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- §

  # Quaternion factory

  Scrawl-canvas uses quaternion objects for some of its calculations - in particular for calculating DOM element 3D rotation values. These objects are not stored in the library; rather, they are kept in a quaternion pool and pulled from it when required.

  TODO: there’s errors in the math here! See in particular Demo Snippets-003 to experiment:

  - Pitch always appears to rotate with reference to the element. Yaw and roll, however, seem to rotate with reference to the stack frame, or the element - or possibly a combination of both - dependant on the values of the other euler attributes.
  - `quaternionMultiply` is almost certainly wrong - caused by trying to convert code meant for a y-axis-upwards frame to code that works in a y-axis-downwards frame
  - The `setFromEuler` function is also (probably) wrong
  - I hate quaternions!
- §

  #### Imports

      import { constructors } from '../core/library.js';

      import { correctForZero, doCreate, isa_number, isa_quaternion, xt, xto, Ωempty } from '../core/utilities.js';

      import { makeVector } from './vector.js';

      import { _radian } from '../core/shared-vars.js';

      import { _acos, _cos, _seal, _sin, _sqrt, T_QUATERNION } from '../core/shared-vars.js';

- §

  #### Quaternion constructor

      const Quaternion = function (items = Ωempty) {

          this.n = items.n || 1;
          this.v = makeVector();

          _seal(this);

          this.set(items);

          return this;
      };

- §

  #### Quaternion prototype

      const P = Quaternion.prototype = doCreate();
      P.type = T_QUATERNION;

- §

  #### Mixins

  Quaternion objects do not use mixins - they are regular Javascript objects. As such, they do not possess packet, clone or kill functionality.

- §

  #### Quaternion attributes

  The name, n and v (Vector object) attributes are set in the Quaternion constructor - the Quaternion object does not have a `defs` object. The Vector attributes v.x, v.y, v.z can also be set directly.

  We strongly advise against setting Quaternion object attributes directly! Quaternions are complex beasts and their `n` and `v` attributes are linked in mysterious (and possibly debauched) ways. Set and manipulate your Quaternion object’s attributes using the functions below.

- §

  #### Get, Set, deltaSet

- §

  Quaternion attributes can be retrieved directly - `myquaternion.n`, `myquaternion.v`. The v attribute is a Vector object, thus its attributes can be retrieved using that object’s convenience functions `myquaternion.v.getXYCoordinate` and `myquaternion.v.getXYZCoordinate` - these functions will return Arrays.

- §

  The Quaternion `set` function is overloaded. It can accept the following arguments:

  - `set(Quaternion)` - a Quaternion object
  - `set(Vector)` - a Vector object
  - `set({x:Number, y:Number, z:Number})` - a Javascript object containing one or more attributes from: x, y, z - with values in degrees (not radians)
  - `set({pitch:Number, yaw:Number, roll:Number})` - a Javascript object containing one or more attributes: pitch (for x-axis rotations); yaw (for y-axis rotations); roll (for z-axis rotations) - with values in degrees (not radians)

      P.set = function (obj = Ωempty) {

          if (isa_quaternion(obj)) return this.setFromQuaternion(obj);

          if (xto(obj.pitch, obj.yaw, obj.roll)) return this.setFromEuler(obj);

          const tv = this.v,
              v = (xt(obj.vector) || xt(obj.v)) ? (obj.vector || obj.v) : false,
              n = (xt(obj.scalar) || xt(obj.n)) ? (obj.scalar || obj.n || 0) : false;

          const x = (v) ? (v.x || 0) : obj.x || false,
              y = (v) ? (v.y || 0) : obj.y || false,
              z = (v) ? (v.z || 0) : obj.z || false;

          this.n = (isa_number(n)) ? n : this.n;

          tv.x = (isa_number(x)) ? x : tv.x;
          tv.y = (isa_number(y)) ? y : tv.y;
          tv.z = (isa_number(z)) ? z : tv.z;

          return this;
      };

      P.setFromQuaternion = function (item) {

          if (!isa_quaternion(item)) throw new Error(`${this.name} Quaternion error - setFromQuaternion() bad argument: ${item}`);

          const tv = this.v,
              iv = item.v;

          this.n = item.n;
          tv.x = iv.x;
          tv.y = iv.y;
          tv.z = iv.z;

          return this;
      };

