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

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

/**
* Creates a matrix from the given Taitâ€“Bryan angles.
*
* Tait-Bryan Euler angle convention using active, intrinsic rotations around the axes in the order z-y-x.
* @see https://en.wikipedia.org/wiki/Euler_angles
*
* @param {mat4} out - receiving matrix
* @param {Number} yaw - Z rotation in radians
* @param {Number} pitch - Y rotation in radians
* @param {Number} roll - X rotation in radians
* @returns {mat4} out
* @alias module:modeling/maths/mat4.fromTaitBryanRotation
* @example
* let matrix = fromTaitBryanRotation(create(), TAU / 4, 0, TAU / 2)
*/
const fromTaitBryanRotation = (out, yaw, pitch, roll) => {
// precompute sines and cosines of Euler angles
const sy = sin(yaw)
const cy = cos(yaw)
const sp = sin(pitch)
const cp = cos(pitch)
const sr = sin(roll)
const cr = cos(roll)

// create and populate rotation matrix
// left-hand-rule rotation
// const els = [
//  cp*cy, sr*sp*cy - cr*sy, sr*sy + cr*sp*cy, 0,
//  cp*sy, cr*cy + sr*sp*sy, cr*sp*sy - sr*cy, 0,
//  -sp, sr*cp, cr*cp, 0,
//  0, 0, 0, 1
// ]
// right-hand-rule rotation
out[0] = cp * cy
out[1] = cp * sy
out[2] = -sp
out[3] = 0
out[4] = sr * sp * cy - cr * sy
out[5] = cr * cy + sr * sp * sy
out[6] = sr * cp
out[7] = 0
out[8] = sr * sy + cr * sp * cy
out[9] = cr * sp * sy - sr * cy
out[10] = cr * cp
out[11] = 0
out[12] = 0
out[13] = 0
out[14] = 0
out[15] = 1
return out
}

module.exports = fromTaitBryanRotation
``````