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############################################################################## |
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# |
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# Copyright (c) 2003-2020 by The University of Queensland |
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# http://www.uq.edu.au |
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# |
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# Primary Business: Queensland, Australia |
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# Licensed under the Apache License, version 2.0 |
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# http://www.apache.org/licenses/LICENSE-2.0 |
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# |
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# Development until 2012 by Earth Systems Science Computational Center (ESSCC) |
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# Development 2012-2013 by School of Earth Sciences |
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# Development from 2014 by Centre for Geoscience Computing (GeoComp) |
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# Development from 2019 by School of Earth and Environmental Sciences |
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# |
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############################################################################## |
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|
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from __future__ import print_function, division |
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|
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__copyright__="""Copyright (c) 2003-2020 by The University of Queensland |
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http://www.uq.edu.au |
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Primary Business: Queensland, Australia""" |
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__license__="""Licensed under the Apache License, version 2.0 |
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http://www.apache.org/licenses/LICENSE-2.0""" |
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__url__="https://launchpad.net/escript-finley" |
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|
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""" |
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transformations |
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|
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:var __author__: name of author |
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:var __copyright__: copyrights |
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:var __license__: licence agreement |
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:var __url__: url entry point on documentation |
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:var __version__: version |
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:var __date__: date of the version |
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:var DEG: unit of degree |
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:var RAD: unit of radiant |
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""" |
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|
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__author__="Lutz Gross, l.gross@uq.edu.au" |
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|
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import numpy |
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import math |
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|
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_TYPE=numpy.float64 |
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DEG=math.pi/180. |
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RAD=1. |
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class Transformation(object): |
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""" |
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General class to define an affine transformation *x->Ax+b*. |
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""" |
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def __init__(self): |
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""" |
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Creates a linear transformation. |
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""" |
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pass |
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|
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def __call__(self,x=numpy.zeros((3,))): |
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""" |
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Applies transformation to ``x``. |
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""" |
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raise NotImplementeError() |
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|
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class Translation(Transformation): |
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""" |
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Defines a translation *x->x+b*. |
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""" |
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def __init__(self,b=numpy.zeros((3,),dtype=_TYPE)): |
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""" |
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Creates the linear transformation *x->x+b*. |
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""" |
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super(Translation, self).__init__() |
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self.__b=numpy.array(b,_TYPE) |
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|
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def __call__(self,x=numpy.zeros((3,))): |
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""" |
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Applies translation to ``x``. |
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""" |
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return numpy.array(x,_TYPE)+self.__b |
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|
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class Rotatation(Transformation): |
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""" |
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Defines a rotation. |
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""" |
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def __init__(self,axis=numpy.ones((3,),dtype=_TYPE),point=numpy.zeros((3,),dtype=_TYPE),angle=0.*RAD): |
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""" |
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Creates a rotation using an axis and a point on the axis. |
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""" |
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self.__axis=numpy.array(axis,dtype=_TYPE) |
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self.__point=numpy.array(point,dtype=_TYPE) |
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lax=numpy.dot(self.__axis,self.__axis) |
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if not lax>0: |
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raise ValueError("points must be distinct.") |
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self.__axis/=math.sqrt(lax) |
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self.__angle=float(angle) |
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|
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def __call__(self,x=numpy.zeros((3,))): |
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""" |
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Applies the rotation to ``x``. |
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""" |
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x=numpy.array(x,_TYPE) |
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z=x-self.__point |
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z0=numpy.dot(z,self.__axis) |
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z_per=z-z0*self.__axis |
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lz_per=numpy.dot(z_per,z_per) |
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if lz_per>0: |
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axis1=z_per/math.sqrt(lz_per) |
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axis2=_cross(axis1,self.__axis) |
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lax2=numpy.dot(axis2,axis2) |
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if lax2>0: |
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axis2/=math.sqrt(lax2) |
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return z0*self.__axis+math.sqrt(lz_per)*(math.cos(self.__angle)*axis1-math.sin(self.__angle)*axis2)+self.__point |
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else: |
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return x |
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else: |
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return x |
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|
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def _cross(x, y): |
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""" |
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Returns the cross product of ``x`` and ``y``. |
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""" |
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return numpy.array([x[1] * y[2] - x[2] * y[1], x[2] * y[0] - x[0] * y[2], x[0] * y[1] - x[1] * y[0]], _TYPE) |
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|
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class Dilation(Transformation): |
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""" |
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Defines a dilation. |
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""" |
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def __init__(self,factor=1.,center=numpy.zeros((3,),dtype=_TYPE)): |
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""" |
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Creates a dilation with a center and a given expansion/contraction |
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factor. |
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""" |
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if not abs(factor)>0: |
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raise ValueError("factor must be non-zero.") |
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self.__factor=factor |
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self.__center=numpy.array(center,dtype=_TYPE) |
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|
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def __call__(self,x=numpy.zeros((3,))): |
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""" |
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Applies dilation to ``x``. |
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""" |
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x=numpy.array(x,_TYPE) |
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return self.__factor*(x-self.__center)+self.__center |
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|
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class Reflection(Transformation): |
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""" |
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Defines a reflection on a plane. |
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""" |
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def __init__(self,normal=numpy.ones((3,),dtype=_TYPE),offset=0.): |
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""" |
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Defines a reflection on a plane defined in normal form. |
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""" |
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self.__normal=numpy.array(normal,dtype=_TYPE) |
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ln=math.sqrt(numpy.dot(self.__normal,self.__normal)) |
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if not ln>0.: |
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raise ValueError("normal must have positive length.") |
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self.__normal/=ln |
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if isinstance(offset,float) or isinstance(offset,int): |
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self.__offset=offset/ln |
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else: |
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self.__offset=numpy.dot(numpy.array(offset,dtype=_TYPE),self.__normal) |
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|
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def __call__(self,x=numpy.zeros((3,))): |
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""" |
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Applies reflection to ``x``. |
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""" |
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x=numpy.array(x,_TYPE) |
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return x - 2*(numpy.dot(x,self.__normal)-self.__offset)*self.__normal |
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