Hypercomplex

A NodeJS package that implements complex and hypercomplex numbers.

Installation

Install using npm:

npm install hypercomplex

Complex Numbers

Polar Conversion

let radius = 1;
let angle = Math.PI/4;
console.log(Complex.fromPolar(radius, angle));
// Complex: {real: 7.071, imag: 7.071}

Binary Operations

let complex1 = new Complex(1,2)
let complex2 = new Complex(3,4)

console.log(complex1.add(complex2));
// Complex: {real: 4, imag: 6}

console.log(complex1.subract(complex2));
// Complex: {real: -2, imag: -2}

console.log(complex1.multiply(complex2));
// Complex: {real: -5, imag: 10}

console.log(complex1.divide(complex2));
// Complex: {real: 0.44, imag: 0.08}

Unary Operations

let complex1 = new Complex(1,2)

console.log(complex1.conjugate();
// Complex: {real: 1, imag: -2}

console.log(complex1.mag();
// Complex: {real: 1, imag: -2}

console.log(complex1.phase();
// 1.047

Quaternions

Instantiation

let Quaternion = new Quaternion(0,1,2,3)
//The first argument represents the scalar component, while the last three represent the vector components <q1,q2,q3>

Binary Operations

let quat1 = new Quaternion(1,2,3,4);
let quat2 = new Quaternion(4,3,2,1)

console.log(quat1.product(quat2));
// Quaternion {q0: -12, q1: 6, q2: 24, q3: 12}

console.log(quat1.add(quat2));
// Quaternion {q0: 5, q1: 5, q2: 5, q3: 5}

console.log(quat1.subtract(quat2)
// Quaternion {q0: -3, q1: -1, q2: 1, q3: 3}


### Unary Operations
```js
let quat1 = new Quaternion(q0: 1,q1: 2,q2: 3,q3: 4);

console.log(quat1.length());
// 5.477

console.log(quat1.inverse());
// Quaternion {q0: 0.033, q1: -0.066, q2: -0.1, q3: -0.133}

Conversion from Axis-Angle

let angle = Math.PI/2
let axisVector = [0, 0, 1]

console.log(Quaternion.fromAxisAngle(angle, axisVector]
// Quarternion {q0: 0.707, q1: 0, q2: 0, q3: 0.707}

Vector3 Class

The Vector3 class is a class that represents 3-dimensional vectors. Their primary purpose is to be rotated by quaternions. There are no class methods other than quaternion rotation, and are instead intended to be used alongside linear algebra packages,.

Initialization

let vector = new Vector3(1,1,1)

Binary Operations

let vec1 = new Vector3(1,2,3)
let vec2 = new Vector3(4,5,6)

console.log(vec1.add(vec2))
// Vector: {x: 5, y: 7, z: 9}

console.log(vec1.subtract(vec2))
// Vector: {x: -3, y: -3, z: -3}

console.log(vec1.dot(vec2))
// 32

Quaternion Rotation

let rotationQuaternion = Quarternion.fromAxisAngle(Math.PI/2, [0,0,1])
let vector = new Vector3(1,0,0)

console.log(vector.rotate(rotationQuaternion))
// Vector3 {x: 0, y: -1; z: 0}