settings;
dt /= 1000; // to seconds
const lPrev = l;
let dlFr = 0;
if (roundNumTo(l - lTarget, precision) === 0) {
// we're done
l = lTarget;
v = 0;
dlFr = 1;
} else if (dt > 0) {
const A = l - lTarget;
const B = v + w0 * A;
const e = MH.exp(-w0 * dt);
l = lTarget + (A + B * dt) * e;
v = (B - w0 * (A + B * dt)) * e;
dlFr = (l - lPrev) / (lTarget - lPrev);
}
return { l, v, dlFr };
};
/**
* An iterator version of {@link criticallyDamped}.
*
* @returns An iterator whose `next` method accepts an optional object with
* updated settings.
* The iterator yields an object containing successive values for:
* - `l`: position
* - `v`: velocity
* - `t`: total time elapsed
* - `dlFr`: fractional (from 0 to 1) change in position since the last frame
*
* @since v1.3.0
*
* @category Math
*/
export function* newCriticallyDampedIterator(
settings: CriticallyDampedSettings,
): Generator<
CriticallyDampedState,
CriticallyDampedState,
Partial<CriticallyDampedSettings>
> {
let { lTarget, dt, lag, l, v, precision } = settings;
let dlFr = 0;
const next = () => {
({ l, v, dlFr } = criticallyDamped({
lTarget,
lag,
l,
dt,
v,
precision,
}));
return { l, v, dlFr };
};
while (true) {
const result = next();
({
lTarget = lTarget,
dt = dt,
lag = lag,
l = l,
v = v,
precision = precision,
} = (yield result) ?? {});
if (l === lTarget) {
return result;
}
}
}
/**
* Returns an array of object's keys sorted by the numeric value they hold.
*
* @category Math
*/
export const sortedKeysByVal = <T extends Record<string, number>>(
obj: T,
descending = false,
): Array<keyof T> => {
if (descending) {
return MH.keysOf(obj).sort((x: keyof T, y: keyof T) => obj[y] - obj[x]);
}
return MH.keysOf(obj).sort((x: keyof T, y: keyof T) => obj[x] - obj[y]);
};
/**
* Returns the key in the given object which holds the largest numeric value.
*
* If the object is empty, returns `undefined`.
*
* @category Math
*/
export const keyWithMaxVal = (
obj: Record<string, number>,
): string | undefined => {
return MH.lastOf(sortedKeysByVal(obj));
};
/**
* Returns the key in the given object which holds the smallest numeric value.
*
* If the object is empty, returns `undefined`.
*
* @category Math
*/
export const keyWithMinVal = (
obj: Record<string, number>,
): string | undefined => {
return MH.firstOf(sortedKeysByVal(obj));
};
/**
* Takes two integers and returns a bitmask that covers all values between
* 1 << start and 1 << end, _including the starting and ending one_.
*
* If pStart > pEnd, they are reversed.
*
* getBitmask(start, start) always returns 1 << start
* getBitmask(start, end) always returns same as getBitmask(end, start)
*
* @category Math
*/
export const getBitmask = (start: number, end: number): number =>
start > end
? getBitmask(end, start)
: (~0 >>> (32 - end - 1 + start)) << start;
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