# modeling/src/maths/mat4/fromRotation.js

``````const { EPS } = require('../constants')

const { sin, cos } = require('../utils/trigonometry')

const identity = require('./identity')

/**
* Creates a matrix from a given angle around a given axis
* This is equivalent to (but much faster than):
*
*     mat4.identity(dest)
*
* @param {mat4} out - receiving matrix
* @param {Number} rad - angle to rotate the matrix by
* @param {vec3} axis - axis of which to rotate around
* @returns {mat4} out
* @alias module:modeling/maths/mat4.fromRotation
* @example
* let matrix = fromRotation(create(), TAU / 4, [0, 0, 3])
*/
const fromRotation = (out, rad, axis) => {
let [x, y, z] = axis
const lengthSquared = x * x + y * y + z * z

if (Math.abs(lengthSquared) < EPS) {
// axis is 0,0,0 or almost
return identity(out)
}

const len = 1 / Math.sqrt(lengthSquared)
x *= len
y *= len
z *= len

const t = 1 - c

// Perform rotation-specific matrix multiplication
out[0] = x * x * t + c
out[1] = y * x * t + z * s
out[2] = z * x * t - y * s
out[3] = 0
out[4] = x * y * t - z * s
out[5] = y * y * t + c
out[6] = z * y * t + x * s
out[7] = 0
out[8] = x * z * t + y * s
out[9] = y * z * t - x * s
out[10] = z * z * t + c
out[11] = 0
out[12] = 0
out[13] = 0
out[14] = 0
out[15] = 1
return out
}

module.exports = fromRotation
``````