three.js/src/math/MathUtils.js

const _lut = [ '00', '01', '02', '03', '04', '05', '06', '07', '08', '09', '0a', '0b', '0c', '0d', '0e', '0f', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19', '1a', '1b', '1c', '1d', '1e', '1f', '20', '21', '22', '23', '24', '25', '26', '27', '28', '29', '2a', '2b', '2c', '2d', '2e', '2f', '30', '31', '32', '33', '34', '35', '36', '37', '38', '39', '3a', '3b', '3c', '3d', '3e', '3f', '40', '41', '42', '43', '44', '45', '46', '47', '48', '49', '4a', '4b', '4c', '4d', '4e', '4f', '50', '51', '52', '53', '54', '55', '56', '57', '58', '59', '5a', '5b', '5c', '5d', '5e', '5f', '60', '61', '62', '63', '64', '65', '66', '67', '68', '69', '6a', '6b', '6c', '6d', '6e', '6f', '70', '71', '72', '73', '74', '75', '76', '77', '78', '79', '7a', '7b', '7c', '7d', '7e', '7f', '80', '81', '82', '83', '84', '85', '86', '87', '88', '89', '8a', '8b', '8c', '8d', '8e', '8f', '90', '91', '92', '93', '94', '95', '96', '97', '98', '99', '9a', '9b', '9c', '9d', '9e', '9f', 'a0', 'a1', 'a2', 'a3', 'a4', 'a5', 'a6', 'a7', 'a8', 'a9', 'aa', 'ab', 'ac', 'ad', 'ae', 'af', 'b0', 'b1', 'b2', 'b3', 'b4', 'b5', 'b6', 'b7', 'b8', 'b9', 'ba', 'bb', 'bc', 'bd', 'be', 'bf', 'c0', 'c1', 'c2', 'c3', 'c4', 'c5', 'c6', 'c7', 'c8', 'c9', 'ca', 'cb', 'cc', 'cd', 'ce', 'cf', 'd0', 'd1', 'd2', 'd3', 'd4', 'd5', 'd6', 'd7', 'd8', 'd9', 'da', 'db', 'dc', 'dd', 'de', 'df', 'e0', 'e1', 'e2', 'e3', 'e4', 'e5', 'e6', 'e7', 'e8', 'e9', 'ea', 'eb', 'ec', 'ed', 'ee', 'ef', 'f0', 'f1', 'f2', 'f3', 'f4', 'f5', 'f6', 'f7', 'f8', 'f9', 'fa', 'fb', 'fc', 'fd', 'fe', 'ff' ];

let _seed = 1234567;


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

// http://stackoverflow.com/questions/105034/how-to-create-a-guid-uuid-in-javascript/21963136#21963136
function generateUUID() {

	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 ];

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

}

function clamp( value, min, max ) {

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

}

// compute euclidean 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;

	// Mulberry32 generator

	let t = _seed += 0x6D2B79F5;

	t = Math.imul( t ^ t >>> 15, t | 1 );

	t ^= t + Math.imul( t ^ t >>> 7, t | 61 );

	return ( ( t ^ t >>> 14 ) >>> 0 ) / 4294967296;

}

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 );

	}

}

function denormalize( value, array ) {

	switch ( array.constructor ) {

		case Float32Array:

			return value;

		case Uint32Array:

			return value / 4294967295.0;

		case Uint16Array:

			return value / 65535.0;

		case Uint8Array:

			return value / 255.0;

		case Int32Array:

			return Math.max( value / 2147483647.0, - 1.0 );

		case Int16Array:

			return Math.max( value / 32767.0, - 1.0 );

		case Int8Array:

			return Math.max( value / 127.0, - 1.0 );

		default:

			throw new Error( 'Invalid component type.' );

	}

}

function normalize( value, array ) {

	switch ( array.constructor ) {

		case Float32Array:

			return value;

		case Uint32Array:

			return Math.round( value * 4294967295.0 );

		case Uint16Array:

			return Math.round( value * 65535.0 );

		case Uint8Array:

			return Math.round( value * 255.0 );

		case Int32Array:

			return Math.round( value * 2147483647.0 );

		case Int16Array:

			return Math.round( value * 32767.0 );

		case Int8Array:

			return Math.round( value * 127.0 );

		default:

			throw new Error( 'Invalid component type.' );

	}

}

const MathUtils = {
	DEG2RAD: DEG2RAD,
	RAD2DEG: RAD2DEG,
	generateUUID: generateUUID,
	clamp: clamp,
	euclideanModulo: euclideanModulo,
	mapLinear: mapLinear,
	inverseLerp: inverseLerp,
	lerp: lerp,
	damp: damp,
	pingpong: pingpong,
	smoothstep: smoothstep,
	smootherstep: smootherstep,
	randInt: randInt,
	randFloat: randFloat,
	randFloatSpread: randFloatSpread,
	seededRandom: seededRandom,
	degToRad: degToRad,
	radToDeg: radToDeg,
	isPowerOfTwo: isPowerOfTwo,
	ceilPowerOfTwo: ceilPowerOfTwo,
	floorPowerOfTwo: floorPowerOfTwo,
	setQuaternionFromProperEuler: setQuaternionFromProperEuler,
	normalize: normalize,
	denormalize: denormalize
};

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