Source: vec3.js

/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV.

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE. */

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);
  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 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 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 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 < -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] && a[1] === b[1] && 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) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a0), Math.abs(b0)) &&
          Math.abs(a1 - b1) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a1), Math.abs(b1)) &&
          Math.abs(a2 - b2) <= 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 < 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;
  };
})();