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    <h1 class="page-title">Source: vec3.js</h1>

    
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            <pre class="prettyprint source linenums"><code>import * as glMatrix from "./common.js";

/**
 * 3 Dimensional Vector
 * @module vec3
 */

/**
 * Creates a new, empty vec3
 *
 * @returns {vec3} a new 3D vector
 */
export function create() {
  let out = new glMatrix.ARRAY_TYPE(3);
  if(glMatrix.ARRAY_TYPE != Float32Array) {
    out[0] = 0;
    out[1] = 0;
    out[2] = 0;
  }
  return out;
}

/**
 * Creates a new vec3 initialized with values from an existing vector
 *
 * @param {vec3} a vector to clone
 * @returns {vec3} a new 3D vector
 */
export function clone(a) {
  var out = new glMatrix.ARRAY_TYPE(3);
  out[0] = a[0];
  out[1] = a[1];
  out[2] = a[2];
  return out;
}

/**
 * Calculates the length of a vec3
 *
 * @param {vec3} a vector to calculate length of
 * @returns {Number} length of a
 */
export function length(a) {
  let x = a[0];
  let y = a[1];
  let z = a[2];
  return Math.sqrt(x*x + y*y + z*z);
}

/**
 * Creates a new vec3 initialized with the given values
 *
 * @param {Number} x X component
 * @param {Number} y Y component
 * @param {Number} z Z component
 * @returns {vec3} a new 3D vector
 */
export function fromValues(x, y, z) {
  let out = new glMatrix.ARRAY_TYPE(3);
  out[0] = x;
  out[1] = y;
  out[2] = z;
  return out;
}

/**
 * Copy the values from one vec3 to another
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the source vector
 * @returns {vec3} out
 */
export function copy(out, a) {
  out[0] = a[0];
  out[1] = a[1];
  out[2] = a[2];
  return out;
}

/**
 * Set the components of a vec3 to the given values
 *
 * @param {vec3} out the receiving vector
 * @param {Number} x X component
 * @param {Number} y Y component
 * @param {Number} z Z component
 * @returns {vec3} out
 */
export function set(out, x, y, z) {
  out[0] = x;
  out[1] = y;
  out[2] = z;
  return out;
}

/**
 * Adds two vec3's
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @returns {vec3} out
 */
export function add(out, a, b) {
  out[0] = a[0] + b[0];
  out[1] = a[1] + b[1];
  out[2] = a[2] + b[2];
  return out;
}

/**
 * Subtracts vector b from vector a
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @returns {vec3} out
 */
export function subtract(out, a, b) {
  out[0] = a[0] - b[0];
  out[1] = a[1] - b[1];
  out[2] = a[2] - b[2];
  return out;
}

/**
 * Multiplies two vec3's
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @returns {vec3} out
 */
export function multiply(out, a, b) {
  out[0] = a[0] * b[0];
  out[1] = a[1] * b[1];
  out[2] = a[2] * b[2];
  return out;
}

/**
 * Divides two vec3's
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @returns {vec3} out
 */
export function divide(out, a, b) {
  out[0] = a[0] / b[0];
  out[1] = a[1] / b[1];
  out[2] = a[2] / b[2];
  return out;
}

/**
 * Math.ceil the components of a vec3
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a vector to ceil
 * @returns {vec3} out
 */
export function ceil(out, a) {
  out[0] = Math.ceil(a[0]);
  out[1] = Math.ceil(a[1]);
  out[2] = Math.ceil(a[2]);
  return out;
}

/**
 * Math.floor the components of a vec3
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a vector to floor
 * @returns {vec3} out
 */
export function floor(out, a) {
  out[0] = Math.floor(a[0]);
  out[1] = Math.floor(a[1]);
  out[2] = Math.floor(a[2]);
  return out;
}

