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3D mathematical functions using NumPy
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adamlwgriffiths/Pyrr
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Provides 3D mathematical functions using the power of NumPy.
- 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
View Pyrr's documentation online.
Maintain a rotation (quaternion) and translation (vector) and convert to a matrix
This is a long winded example to demonstrate various features.
frompyrrimportQuaternion,Matrix44,Vector3importnumpyasnppoint=Vector3([1.,2.,3.])orientation=Quaternion()translation=Vector3()scale=Vector3([1.,1.,1.])# translate along X by 1translation+= [1.0,0.0,0.0]# rotate about Y by pi/2rotation=Quaternion.from_y_rotation(np.pi/2.0)orientation=rotation*orientation# create a matrixmatrix=Matrix44.identity()# apply our translationmatrix=matrix*Matrix44.from_translation(translation)# apply our orientation# we can multiply matricies and quaternions directly!matrix=matrix*orientation# apply our scalematrix=matrix*Matrix44.from_scale(scale)# transform our point by the matrix# vectors are transformable by matrices and quaternions directlypoint=matrix*point
frompyrrimportquaternion,matrix44,vector3importnumpyasnppoint=vector3.create(1.,2.,3.)orientation=quaternion.create()translation=vector3.create()scale=vector3.create(1,1,1)# translate along X by 1translation+= [1.0,0.0,0.0]# rotate about Y by pi/2rotation=quaternion.create_from_y_rotation(np.pi/2.0)orientation=quaternion.cross(rotation,orientation)# create a matrixmatrix=matrix44.create_identity()# apply our translationtranslation_matrix=matrix44.create_from_translation(translation)matrix=matrix44.multiply(matrix,translation_matrix)# apply our orientationorientation_matrix=matrix44.create_from_quaternion(orientation)matrix=matrix44.multiply(matrix,orientation_matrix)# start our matrix off using the scalescale_matrix=matrix44.create_from_scale(scale)matrix=matrix44.multiply(matrix,scale_matrix)# transform our point by the matrixpoint=matrix44.apply_to_vector(matrix,point)
frompyrrimportQuaternion,Matrix33,Matrix44,Vector3,Vector4v3=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().matrix33m44=Matrix33().matrix44q=Matrix44().quaternionq=Matrix33().quaternionm33=Quaternion().matrix33m44=Quaternion().matrix44
frompyrrimportQuaternion,Matrix44,Matrix33,Vector3,Vector4importnumpyasnp# matrix multiplicationm=Matrix44()*Matrix33()m=Matrix44()*Quaternion()m=Matrix33()*Quaternion()# matrix inversem=~Matrix44.from_x_rotation(np.pi)# quaternion multiplicationq=Quaternion()*Quaternion()q=Quaternion()*Matrix44()q=Quaternion()*Matrix33()# quaternion inverse (conjugate)q=~Quaternion()# quaternion dot productd=Quaternion()|Quaternion()# vector operationsv=Vector3()+Vector3()v=Vector4()-Vector4()# vector transformv=Quaternion()*Vector3()v=Matrix44()*Vector3()v=Matrix44()*Vector4()v=Matrix33()*Vector3()# dot and cross productsdot=Vector3()|Vector3()cross=Vector3()^Vector3()
Pyrr is in the PyPI database and can be installed via pip:
pip install pyrrPyrr requires the following software:
- Python 2.7+ / 3.4+
- NumPy
- multipledispatch
Contributions are welcome.
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 withoutmodification, are permitted provided that the following conditions are met:
- Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
- 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" ANDANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIEDWARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE AREDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FORANY 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 ANDON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THISSOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
The views and conclusions contained in the software and documentation are thoseof the authors and should not be interpreted as representing official policies,either expressed or implied, of the FreeBSD Project.
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3D mathematical functions using NumPy