# Source: quat.js

``````import * as glMatrix from "./common.js";
import * as mat3 from "./mat3.js";
import * as vec3 from "./vec3.js";
import * as vec4 from "./vec4.js";

/**
* Quaternion
* @module quat
*/

/**
* Creates a new identity quat
*
* @returns {quat} a new quaternion
*/
export function create() {
let out = new glMatrix.ARRAY_TYPE(4);
if (glMatrix.ARRAY_TYPE != Float32Array) {
out[0] = 0;
out[1] = 0;
out[2] = 0;
}
out[3] = 1;
return out;
}

/**
* Set a quat to the identity quaternion
*
* @param {quat} out the receiving quaternion
* @returns {quat} out
*/
export function identity(out) {
out[0] = 0;
out[1] = 0;
out[2] = 0;
out[3] = 1;
return out;
}

/**
* Sets a quat from the given angle and rotation axis,
* then returns it.
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyVec3} axis the axis around which to rotate
* @returns {quat} out
**/
export function setAxisAngle(out, axis, rad) {
out[0] = s * axis[0];
out[1] = s * axis[1];
out[2] = s * axis[2];
return out;
}

/**
* Gets the rotation axis and angle for a given
*  quaternion. If a quaternion is created with
*  setAxisAngle, this method will return the same
*  values as providied in the original parameter list
*  OR functionally equivalent values.
* Example: The quaternion formed by axis [0, 0, 1] and
*  angle -90 is the same as the quaternion formed by
*  [0, 0, 1] and 270. This method favors the latter.
* @param  {vec3} out_axis  Vector receiving the axis of rotation
* @param  {ReadonlyQuat} q     Quaternion to be decomposed
* @return {Number}     Angle, in radians, of the rotation
*/
export function getAxisAngle(out_axis, q) {
let rad = Math.acos(q[3]) * 2.0;
let s = Math.sin(rad / 2.0);
if (s > glMatrix.EPSILON) {
out_axis[0] = q[0] / s;
out_axis[1] = q[1] / s;
out_axis[2] = q[2] / s;
} else {
// If s is zero, return any axis (no rotation - axis does not matter)
out_axis[0] = 1;
out_axis[1] = 0;
out_axis[2] = 0;
}
}

/**
* Gets the angular distance between two unit quaternions
*
* @param  {ReadonlyQuat} a     Origin unit quaternion
* @param  {ReadonlyQuat} b     Destination unit quaternion
* @return {Number}     Angle, in radians, between the two quaternions
*/
export function getAngle(a, b) {
let dotproduct = dot(a, b);

return Math.acos(2 * dotproduct * dotproduct - 1);
}

/**
* Multiplies two quat's
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a the first operand
* @param {ReadonlyQuat} b the second operand
* @returns {quat} out
*/
export function multiply(out, a, b) {
let ax = a[0],
ay = a[1],
az = a[2],
aw = a[3];
let bx = b[0],
by = b[1],
bz = b[2],
bw = b[3];

out[0] = ax * bw + aw * bx + ay * bz - az * by;
out[1] = ay * bw + aw * by + az * bx - ax * bz;
out[2] = az * bw + aw * bz + ax * by - ay * bx;
out[3] = aw * bw - ax * bx - ay * by - az * bz;
return out;
}

/**
* Rotates a quaternion by the given angle about the X axis
*
* @param {quat} out quat receiving operation result
* @param {ReadonlyQuat} a quat to rotate
* @returns {quat} out
*/
export function rotateX(out, a, rad) {

let ax = a[0],
ay = a[1],
az = a[2],
aw = a[3];

out[0] = ax * bw + aw * bx;
out[1] = ay * bw + az * bx;
out[2] = az * bw - ay * bx;
out[3] = aw * bw - ax * bx;
return out;
}

/**
* Rotates a quaternion by the given angle about the Y axis
*
* @param {quat} out quat receiving operation result
* @param {ReadonlyQuat} a quat to rotate
* @returns {quat} out
*/
export function rotateY(out, a, rad) {

let ax = a[0],
ay = a[1],
az = a[2],
aw = a[3];

out[0] = ax * bw - az * by;
out[1] = ay * bw + aw * by;
out[2] = az * bw + ax * by;
out[3] = aw * bw - ay * by;
return out;
}

/**
* Rotates a quaternion by the given angle about the Z axis
*
* @param {quat} out quat receiving operation result
* @param {ReadonlyQuat} a quat to rotate
* @returns {quat} out
*/
export function rotateZ(out, a, rad) {

let ax = a[0],
ay = a[1],
az = a[2],
aw = a[3];

out[0] = ax * bw + ay * bz;
out[1] = ay * bw - ax * bz;
out[2] = az * bw + aw * bz;
out[3] = aw * bw - az * bz;
return out;
}

/**
* Calculates the W component of a quat from the X, Y, and Z components.
* Assumes that quaternion is 1 unit in length.
* Any existing W component will be ignored.
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a quat to calculate W component of
* @returns {quat} out
*/
export function calculateW(out, a) {
let x = a[0],
y = a[1],
z = a[2];

out[0] = x;
out[1] = y;
out[2] = z;
out[3] = Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z));
return out;
}

/**
* Calculate the exponential of a unit quaternion.
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a quat to calculate the exponential of
* @returns {quat} out
*/
export function exp(out, a) {
let x = a[0],
y = a[1],
z = a[2],
w = a[3];

let r = Math.sqrt(x * x + y * y + z * z);
let et = Math.exp(w);
let s = r > 0 ? (et * Math.sin(r)) / r : 0;

out[0] = x * s;
out[1] = y * s;
out[2] = z * s;
out[3] = et * Math.cos(r);

return out;
}

/**
* Calculate the natural logarithm of a unit quaternion.
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a quat to calculate the exponential of
* @returns {quat} out
*/
export function ln(out, a) {
let x = a[0],
y = a[1],
z = a[2],
w = a[3];

let r = Math.sqrt(x * x + y * y + z * z);
let t = r > 0 ? Math.atan2(r, w) / r : 0;

out[0] = x * t;
out[1] = y * t;
out[2] = z * t;
out[3] = 0.5 * Math.log(x * x + y * y + z * z + w * w);

return out;
}

/**
* Calculate the scalar power of a unit quaternion.
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a quat to calculate the exponential of
* @param {Number} b amount to scale the quaternion by
* @returns {quat} out
*/
export function pow(out, a, b) {
ln(out, a);
scale(out, out, b);
exp(out, out);
return out;
}

/**
* Performs a spherical linear interpolation between two quat
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a the first operand
* @param {ReadonlyQuat} b the second operand
* @param {Number} t interpolation amount, in the range [0-1], between the two inputs
* @returns {quat} out
*/
export function slerp(out, a, b, t) {
// benchmarks:
//    http://jsperf.com/quaternion-slerp-implementations
let ax = a[0],
ay = a[1],
az = a[2],
aw = a[3];
let bx = b[0],
by = b[1],
bz = b[2],
bw = b[3];

let omega, cosom, sinom, scale0, scale1;

// calc cosine
cosom = ax * bx + ay * by + az * bz + aw * bw;
if (cosom < 0.0) {
cosom = -cosom;
bx = -bx;
by = -by;
bz = -bz;
bw = -bw;
}
// calculate coefficients
if (1.0 - cosom > glMatrix.EPSILON) {
// standard case (slerp)
omega = Math.acos(cosom);
sinom = Math.sin(omega);
scale0 = Math.sin((1.0 - t) * omega) / sinom;
scale1 = Math.sin(t * omega) / sinom;
} else {
// "from" and "to" quaternions are very close
//  ... so we can do a linear interpolation
scale0 = 1.0 - t;
scale1 = t;
}
// calculate final values
out[0] = scale0 * ax + scale1 * bx;
out[1] = scale0 * ay + scale1 * by;
out[2] = scale0 * az + scale1 * bz;
out[3] = scale0 * aw + scale1 * bw;

return out;
}

/**
* Generates a random unit quaternion
*
* @param {quat} out the receiving quaternion
* @returns {quat} out
*/
export function random(out) {
// Implementation of http://planning.cs.uiuc.edu/node198.html
// TODO: Calling random 3 times is probably not the fastest solution
let u1 = glMatrix.RANDOM();
let u2 = glMatrix.RANDOM();
let u3 = glMatrix.RANDOM();

let sqrt1MinusU1 = Math.sqrt(1 - u1);
let sqrtU1 = Math.sqrt(u1);

out[0] = sqrt1MinusU1 * Math.sin(2.0 * Math.PI * u2);
out[1] = sqrt1MinusU1 * Math.cos(2.0 * Math.PI * u2);
out[2] = sqrtU1 * Math.sin(2.0 * Math.PI * u3);
out[3] = sqrtU1 * Math.cos(2.0 * Math.PI * u3);
return out;
}

/**
* Calculates the inverse of a quat
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a quat to calculate inverse of
* @returns {quat} out
*/
export function invert(out, a) {
let a0 = a[0],
a1 = a[1],
a2 = a[2],
a3 = a[3];
let dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;
let invDot = dot ? 1.0 / dot : 0;

// TODO: Would be faster to return [0,0,0,0] immediately if dot == 0

out[0] = -a0 * invDot;
out[1] = -a1 * invDot;
out[2] = -a2 * invDot;
out[3] = a3 * invDot;
return out;
}

/**
* Calculates the conjugate of a quat
* If the quaternion is normalized, this function is faster than quat.inverse and produces the same result.
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a quat to calculate conjugate of
* @returns {quat} out
*/
export function conjugate(out, a) {
out[0] = -a[0];
out[1] = -a[1];
out[2] = -a[2];
out[3] = a[3];
return out;
}

/**
* Creates a quaternion from the given 3x3 rotation matrix.
*
* NOTE: The resultant quaternion is not normalized, so you should be sure
* to renormalize the quaternion yourself where necessary.
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyMat3} m rotation matrix
* @returns {quat} out
* @function
*/
export function fromMat3(out, m) {
// Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
// article "Quaternion Calculus and Fast Animation".
let fTrace = m[0] + m[4] + m[8];
let fRoot;

if (fTrace > 0.0) {
// |w| > 1/2, may as well choose w > 1/2
fRoot = Math.sqrt(fTrace + 1.0); // 2w
out[3] = 0.5 * fRoot;
fRoot = 0.5 / fRoot; // 1/(4w)
out[0] = (m[5] - m[7]) * fRoot;
out[1] = (m[6] - m[2]) * fRoot;
out[2] = (m[1] - m[3]) * fRoot;
} else {
// |w| <= 1/2
let i = 0;
if (m[4] > m[0]) i = 1;
if (m[8] > m[i * 3 + i]) i = 2;
let j = (i + 1) % 3;
let k = (i + 2) % 3;

fRoot = Math.sqrt(m[i * 3 + i] - m[j * 3 + j] - m[k * 3 + k] + 1.0);
out[i] = 0.5 * fRoot;
fRoot = 0.5 / fRoot;
out[3] = (m[j * 3 + k] - m[k * 3 + j]) * fRoot;
out[j] = (m[j * 3 + i] + m[i * 3 + j]) * fRoot;
out[k] = (m[k * 3 + i] + m[i * 3 + k]) * fRoot;
}

return out;
}

/**
* Creates a quaternion from the given euler angle x, y, z.
*
* @param {quat} out the receiving quaternion
* @param {x} Angle to rotate around X axis in degrees.
* @param {y} Angle to rotate around Y axis in degrees.
* @param {z} Angle to rotate around Z axis in degrees.
* @returns {quat} out
* @function
*/
export function fromEuler(out, x, y, z) {
let halfToRad = (0.5 * Math.PI) / 180.0;

let sx = Math.sin(x);
let cx = Math.cos(x);
let sy = Math.sin(y);
let cy = Math.cos(y);
let sz = Math.sin(z);
let cz = Math.cos(z);

out[0] = sx * cy * cz - cx * sy * sz;
out[1] = cx * sy * cz + sx * cy * sz;
out[2] = cx * cy * sz - sx * sy * cz;
out[3] = cx * cy * cz + sx * sy * sz;

return out;
}

/**
* Returns a string representation of a quaternion
*
* @param {ReadonlyQuat} a vector to represent as a string
* @returns {String} string representation of the vector
*/
export function str(a) {
return "quat(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ")";
}

/**
* Creates a new quat initialized with values from an existing quaternion
*
* @param {ReadonlyQuat} a quaternion to clone
* @returns {quat} a new quaternion
* @function
*/
export const clone = vec4.clone;

/**
* Creates a new quat initialized with the given values
*
* @param {Number} x X component
* @param {Number} y Y component
* @param {Number} z Z component
* @param {Number} w W component
* @returns {quat} a new quaternion
* @function
*/
export const fromValues = vec4.fromValues;

/**
* Copy the values from one quat to another
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a the source quaternion
* @returns {quat} out
* @function
*/
export const copy = vec4.copy;

/**
* Set the components of a quat to the given values
*
* @param {quat} out the receiving quaternion
* @param {Number} x X component
* @param {Number} y Y component
* @param {Number} z Z component
* @param {Number} w W component
* @returns {quat} out
* @function
*/
export const set = vec4.set;

/**
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a the first operand
* @param {ReadonlyQuat} b the second operand
* @returns {quat} out
* @function
*/

/**
* @function
*/
export const mul = multiply;

/**
* Scales a quat by a scalar number
*
* @param {quat} out the receiving vector
* @param {ReadonlyQuat} a the vector to scale
* @param {Number} b amount to scale the vector by
* @returns {quat} out
* @function
*/
export const scale = vec4.scale;

/**
* Calculates the dot product of two quat's
*
* @param {ReadonlyQuat} a the first operand
* @param {ReadonlyQuat} b the second operand
* @returns {Number} dot product of a and b
* @function
*/
export const dot = vec4.dot;

/**
* Performs a linear interpolation between two quat's
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a the first operand
* @param {ReadonlyQuat} b the second operand
* @param {Number} t interpolation amount, in the range [0-1], between the two inputs
* @returns {quat} out
* @function
*/
export const lerp = vec4.lerp;

/**
* Calculates the length of a quat
*
* @param {ReadonlyQuat} a vector to calculate length of
* @returns {Number} length of a
*/
export const length = vec4.length;

/**
* @function
*/
export const len = length;

/**
* Calculates the squared length of a quat
*
* @param {ReadonlyQuat} a vector to calculate squared length of
* @returns {Number} squared length of a
* @function
*/
export const squaredLength = vec4.squaredLength;

/**
* @function
*/
export const sqrLen = squaredLength;

/**
* Normalize a quat
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a quaternion to normalize
* @returns {quat} out
* @function
*/
export const normalize = vec4.normalize;

/**
* Returns whether or not the quaternions have exactly the same elements in the same position (when compared with ===)
*
* @param {ReadonlyQuat} a The first quaternion.