/**
 * Returns the minimum of two vec3's
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @returns {vec3} out
 */
export function min(out, a, b) {
  out[0] = Math.min(a[0], b[0]);
  out[1] = Math.min(a[1], b[1]);
  out[2] = Math.min(a[2], b[2]);
  return out;
}

/**
 * Returns the maximum of two vec3's
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @returns {vec3} out
 */
export function max(out, a, b) {
  out[0] = Math.max(a[0], b[0]);
  out[1] = Math.max(a[1], b[1]);
  out[2] = Math.max(a[2], b[2]);
  return out;
}

/**
 * Math.round the components of a vec3
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a vector to round
 * @returns {vec3} out
 */
export function round(out, a) {
  out[0] = Math.round(a[0]);
  out[1] = Math.round(a[1]);
  out[2] = Math.round(a[2]);
  return out;
}

/**
 * Scales a vec3 by a scalar number
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the vector to scale
 * @param {Number} b amount to scale the vector by
 * @returns {vec3} out
 */
export function scale(out, a, b) {
  out[0] = a[0] * b;
  out[1] = a[1] * b;
  out[2] = a[2] * b;
  return out;
}

/**
 * Adds two vec3's after scaling the second operand by a scalar value
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @param {Number} scale the amount to scale b by before adding
 * @returns {vec3} out
 */
export function scaleAndAdd(out, a, b, scale) {
  out[0] = a[0] + (b[0] * scale);
  out[1] = a[1] + (b[1] * scale);
  out[2] = a[2] + (b[2] * scale);
  return out;
}

/**
 * Calculates the euclidian distance between two vec3's
 *
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @returns {Number} distance between a and b
 */
export function distance(a, b) {
  let x = b[0] - a[0];
  let y = b[1] - a[1];
  let z = b[2] - a[2];
  return Math.sqrt(x*x + y*y + z*z);
}

/**
 * Calculates the squared euclidian distance between two vec3's
 *
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @returns {Number} squared distance between a and b
 */
export function squaredDistance(a, b) {
  let x = b[0] - a[0];
  let y = b[1] - a[1];
  let z = b[2] - a[2];
  return x*x + y*y + z*z;
}

/**
 * Calculates the squared length of a vec3
 *
 * @param {vec3} a vector to calculate squared length of
 * @returns {Number} squared length of a
 */
export function squaredLength(a) {
  let x = a[0];
  let y = a[1];
  let z = a[2];
  return x*x + y*y + z*z;
}

/**
 * Negates the components of a vec3
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a vector to negate
 * @returns {vec3} out
 */
export function negate(out, a) {
  out[0] = -a[0];
  out[1] = -a[1];
  out[2] = -a[2];
  return out;
}

/**
 * Returns the inverse of the components of a vec3
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a vector to invert
 * @returns {vec3} out
 */
export function inverse(out, a) {
  out[0] = 1.0 / a[0];
  out[1] = 1.0 / a[1];
  out[2] = 1.0 / a[2];
  return out;
}

/**
 * Normalize a vec3
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a vector to normalize
 * @returns {vec3} out
 */
export function normalize(out, a) {
  let x = a[0];
  let y = a[1];
  let z = a[2];
  let len = x*x + y*y + z*z;
  if (len > 0) {
    //TODO: evaluate use of glm_invsqrt here?
    len = 1 / Math.sqrt(len);
    out[0] = a[0] * len;
    out[1] = a[1] * len;
    out[2] = a[2] * len;
  }
  return out;
}

/**
 * Calculates the dot product of two vec3's
 *
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @returns {Number} dot product of a and b
 */
export function dot(a, b) {
  return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}

/**
 * Computes the cross product of two vec3's
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @returns {vec3} out
 */
export function cross(out, a, b) {
  let ax = a[0], ay = a[1], az = a[2];
  let bx = b[0], by = b[1], bz = b[2];

