VECTORS.md

Using vectors

Since version 0.0.3 Units library supports 2- and 3-dimensional vectors over the field of real numbers.

All components of a vector have to be of the same unit. Here are some examples for 3D vectors:

Vector3U(1.of[metre], 2.of[metre], 3.of[metre])

(1, 2, 3).of[metre]  // (Int, Int, Int) and (Double, Double, Double) work here

Vector3U.of[metre](1, 2, 3)

You can add and subtract vectors:

(1, 2).of[s] + (1, 2).of[s] // == (2, 4).of[s]

You can multiply or divide them by a scalar:

(1, 2).of[m] * 4          // == (4, 8).of[m]

2.of[m/s] * (5, 5).of[s]  // == (10, 10).of[m]

You can calculate their dot products:

	(1, 2).of[m] * (1, 2).of[m]    // == 5.of[m]

and (in case of 3D vectors) their vector products:

(1, 0, 0).of[m] *** (0, 1, 0).of[m]  // == (0, 0, 1).of[m]

You can calculate their various properties:

(1, 2, 2).of[m].length     // == 3.of[m]
(1, 2, 2).of[m].lengthSq   // == 9.of[square[m]]
(6, 8, 0).of[m].unit       // == (0.6, 0.8, 0).of[_1], unit-less vector of length 1

And finally, you can convert them:

(1, 0).of[metre].convert[centimetre]   // (100, 0).of[centimetre]

Vector arrays

To facilitate compact storing of vectors, there are available classes: Vector2AArray, Vector2UArray, Vector3AArray, Vector3UArray. They store the vector array as an array od Double values. A single vector occupies a contiguous chunk of memory to minimalise cache misses.

All of the array classes implement IndexedSeq and can be used like standard collection classes.

They can be created in several ways:

import io.github.karols.units.arrays._

Vector2UArray.of[metre]((1,2), (4,5))

Vector2UArray((1,2).of[metre], (4,5).of[metre])

Vector2UArray.fill (5) ((4,4).of[metre])