Vector

Numbers are great!

When we measure things with one number, it's technically called a scalar.

When we measure things with more than one number, it's called a vector

We can do lots of things with vectors. We can add or substract them, multiply and divide them.

Vectors are very useful.

This module helps you use Vectors in PowerShell

Vectors in PowerShell

Vectors are actually built into PowerShell.

Because PowerShell is built atop of the .NET Framework, and the .NET Framework has had vector support for over a decade, PowerShell has had vectors for over a decade.

# Create a 2D vector
[Numerics.Vector2]::new(1,2)
# Create a 3D vector
[Numerics.Vector3]::new(1,2,3)
# Create a 4D vector
[Numerics.Vector4]::new(1,2,3,4)

This module exists to make vectors a bit more useful by providing commands to construct them.

Installing and Importing

We can install the Vector module from the gallery:

# Install the module from the PowerShell gallery 
Install-Module Vector

Once installed, we can import the Vector module with Import-Module:

Import-Module Vector

Getting Vectors

There are a few commands in this module:

• Get-Vector2
• Get-Vector3
• Get-Vector4

Each command constructs a vector of the corresponding size.

We can also drop the Get and just refer to them by vector number

Vector2 1 2 
Vector3 1 2 3
Vector4 1 2 3 4

We can be even shorter, and use V2, V3, and V4

v2 1 2
v3 1 2 3
v4 1 2 3 4

We can turn anything into a series of vectors.

v2 1
v3 1
v4 1

Strings can become vectors, too! (after all, each byte is already a number)

v2 "hi"
v3 "hi"
v4 "hi"

Vector Operators

.NET vectors are very powerful, and overload many operators.

For example, we can add, subtract, multiply, or divide by a scalar.

# Let's start with addition.  
# We can add a scalar to a vector.
(v2 1 2) + 1 
(v3 1 2 3) + 1 
(v4 1 2 3 4) + 1

# Let's try substraction:
(v2 1 2) - 1 
(v3 1 2 3) - 1 
(v4 1 2 3 4) - 1

# How about multiplication?
(v2 1 2) * 2
(v3 1 2 3) * 2
(v4 1 2 3 4) * 2

# What about division?
(v2 1 2) / 2
(v3 1 2 3) / 2
(v4 1 2 3 4) / 2

We can also work with other vectors:

# Adding vectors:
(v2 1 2) + (v2 1 2)
(v3 1 2 3) + (v3 1 2 3)
(v4 1 2 3 4) + (v4 1 2 3 4)

# Subtracting vectors:
(v2 1 2) - (v2 1 2)
(v3 1 2 3) - (v3 1 2 3)
(v4 1 2 3 4) - (v4 1 2 3 4)

# Multiplying vectors:
(v2 1 2) * (v2 1 2)
(v3 1 2 3) * (v3 1 2 3)
(v4 1 2 3 4) * (v4 1 2 3 4)

# Dividing vectors:
(v2 1 2) / (v2 1 2)
(v3 1 2 3) / (v3 1 2 3)
(v4 1 2 3 4) / (v4 1 2 3 4)

Vector Methods

Vectors have a large number of methods to work with.

Let's start simple, by calculating the length of a given vector.

(v2 1 1).Length()
(v3 1 1 1).Length()
(v4 1 1 1 1).Length()

Many of the most useful things we can do with a vector are exposed as a static methods:

(v2 1 1) | Get-Member -Static
(v3 1 1 1) | Get-Member -Static
(v4 1 1 1 1) | Get-Member -Static

We can access static method with ::

For a small example, let's find the distance between vectors:

$vector1 = v2 1 2
$vector2 = v2 2 1
$vector1::Distance($vector1, $vector2)

For another simple example, let's find a few point between two points, using Linear Interpolation lerp

$vector1 = v2 1 5
$vector2 = v2 1 -5
$vector1::Lerp($vector1, $vector2, 0.25)
$vector1::Lerp($vector1, $vector2, 0.5)
$vector1::Lerp($vector1, $vector2, 0.75)

All of this would not be possible without the great work of the .NET team to build such incredibly useful data structures.

Hopefully this module helps us all work with vectors!