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

/**
 * Performs a linear interpolation between two vec3's
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
 * @returns {vec3} out
 */
export function lerp(out, a, b, t) {
  let ax = a[0];
  let ay = a[1];
  let az = a[2];
  out[0] = ax + t * (b[0] - ax);
  out[1] = ay + t * (b[1] - ay);
  out[2] = az + t * (b[2] - az);
  return out;
}

/**
 * Performs a hermite interpolation with two control points
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @param {vec3} c the third operand
 * @param {vec3} d the fourth operand
 * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
 * @returns {vec3} out
 */
export function hermite(out, a, b, c, d, t) {
  let factorTimes2 = t * t;
  let factor1 = factorTimes2 * (2 * t - 3) + 1;
  let factor2 = factorTimes2 * (t - 2) + t;
  let factor3 = factorTimes2 * (t - 1);
  let factor4 = factorTimes2 * (3 - 2 * t);

  out[0] = a[0] * factor1 + b[0] * factor2 + c[0] * factor3 + d[0] * factor4;
  out[1] = a[1] * factor1 + b[1] * factor2 + c[1] * factor3 + d[1] * factor4;
  out[2] = a[2] * factor1 + b[2] * factor2 + c[2] * factor3 + d[2] * factor4;

  return out;
}

/**
 * Performs a bezier interpolation with two control points
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the first operand
 * @param {vec3} b the second operand
 * @param {vec3} c the third operand
 * @param {vec3} d the fourth operand
 * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
 * @returns {vec3} out
 */
export function bezier(out, a, b, c, d, t) {
  let inverseFactor = 1 - t;
  let inverseFactorTimesTwo = inverseFactor * inverseFactor;
  let factorTimes2 = t * t;
  let factor1 = inverseFactorTimesTwo * inverseFactor;
  let factor2 = 3 * t * inverseFactorTimesTwo;
  let factor3 = 3 * factorTimes2 * inverseFactor;
  let factor4 = factorTimes2 * t;

  out[0] = a[0] * factor1 + b[0] * factor2 + c[0] * factor3 + d[0] * factor4;
  out[1] = a[1] * factor1 + b[1] * factor2 + c[1] * factor3 + d[1] * factor4;
  out[2] = a[2] * factor1 + b[2] * factor2 + c[2] * factor3 + d[2] * factor4;

  return out;
}

/**
 * Generates a random vector with the given scale
 *
 * @param {vec3} out the receiving vector
 * @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned
 * @returns {vec3} out
 */
export function random(out, scale) {
  scale = scale || 1.0;

  let r = glMatrix.RANDOM() * 2.0 * Math.PI;
  let z = (glMatrix.RANDOM() * 2.0) - 1.0;
  let zScale = Math.sqrt(1.0-z*z) * scale;

  out[0] = Math.cos(r) * zScale;
  out[1] = Math.sin(r) * zScale;
  out[2] = z * scale;
  return out;
}

/**
 * Transforms the vec3 with a mat4.
 * 4th vector component is implicitly '1'
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the vector to transform
 * @param {mat4} m matrix to transform with
 * @returns {vec3} out
 */
export function transformMat4(out, a, m) {
  let x = a[0], y = a[1], z = a[2];
  let w = m[3] * x + m[7] * y + m[11] * z + m[15];
  w = w || 1.0;
  out[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;
  out[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;
  out[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;
  return out;
}

/**
 * Transforms the vec3 with a mat3.
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the vector to transform
 * @param {mat3} m the 3x3 matrix to transform with
 * @returns {vec3} out
 */
export function transformMat3(out, a, m) {
  let x = a[0], y = a[1], z = a[2];
  out[0] = x * m[0] + y * m[3] + z * m[6];
  out[1] = x * m[1] + y * m[4] + z * m[7];
  out[2] = x * m[2] + y * m[5] + z * m[8];
  return out;
}

