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vektor

A robotics-focused linear algebra module

About

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.

add two vectors

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] ]

adding two matrices

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

Homogenous Matrices (aka Transforms)

  • 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 ]

Examples

  • Manipulator

Coming Soon

  • Tutorials :-)

Contributions

Please, please, please help make this module more robust!

  • Send in pull requests (make sure the tests pass)
  • Discuss additional features in the Issues section
  • Add your name and Github handle here: