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    <h1 class="page-title">Source: quat.js</h1>

    
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            <pre class="prettyprint source linenums"><code>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 {vec3} axis the axis around which to rotate
 * @param {Number} rad the angle in radians
 * @returns {quat} out
 **/
export function setAxisAngle(out, axis, rad) {
  rad = rad * 0.5;
  let s = Math.sin(rad);
  out[0] = s * axis[0];
  out[1] = s * axis[1];
  out[2] = s * axis[2];
  out[3] = Math.cos(rad);
  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  {quat} 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;
  }
  return rad;
}

/**
 * Multiplies two quat's
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a the first operand
 * @param {quat} 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 {quat} a quat to rotate
 * @param {number} rad angle (in radians) to rotate
 * @returns {quat} out
 */
export function rotateX(out, a, rad) {
  rad *= 0.5;

  let ax = a[0], ay = a[1], az = a[2], aw = a[3];
  let bx = Math.sin(rad), bw = Math.cos(rad);

  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 {quat} a quat to rotate
 * @param {number} rad angle (in radians) to rotate
 * @returns {quat} out
 */
export function rotateY(out, a, rad) {
  rad *= 0.5;

  let ax = a[0], ay = a[1], az = a[2], aw = a[3];
  let by = Math.sin(rad), bw = Math.cos(rad);

  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 {quat} a quat to rotate
 * @param {number} rad angle (in radians) to rotate
 * @returns {quat} out
 */
export function rotateZ(out, a, rad) {
  rad *= 0.5;

  let ax = a[0], ay = a[1], az = a[2], aw = a[3];
  let bz = Math.sin(rad), bw = Math.cos(rad);

  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 {quat} 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;
}

/**
 * Performs a spherical linear interpolation between two quat
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a the first operand
 * @param {quat} 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;
  // adjust signs (if necessary)
  if ( cosom &lt; 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 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 {quat} 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 {quat} 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 {mat3} 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| &lt;= 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;
    x *= halfToRad;
    y *= halfToRad;
    z *= halfToRad;

    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 quatenion
 *
 * @param {quat} 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 {quat} 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 {quat} 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;

/**
 * Adds two quat's
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a the first operand
 * @param {quat} b the second operand
 * @returns {quat} out
 * @function
 */
export const add = vec4.add;

/**
 * Alias for {@link quat.multiply}
 * @function
 */
export const mul = multiply;

/**
 * Scales a quat by a scalar number
 *
 * @param {quat} out the receiving vector
 * @param {quat} 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 {quat} a the first operand
 * @param {quat} 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 {quat} a the first operand
 * @param {quat} 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 {quat} a vector to calculate length of
 * @returns {Number} length of a
 */
export const length = vec4.length;

/**
 * Alias for {@link quat.length}
 * @function
 */
export const len = length;

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

/**
 * Alias for {@link quat.squaredLength}
 * @function
 */
export const sqrLen = squaredLength;

/**
 * Normalize a quat
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} 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 {quat} a The first quaternion.
 * @param {quat} 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 {quat} a The first vector.
 * @param {quat} 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 {vec3} a the initial vector
 * @param {vec3} 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 &lt; -0.999999) {
      vec3.cross(tmpvec3, xUnitVec3, a);
      if (vec3.len(tmpvec3) &lt; 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 {quat} a the first operand
 * @param {quat} b the second operand
 * @param {quat} c the third operand
 * @param {quat} 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 {vec3} view  the vector representing the viewing direction
 * @param {vec3} right the vector representing the local "right" direction
 * @param {vec3} 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));
  };
})();
</code></pre>
        </article>
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