# Pyrr

[![Build Status](https://travis-ci.org/adamlwgriffiths/Pyrr.png?branch=master)](https://travis-ci.org/adamlwgriffiths/Pyrr)

Provides 3D mathematical functions using the power of NumPy.

## Features

- Object Oriented and Procedural interfaces
- Matrix (3x3, 4x4)
- Quaternion
- Vector (3D, 4D)
- Plane
- Ray
- Line / Line Segment (3D)
- Rectangle (2D)
- Axis Aligned Bounding Box (AABB / AAMBB)
- Geometric collision / intersection testing

## Documentation

[View Pyrr's documentation online](https://pyrr.readthedocs.org/en/latest/).

## Examples

Maintain a rotation (quaternion) and translation (vector) and convert to a matrix

### Object Oriented Interface

This is a long winded example to demonstrate various features.

```python
from pyrr import Quaternion, Matrix44, Vector3
import numpy as np

point = Vector3([1.,2.,3.])
orientation = Quaternion()
translation = Vector3()
scale = Vector3([1.,1.,1.])

# translate along X by 1
translation += [1.0, 0.0, 0.0]

# rotate about Y by pi/2
rotation = Quaternion.from_y_rotation(np.pi / 2.0)
orientation = rotation * orientation

# create a matrix
matrix = Matrix44.identity()

# apply our translation
matrix = matrix * Matrix44.from_translation(translation)

# apply our orientation
# we can multiply matricies and quaternions directly!
matrix = matrix * orientation

# apply our scale
matrix = matrix * Matrix44.from_scale(scale)

# transform our point by the matrix
# vectors are transformable by matrices and quaternions directly
point = matrix * point
```

### Procedural Interface

```python
from pyrr import quaternion, matrix44, vector3
import numpy as np

point = vector3.create(1.,2.,3.)
orientation = quaternion.create()
translation = vector3.create()
scale = vector3.create(1,1,1)

# translate along X by 1
translation += [1.0, 0.0, 0.0]

# rotate about Y by pi/2
rotation = quaternion.create_from_y_rotation(np.pi / 2.0)
orientation = quaternion.cross(rotation, orientation)

# create a matrix
matrix = matrix44.create_identity()

# apply our translation
translation_matrix = matrix44.create_from_translation(translation)
matrix = matrix44.multiply(matrix, translation_matrix)

# apply our orientation
orientation_matrix = matrix44.create_from_quaternion(orientation)
matrix = matrix44.multiply(matrix, orientation_matrix)

# start our matrix off using the scale
scale_matrix = matrix44.create_from_scale(scale)
matrix = matrix44.multiply(matrix, scale_matrix)

# transform our point by the matrix
point = matrix44.apply_to_vector(matrix, point)
```

## Object Oriented Features

### Convertable types

```python
from pyrr import Quaternion, Matrix33, Matrix44, Vector3, Vector4

v3 = Vector3([1.,0.,0.])
v4 = Vector4.from_vector3(v3, w=1.0)
v3, w = Vector3.from_vector4(v4)

m44 = Matrix44()
q = Quaternion(m44)
m33 = Matrix33(q)

m33 = Matrix44().matrix33
m44 = Matrix33().matrix44
q = Matrix44().quaternion
q = Matrix33().quaternion

m33 = Quaternion().matrix33
m44 = Quaternion().matrix44
```

### Convenient Operators

```python
from pyrr import Quaternion, Matrix44, Matrix33, Vector3, Vector4
import numpy as np

# matrix multiplication
m = Matrix44() * Matrix33()
m = Matrix44() * Quaternion()
m = Matrix33() * Quaternion()

# matrix inverse
m = ~Matrix44.from_x_rotation(np.pi)

# quaternion multiplication
q = Quaternion() * Quaternion()
q = Quaternion() * Matrix44()
q = Quaternion() * Matrix33()

# quaternion inverse (conjugate)
q = ~Quaternion()

# quaternion dot product
d = Quaternion() | Quaternion()

# vector oprations
v = Vector3() + Vector3()
v = Vector4() - Vector4()

# vector transform
v = Quaternion() * Vector3()
v = Matrix44() * Vector3()
v = Matrix44() * Vector4()
v = Matrix33() * Vector3()

# dot and cross products
dot = Vector3() | Vector3()
cross = Vector3() ^ Vector3()
```

## Installation

Pyrr is in the PyPI database and can be installed via pip:

```s
pip install pyrr
```

Pyrr requires the following software:

- Python 2.7+ / 3.4+
- NumPy
- [multipledispatch](https://github.com/mrocklin/multipledispatch/)

## Changelog

[View the changelog](CHANGELOG.md).

## Authors

- [Adam Griffiths](https://github.com/adamlwgriffiths/)
- [Chris Bates](https://github.com/chrsbats/)
- [Jakub Stasiak](https://github.com/jstasiak/)
- [Bogdan Teleaga](https://github.com/bogdanteleaga/)
- [Szabolcs Dombi](https://github.com/cprogrammer1994/)
- [Korijn van Golen](https://github.com/Korijn/)
- [Armin Becher](https://github.com/ArminBecher)

Contributions are welcome.

## License

Pyrr is released under the BSD 2-clause license (a very relaxed licence), but it is encouraged that any modifications are submitted back to the master for inclusion.

Created by Adam Griffiths.

Copyright (c) 2012, Twisted Pair Development.
All rights reserved.

twistedpairdevelopment.wordpress.com
@twistedpairdev

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
1. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

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