This little project started at a little game jam with the topic “electricity”. I wanted to do something with particles and controlling their flow with formulas, but the available methods for creating vector fields at the time where either too complicated for this small task, or too time consuming or bound to purchasing a software license. So instead I wrote this package.

These are scripts to create vector fields and flowmaps that can be used in game engines like Unreal Engine 4 and Unity 3D.

To learn more about those have a look at UE4’s documentation, for example.
Of course, this package cannot compete with GUI software like VectorayGen, but it’s free and open source.

## Installation

### via Python Package Index

`pip install vectorfields`

### Bleeding Edge

- To install using development mode:

`pip install -e git+https://github.com/OlafHaag/[email protected]#egg=vectorfields`

- To install using regular mode (building the package):

`pip install https://github.com/OlafHaag/vectorfields/archive/master.zip`

Source: https://github.com/OlafHaag/vectorfields/

### Anaconda Warning

To cite Ralf Gommers:
> **please never install numpy with pip into a conda/anaconda install!**
> This will result in all sorts of pain down the line.

So if you use the Anaconda distribution and you run into the issue `Importing the multiarray numpy extension module failed.`

:
Use conda to install numpy beforehand or `pip uninstall numpy`

and reinstall numpy with `conda install numpy`

into your environment.

## Usage

You have to know a bit of python and math.

The abstract base classes VectorField and VectorField2D can’t be instantiated.

Instantiate a specific vector field, like ElectricDipole2D.

You can use the ** save method to write the vector field to disk in FGA or VF format**. To be able to save in vf format, you have to turn instances of VectorField2D subclasses into 3D vector fields with the

*to_3d*method. If I’m not mistaken Unity expects

*cubic*vector fields with resolution x=y=z. You can also save instances of Vectorfield2D’s sub classes to

**flow maps**(e.g. png).

It’s best to preview your vector field directly in engine. Saving to disk usually reloads the file in Unity.

For other purposes you can use the plot-method of the Vectorfield2D class to get a preview.

### Special classes

#### Vortex2D

Has parameters **radius** and **pull**.

#### TwirlFlow2D

#### ElectricDipole2D

ElectricDipole2D has 2 special methods to either normalize the vectors and lose all information on field strength or to clamp the field strength to a maximum value. This was necessary, because the physical properties of this field aren’t visually pleasing.

#### Belt2D

With this you can place rotating areas in the field that more or less merge together, hence creating the impression of a belt running over pulleys.

Besides their x and y coordinates each *pulley* has a radius, thickness and speed (negative speed to change direction).

As a flowmap:

#### CustomUVW

This is a class for quick prototyping and generation of vector fields.

You provide custom functions to the constructor for creating the U, V and W vector components.

These functions must take 3 parameters that will be substituted for the class’ data members grid_x, grid_y, grid_z.

The return value must be an array of the same shape as grid_x, grid_y or grid_z respectively.

#### CustomUV2D

This is a class for quick prototyping and generation of 2D vectorfields.

You provide custom functions to the constructor for creating the U and V vector components.

These functions must take 2 parameters that will be substituted for the class’ data members grid_x and grid_y.
The return value must be an array of the same shape as grid_x or grid_y respectively.

**2D Examples:**

non-square sine vector field

```
import numpy as np
from vectorfields import CustomUV2D
ufunc = lambda x,y: np.ones(x.shape) # Flow in one direction.
vfunc = lambda x,y: np.sin(x)
vf = CustomUV2D(ufunc, vfunc, size=[8,2], resolution=[32,8])
```

square example:

regular cosine whirls

```
import numpy as np
from vectorfields import CustomUV2D
ufunc = lambda x,y: np.cos(y)
vfunc = lambda x,y: np.cos(x)
vf = CustomUV2D(ufunc, vfunc, size=16)
```

“flowers”

```
import numpy as np
from vectorfields import CustomUV2D
ufunc = lambda x,y: np.sin(y + x)
vfunc = lambda x,y: np.cos(x - y)
vf = CustomUV2D(ufunc, vfunc, size=12, resolution=48)
```

some diagonal flow thingy

```
import numpy as np
from vectorfields import CustomUV2D
ufunc = lambda x,y: np.cos(np.sqrt(np.abs(x)))
vfunc = lambda x,y: np.cos(np.sqrt(np.abs(y)))
vf = CustomUV2D(ufunc, vfunc)
```

anvaka’s square flow tiles (seriously, it’s hard to find names for this stuff)

```
import numpy as np
from vectorfields import CustomUV2D
ufunc = lambda x,y: 2.0 * np.mod(np.floor(-y), 2.0) - 1.0
vfunc = lambda x,y: 2.0 * np.mod(np.floor(-x), -2.0) + 1.0
vf = CustomUV2D(ufunc, vfunc, size=5.9, resolution=24)
```

beautiful twirls

```
import numpy as np
from vectorfields import CustomUV2D
ufunc = lambda x,y: np.cos(np.linalg.norm(np.dstack((x, y)), axis=2))[:,:,np.newaxis]
vfunc = lambda x,y: np.cos(x-y)
vf = CustomUV2D(ufunc, vfunc, size=16)
```

twirl column

```
import numpy as np
from vectorfields import CustomUV2D
ufunc = lambda x,y: np.sin(y)
vfunc = lambda x,y: x
vf = CustomUV2D(ufunc, vfunc, size=[12, 16], resolution=[24, 32])
```

One last thingy…

```
import numpy as np
from vectorfields import CustomUV2D
ufunc = lambda x,y: np.cos(y**2)
vfunc = lambda x,y: np.cos(y*x)
vf = CustomUV2D(ufunc, vfunc, size=[24, 16], resolution=[48,32])
```

## Development

Since it did what I needed it got stuck in early development stage. For example, there’s a lack of three-dimensional vector field examples and there are no unit-tests.

I’d like to see people creating other vector fields with this and improve and advance the code.

This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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