three.js/src/math/MathUtils.js

let _seed = 1234567;

const DEG2RAD = Math.PI / 180;
const RAD2DEG = 180 / Math.PI;

//

const _lut = [];

for ( let i = 0; i < 256; i ++ ) {

	_lut[ i ] = ( i < 16 ? '0' : '' ) + ( i ).toString( 16 );

}

const hasRandomUUID = typeof crypto !== 'undefined' && 'randomUUID' in crypto;

function generateUUID() {

	if ( hasRandomUUID ) {

		return crypto.randomUUID().toUpperCase();

	}

	// TODO Remove this code when crypto.randomUUID() is available everywhere
	// http://stackoverflow.com/questions/105034/how-to-create-a-guid-uuid-in-javascript/21963136#21963136

	const d0 = Math.random() * 0xffffffff | 0;
	const d1 = Math.random() * 0xffffffff | 0;
	const d2 = Math.random() * 0xffffffff | 0;
	const d3 = Math.random() * 0xffffffff | 0;
	const uuid = _lut[ d0 & 0xff ] + _lut[ d0 >> 8 & 0xff ] + _lut[ d0 >> 16 & 0xff ] + _lut[ d0 >> 24 & 0xff ] + '-' +
			_lut[ d1 & 0xff ] + _lut[ d1 >> 8 & 0xff ] + '-' + _lut[ d1 >> 16 & 0x0f | 0x40 ] + _lut[ d1 >> 24 & 0xff ] + '-' +
			_lut[ d2 & 0x3f | 0x80 ] + _lut[ d2 >> 8 & 0xff ] + '-' + _lut[ d2 >> 16 & 0xff ] + _lut[ d2 >> 24 & 0xff ] +
			_lut[ d3 & 0xff ] + _lut[ d3 >> 8 & 0xff ] + _lut[ d3 >> 16 & 0xff ] + _lut[ d3 >> 24 & 0xff ];

	// .toUpperCase() here flattens concatenated strings to save heap memory space.
	return uuid.toUpperCase();

}

function clamp( value, min, max ) {

	return Math.max( min, Math.min( max, value ) );

}

// compute euclidian modulo of m % n
// https://en.wikipedia.org/wiki/Modulo_operation
function euclideanModulo( n, m ) {

	return ( ( n % m ) + m ) % m;

}

// Linear mapping from range <a1, a2> to range <b1, b2>
function mapLinear( x, a1, a2, b1, b2 ) {

	return b1 + ( x - a1 ) * ( b2 - b1 ) / ( a2 - a1 );

}

// https://www.gamedev.net/tutorials/programming/general-and-gameplay-programming/inverse-lerp-a-super-useful-yet-often-overlooked-function-r5230/
function inverseLerp( x, y, value ) {

	if ( x !== y ) {

		return ( value - x ) / ( y - x );

	} else {

		return 0;

	}

}

// https://en.wikipedia.org/wiki/Linear_interpolation
function lerp( x, y, t ) {

	return ( 1 - t ) * x + t * y;

}

// http://www.rorydriscoll.com/2016/03/07/frame-rate-independent-damping-using-lerp/
function damp( x, y, lambda, dt ) {

	return lerp( x, y, 1 - Math.exp( - lambda * dt ) );

}

// https://www.desmos.com/calculator/vcsjnyz7x4
function pingpong( x, length = 1 ) {

	return length - Math.abs( euclideanModulo( x, length * 2 ) - length );

}

// http://en.wikipedia.org/wiki/Smoothstep
function smoothstep( x, min, max ) {

	if ( x <= min ) return 0;
	if ( x >= max ) return 1;

	x = ( x - min ) / ( max - min );

	return x * x * ( 3 - 2 * x );

}

function smootherstep( x, min, max ) {

	if ( x <= min ) return 0;
	if ( x >= max ) return 1;

	x = ( x - min ) / ( max - min );

	return x * x * x * ( x * ( x * 6 - 15 ) + 10 );

}

// Random integer from <low, high> interval
function randInt( low, high ) {

	return low + Math.floor( Math.random() * ( high - low + 1 ) );

}

// Random float from <low, high> interval
function randFloat( low, high ) {

	return low + Math.random() * ( high - low );

}

// Random float from <-range/2, range/2> interval
function randFloatSpread( range ) {

	return range * ( 0.5 - Math.random() );

}

// Deterministic pseudo-random float in the interval [ 0, 1 ]
function seededRandom( s ) {

	if ( s !== undefined ) _seed = s % 2147483647;

	// Park-Miller algorithm

	_seed = _seed * 16807 % 2147483647;

	return ( _seed - 1 ) / 2147483646;

}

function degToRad( degrees ) {

	return degrees * DEG2RAD;

}

function radToDeg( radians ) {

	return radians * RAD2DEG;

}

function isPowerOfTwo( value ) {

	return ( value & ( value - 1 ) ) === 0 && value !== 0;

}

function ceilPowerOfTwo( value ) {

	return Math.pow( 2, Math.ceil( Math.log( value ) / Math.LN2 ) );

}

function floorPowerOfTwo( value ) {

	return Math.pow( 2, Math.floor( Math.log( value ) / Math.LN2 ) );

}

function setQuaternionFromProperEuler( q, a, b, c, order ) {

	// Intrinsic Proper Euler Angles - see https://en.wikipedia.org/wiki/Euler_angles

	// rotations are applied to the axes in the order specified by 'order'
	// rotation by angle 'a' is applied first, then by angle 'b', then by angle 'c'
	// angles are in radians

	const cos = Math.cos;
	const sin = Math.sin;

	const c2 = cos( b / 2 );
	const s2 = sin( b / 2 );

	const c13 = cos( ( a + c ) / 2 );
	const s13 = sin( ( a + c ) / 2 );

	const c1_3 = cos( ( a - c ) / 2 );
	const s1_3 = sin( ( a - c ) / 2 );

	const c3_1 = cos( ( c - a ) / 2 );
	const s3_1 = sin( ( c - a ) / 2 );

	switch ( order ) {

		case 'XYX':
			q.set( c2 * s13, s2 * c1_3, s2 * s1_3, c2 * c13 );
			break;

		case 'YZY':
			q.set( s2 * s1_3, c2 * s13, s2 * c1_3, c2 * c13 );
			break;

		case 'ZXZ':
			q.set( s2 * c1_3, s2 * s1_3, c2 * s13, c2 * c13 );
			break;

		case 'XZX':
			q.set( c2 * s13, s2 * s3_1, s2 * c3_1, c2 * c13 );
			break;

		case 'YXY':
			q.set( s2 * c3_1, c2 * s13, s2 * s3_1, c2 * c13 );
			break;

		case 'ZYZ':
			q.set( s2 * s3_1, s2 * c3_1, c2 * s13, c2 * c13 );
			break;

		default:
			console.warn( 'THREE.MathUtils: .setQuaternionFromProperEuler() encountered an unknown order: ' + order );

	}

}




export {
	DEG2RAD,
	RAD2DEG,
	generateUUID,
	clamp,
	euclideanModulo,
	mapLinear,
	inverseLerp,
	lerp,
	damp,
	pingpong,
	smoothstep,
	smootherstep,
	randInt,
	randFloat,
	randFloatSpread,
	seededRandom,
	degToRad,
	radToDeg,
	isPowerOfTwo,
	ceilPowerOfTwo,
	floorPowerOfTwo,
	setQuaternionFromProperEuler,
};