* @param {ReadonlyQuat} b The second quaternion.
* @returns {Boolean} True if the vectors are equal, false otherwise.
*/
export const exactEquals = vec4.exactEquals;

/**
* Returns whether or not the quaternions have approximately the same elements in the same position.
*
* @param {ReadonlyQuat} a The first vector.
* @param {ReadonlyQuat} b The second vector.
* @returns {Boolean} True if the vectors are equal, false otherwise.
*/
export const equals = vec4.equals;

/**
* Sets a quaternion to represent the shortest rotation from one
* vector to another.
*
* Both vectors are assumed to be unit length.
*
* @param {quat} out the receiving quaternion.
* @param {ReadonlyVec3} a the initial vector
* @param {ReadonlyVec3} b the destination vector
* @returns {quat} out
*/
export const rotationTo = (function() {
let tmpvec3 = vec3.create();
let xUnitVec3 = vec3.fromValues(1, 0, 0);
let yUnitVec3 = vec3.fromValues(0, 1, 0);

return function(out, a, b) {
let dot = vec3.dot(a, b);
if (dot < -0.999999) {
vec3.cross(tmpvec3, xUnitVec3, a);
if (vec3.len(tmpvec3) < 0.000001) vec3.cross(tmpvec3, yUnitVec3, a);
vec3.normalize(tmpvec3, tmpvec3);
setAxisAngle(out, tmpvec3, Math.PI);
return out;
} else if (dot > 0.999999) {
out[0] = 0;
out[1] = 0;
out[2] = 0;
out[3] = 1;
return out;
} else {
vec3.cross(tmpvec3, a, b);
out[0] = tmpvec3[0];
out[1] = tmpvec3[1];
out[2] = tmpvec3[2];
out[3] = 1 + dot;
return normalize(out, out);
}
};
})();

/**
* Performs a spherical linear interpolation with two control points
*
* @param {quat} out the receiving quaternion
* @param {ReadonlyQuat} a the first operand
* @param {ReadonlyQuat} b the second operand
* @param {ReadonlyQuat} c the third operand
* @param {ReadonlyQuat} d the fourth operand
* @param {Number} t interpolation amount, in the range [0-1], between the two inputs
* @returns {quat} out
*/
export const sqlerp = (function() {
let temp1 = create();
let temp2 = create();

return function(out, a, b, c, d, t) {
slerp(temp1, a, d, t);
slerp(temp2, b, c, t);
slerp(out, temp1, temp2, 2 * t * (1 - t));

return out;
};
})();

/**
* Sets the specified quaternion with values corresponding to the given
* axes. Each axis is a vec3 and is expected to be unit length and
* perpendicular to all other specified axes.
*
* @param {ReadonlyVec3} view  the vector representing the viewing direction
* @param {ReadonlyVec3} right the vector representing the local "right" direction
* @param {ReadonlyVec3} up    the vector representing the local "up" direction
* @returns {quat} out
*/
export const setAxes = (function() {
let matr = mat3.create();

return function(out, view, right, up) {
matr[0] = right[0];
matr[3] = right[1];
matr[6] = right[2];

matr[1] = up[0];
matr[4] = up[1];
matr[7] = up[2];

matr[2] = -view[0];
matr[5] = -view[1];
matr[8] = -view[2];

return normalize(out, fromMat3(out, matr));
};
})();
``````