fagan2888 / pyrr

3D mathematical functions using NumPy

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.

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.

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

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

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

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:

pip install pyrr

Pyrr requires the following software:

• Python 2.7+ / 3.4+
• NumPy
• multipledispatch

Changelog

View the changelog.

Authors

• Adam Griffiths
• Chris Bates
• Jakub Stasiak
• Bogdan Teleaga
• Szabolcs Dombi
• Korijn van Golen
• Armin Becher

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.
2. 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.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

The views and conclusions contained in the software and documentation are those of the authors and should not be interpreted as representing official policies, either expressed or implied, of the FreeBSD Project.