      P.setFromEuler = function (items = Ωempty) {

          const tv = this.v;

          const pitch = (items.pitch || items.x || 0) * _radian,
              yaw = (items.yaw || items.y || 0) * _radian,
              roll = (items.roll || items.z || 0) * _radian;

          const c1 = _cos( pitch / 2 ),
              c2 = _cos( yaw / 2 ),
              c3 = _cos( roll / 2 );

          const s1 = _sin( pitch / 2 ),
              s2 = _sin( yaw / 2 ),
              s3 = _sin( roll / 2 );

          tv.x = s1 * c2 * c3 + c1 * s2 * s3;
          tv.y = c1 * s2 * c3 + s1 * c2 * s3;
          tv.z = c1 * c2 * s3 - s1 * s2 * c3;

          this.n = c1 * c2 * c3 - s1 * s2 * s3;

          return this;
      };

- §

  #### Prototype functions

- §

  Set the Quaternion attributes to their default values

      P.zero = function () {

          const v = this.v;

          this.n = 1;
          v.x = 0;
          v.y = 0;
          v.z = 0;

          return this;
      };

- §

  Get the Quaternion’s magnitude value

      P.getMagnitude = function () {

          const v = this.v;

          return _sqrt((this.n * this.n) + (v.x * v.x) + (v.y * v.y) + (v.z * v.z));
      };

- §

  Normalize the Quaternion

      P.normalize = function () {

          const mag = this.getMagnitude(),
              v = this.v;

          if (!mag) throw new Error(`${this.name} Quaternion error - normalize() division by zero: ${mag}`);

          this.n = correctForZero(this.n / mag);
          v.x = correctForZero(v.x / mag);
          v.y = correctForZero(v.y / mag);
          v.z = correctForZero(v.z / mag);

          return this;
      };

- §

  Multiply the Quaternion by another Quaternion

      P.quaternionMultiply = function (item) {

          if (!isa_quaternion(item)) throw new Error(`${this.name} Quaternion error - quaternionMultiply() bad argument: ${item}`);

          const tv = this.v,
              iv = item.v,

              n1 = this.n,
              x1 = tv.x,
              y1 = tv.y,
              z1 = tv.z,

              n2 = item.n,
              x2 = iv.x,
              y2 = iv.y,
              z2 = iv.z;

          this.n = (n1 * n2) - (x1 * x2) - (y1 * y2) - (z1 * z2);

          tv.x = (n1 * x2) + (x1 * n2) + (y1 * z2) - (z1 * y2);
          tv.y = (n1 * y2) + (y1 * n2) + (z1 * x2) - (x1 * z2);
          tv.z = (n1 * z2) + (z1 * n2) + (x1 * y2) - (y1 * x2);

          return this;
      };

- §

  Retrieve the Quaternion’s current angle (returns a Number representing degrees, not radians)

      P.getAngle = function (degree) {

          let result;

          degree = (xt(degree)) ? degree : false;

          result = 2 * _acos(this.n);

          if(degree){

              result *= (1 / _radian);
          }

          return correctForZero(result);
      };

- §

  Rotate the Quaternion using another Quaternion’s values

      P.quaternionRotate = function (item) {

          if (!isa_quaternion(item)) throw new Error(`${this.name} Quaternion error - quaternionRotate() bad argument: ${item}`);

          const q4 = requestQuaternion(item),
              q5 = requestQuaternion(this);

          this.setFromQuaternion(q4.quaternionMultiply(q5));

          releaseQuaternion(q4);
          releaseQuaternion(q5);

          return this
      };

- §

  #### Quaternion pool

  An attempt to reuse quaternions rather than constantly creating and deleting them

      const quaternionPool = [];

- §

  `exported function` - retrieve a Quaternion from the quaternion pool

      export const requestQuaternion = function (items) {

          if (!quaternionPool.length) quaternionPool.push(makeQuaternion());

          const q = quaternionPool.shift();

          q.set(items);

          return q
      };

- §

  `exported function` - return a Quaternion to the quaternion pool. Failing to return Quaternion to the pool may lead to more inefficient code and possible memory leaks.

      export const releaseQuaternion = function (q) {

          if (q && q.type == T_QUATERNION) {

              quaternionPool.push(q.zero());
          }
      };

- §

  #### Factory

      export const makeQuaternion = function (items) {

          return new Quaternion(items);
      };

      constructors.Quaternion = Quaternion;