/**
 * Transforms the vec3 with a quat
 * Can also be used for dual quaternions. (Multiply it with the real part)
 *
 * @param {vec3} out the receiving vector
 * @param {vec3} a the vector to transform
 * @param {quat} q quaternion to transform with
 * @returns {vec3} out
 */
export function transformQuat(out, a, q) {
    // benchmarks: https://jsperf.com/quaternion-transform-vec3-implementations-fixed
    let qx = q[0], qy = q[1], qz = q[2], qw = q[3];
    let x = a[0], y = a[1], z = a[2];
    // var qvec = [qx, qy, qz];
    // var uv = vec3.cross([], qvec, a);
    let uvx = qy * z - qz * y,
        uvy = qz * x - qx * z,
        uvz = qx * y - qy * x;
    // var uuv = vec3.cross([], qvec, uv);
    let uuvx = qy * uvz - qz * uvy,
        uuvy = qz * uvx - qx * uvz,
        uuvz = qx * uvy - qy * uvx;
    // vec3.scale(uv, uv, 2 * w);
    let w2 = qw * 2;
    uvx *= w2;
    uvy *= w2;
    uvz *= w2;
    // vec3.scale(uuv, uuv, 2);
    uuvx *= 2;
    uuvy *= 2;
    uuvz *= 2;
    // return vec3.add(out, a, vec3.add(out, uv, uuv));
    out[0] = x + uvx + uuvx;
    out[1] = y + uvy + uuvy;
    out[2] = z + uvz + uuvz;
    return out;
}

/**
 * Rotate a 3D vector around the x-axis
 * @param {vec3} out The receiving vec3
 * @param {vec3} a The vec3 point to rotate
 * @param {vec3} b The origin of the rotation
 * @param {Number} c The angle of rotation
 * @returns {vec3} out
 */
export function rotateX(out, a, b, c){
  let p = [], r=[];
  //Translate point to the origin
  p[0] = a[0] - b[0];
  p[1] = a[1] - b[1];
  p[2] = a[2] - b[2];

  //perform rotation
  r[0] = p[0];
  r[1] = p[1]*Math.cos(c) - p[2]*Math.sin(c);
  r[2] = p[1]*Math.sin(c) + p[2]*Math.cos(c);

  //translate to correct position
  out[0] = r[0] + b[0];
  out[1] = r[1] + b[1];
  out[2] = r[2] + b[2];

  return out;
}

/**
 * Rotate a 3D vector around the y-axis
 * @param {vec3} out The receiving vec3
 * @param {vec3} a The vec3 point to rotate
 * @param {vec3} b The origin of the rotation
 * @param {Number} c The angle of rotation
 * @returns {vec3} out
 */
export function rotateY(out, a, b, c){
  let p = [], r=[];
  //Translate point to the origin
  p[0] = a[0] - b[0];
  p[1] = a[1] - b[1];
  p[2] = a[2] - b[2];

  //perform rotation
  r[0] = p[2]*Math.sin(c) + p[0]*Math.cos(c);
  r[1] = p[1];
  r[2] = p[2]*Math.cos(c) - p[0]*Math.sin(c);

  //translate to correct position
  out[0] = r[0] + b[0];
  out[1] = r[1] + b[1];
  out[2] = r[2] + b[2];

  return out;
}

/**
 * Rotate a 3D vector around the z-axis
 * @param {vec3} out The receiving vec3
 * @param {vec3} a The vec3 point to rotate
 * @param {vec3} b The origin of the rotation
 * @param {Number} c The angle of rotation
 * @returns {vec3} out
 */
export function rotateZ(out, a, b, c){
  let p = [], r=[];
  //Translate point to the origin
  p[0] = a[0] - b[0];
  p[1] = a[1] - b[1];
  p[2] = a[2] - b[2];

  //perform rotation
  r[0] = p[0]*Math.cos(c) - p[1]*Math.sin(c);
  r[1] = p[0]*Math.sin(c) + p[1]*Math.cos(c);
  r[2] = p[2];

