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vektor

A robotics-focused linear algebra module

This code was officially presented at JSConf US 2013. There are slides from the talk here: AI.js: Robots with Brains

Install

`npm install vektor`

Running Tests

`npm test`

Vectors

initializing a vector

```var v = require('vektor').vector;

var a = new v(1, 0, 0);
// or
var b = new v({x: 1, y: 2, z: 3});```

Note: Vectors can be initialized with 2 or 3 arguments only.

`var c = a.add(b); // [2, 2, 3]`

dot product

`var c = a.dot(b); // 1`

cross product

`var c = a.cross(b); // [0, -3, 2]`

distance between two vectors

`var c = a.distanceFrom(b); // 3.6`

length

`var c = b.length(); // 3.74`

scale

`var c = b.scale(2); // [2, 4, 6]`

Matrices

initializing a matrix

Note: matrices can be of any size

```var m = require('vektor').matrix;

var A = new m(2); // a 2x2 empty matrix
var B = new m(2, 3); // a 2x3 empty matrix
var I_3 = new m(3, 3, true); // a 3x3 identity matrix```

setting values

```/* our matrices:

A = [ [1, 2],
[3, 4] ];

B = [ [5, 6],
[7, 8] ];
*/

A.set(0,0,1);
A.set(0,1,2);
A.set(1,0,3);
A.set(1,1,4);

B.set(0,0,5);
B.set(0,1,6);
B.set(1,0,7);
B.set(1,1,8);```

getting values

`var c = A.get(1,1); // 4`

scaling a matrix

`var C = A.scale(-1); // A = [ [-1, -2], [-3, -4] ]`

`var C = A.add(B); // C = [ [6, 8], [10, 12] ]`

multiplying two matrices

`var C = A.dot(B); // C = [ [19, 22], [43, 50] ]`

getting the transpose

`var C = A.transpose(); // C = [ [1, 3], [2, 4] ]`

calculating the determinant

`var c = A.det(); // c = -2`

calculating the trace

Note: only works with square matrices... for now.

`var c = A.trace(); // c = 5`

• Translations

Rotations

initializing a rotation matrix

```var r = require('vektor').rotate;

// if the second argument is true, the first argument is in degrees
var a = new r.RotX(90, true); // matrix for a 90 degree rotation about the x axis
var b = new r.RotY(180, true); // matrix for a 180 degree rotation about the y axis
// if the second argument is false or not set, the first argument is in radians
var c = new r.RotZ(2 * Math.PI); // matrix for a 2 Pi radians (360 degrees) rotation about the z axis
assert.deepEqual(new r.RotX(0, true), new r.RotX(360, true));
assert.deepEqual(new r.RotX(0), new r.RotX(2 * Math.PI));```

rotate a vector around axes

```var v = require('vektor').vector;
var vector = new v([1,0,0]); // original vector

// Rotate (1, 0, 0) by 90 degrees on the Z axis and then by 45 degrees on the X axis

var rotationMatrix = new r.RotZ(Math.PI/2); // z-axis rotation matrix for Pi/2 radians (90 degrees)
vector = rotationMatrix.dot(vector); // multiply rotation matrix by vector to rotate the vector
rotationMatrix = new r.RotX(45, true); // y-axis rotation matrix for 45 degrees (Pi/4 radians)
vector = rotationMatrix.dot(vector);
var coordinates = vector.v // [ -0.707106781187, -0.500000000001, 0.500000000001 ]```

• Manipulator

Coming Soon

• Tutorials :-)