  //translate to correct position
  out[0] = r[0] + b[0];
  out[1] = r[1] + b[1];
  out[2] = r[2] + b[2];

  return out;
}

/**
 * Get the angle between two 3D vectors
 * @param {vec3} a The first operand
 * @param {vec3} b The second operand
 * @returns {Number} The angle in radians
 */
export function angle(a, b) {
  let tempA = fromValues(a[0], a[1], a[2]);
  let tempB = fromValues(b[0], b[1], b[2]);

  normalize(tempA, tempA);
  normalize(tempB, tempB);

  let cosine = dot(tempA, tempB);

  if(cosine > 1.0) {
    return 0;
  }
  else if(cosine &lt; -1.0) {
    return Math.PI;
  } else {
    return Math.acos(cosine);
  }
}

/**
 * Returns a string representation of a vector
 *
 * @param {vec3} a vector to represent as a string
 * @returns {String} string representation of the vector
 */
export function str(a) {
  return 'vec3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ')';
}

/**
 * Returns whether or not the vectors have exactly the same elements in the same position (when compared with ===)
 *
 * @param {vec3} a The first vector.
 * @param {vec3} b The second vector.
 * @returns {Boolean} True if the vectors are equal, false otherwise.
 */
export function exactEquals(a, b) {
  return a[0] === b[0] &amp;&amp; a[1] === b[1] &amp;&amp; a[2] === b[2];
}

/**
 * Returns whether or not the vectors have approximately the same elements in the same position.
 *
 * @param {vec3} a The first vector.
 * @param {vec3} b The second vector.
 * @returns {Boolean} True if the vectors are equal, false otherwise.
 */
export function equals(a, b) {
  let a0 = a[0], a1 = a[1], a2 = a[2];
  let b0 = b[0], b1 = b[1], b2 = b[2];
  return (Math.abs(a0 - b0) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a0), Math.abs(b0)) &amp;&amp;
          Math.abs(a1 - b1) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a1), Math.abs(b1)) &amp;&amp;
          Math.abs(a2 - b2) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a2), Math.abs(b2)));
}

/**
 * Alias for {@link vec3.subtract}
 * @function
 */
export const sub = subtract;

/**
 * Alias for {@link vec3.multiply}
 * @function
 */
export const mul = multiply;

/**
 * Alias for {@link vec3.divide}
 * @function
 */
export const div = divide;

/**
 * Alias for {@link vec3.distance}
 * @function
 */
export const dist = distance;

/**
 * Alias for {@link vec3.squaredDistance}
 * @function
 */
export const sqrDist = squaredDistance;

/**
 * Alias for {@link vec3.length}
 * @function
 */
export const len = length;

/**
 * Alias for {@link vec3.squaredLength}
 * @function
 */
export const sqrLen = squaredLength;

/**
 * Perform some operation over an array of vec3s.
 *
 * @param {Array} a the array of vectors to iterate over
 * @param {Number} stride Number of elements between the start of each vec3. If 0 assumes tightly packed
 * @param {Number} offset Number of elements to skip at the beginning of the array
 * @param {Number} count Number of vec3s to iterate over. If 0 iterates over entire array
 * @param {Function} fn Function to call for each vector in the array
 * @param {Object} [arg] additional argument to pass to fn
 * @returns {Array} a
 * @function
 */
export const forEach = (function() {
  let vec = create();

  return function(a, stride, offset, count, fn, arg) {
    let i, l;
    if(!stride) {
      stride = 3;
    }

    if(!offset) {
      offset = 0;
    }

    if(count) {
      l = Math.min((count * stride) + offset, a.length);
    } else {
      l = a.length;
    }

    for(i = offset; i &lt; l; i += stride) {
      vec[0] = a[i]; vec[1] = a[i+1]; vec[2] = a[i+2];
      fn(vec, vec, arg);
      a[i] = vec[0]; a[i+1] = vec[1]; a[i+2] = vec[2];
    }

    return a;
  };
})();
</code></pre>
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