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# $Id:$ |
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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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__copyright__=""" Copyright (c) 2006 by ACcESS MNRF |
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http://www.access.edu.au |
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Primary Business: Queensland, Australia""" |
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__license__="""Licensed under the Open Software License version 3.0 |
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http://www.opensource.org/licenses/osl-3.0.php""" |
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__url__="http://www.iservo.edu.au/esys/escript" |
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__version__="$Revision:$" |
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__date__="$Date:$" |
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|
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import numarray |
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import math |
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|
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_TYPE=numarray.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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create a linear transformation |
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""" |
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pass |
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def __call__(self,x=numarray.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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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=numarray.zeros((3,),type=_TYPE)): |
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""" |
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create linear transformation x->x+b |
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""" |
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super(Translation, self).__init__() |
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self.__b=numarray.array(b,_TYPE) |
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def __call__(self,x=numarray.zeros((3,))): |
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""" |
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applies translation to x |
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""" |
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return numarray.array(x,_TYPE)+self.__b |
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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,point0=numarray.zeros((3,),type=_TYPE),point1=numarray.ones((3,),type=_TYPE),angle=0.*RAD): |
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""" |
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creates a rotation using to points to define the axis and a rotation angle |
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""" |
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self.__point0=numarray.array(point0,type=_TYPE) |
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self.__point1=numarray.array(point1,type=_TYPE) |
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self.__axis=self.__point1-self.__point0 |
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lax=numarray.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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def __call__(self,x=numarray.zeros((3,))): |
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""" |
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applies rotatation to x |
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""" |
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x=numarray.array(x,_TYPE) |
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z=x-self.__point0 |
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z0=numarray.dot(z,self.__axis) |
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z_per=z-z0*self.__axis |
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lz_per=numarray.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=numarray.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.__point0 |
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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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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 numarray.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=numarray.zeros((3,),type=_TYPE)): |
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""" |
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creates a dilation with a center an a given expansion/contraction factor |
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""" |
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if not factor>0: |
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raise ValueError("factor must be positive.") |
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self.__factor=factor |
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self.__center=numarray.array(center,type=_TYPE) |
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def __call__(self,x=numarray.zeros((3,))): |
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""" |
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applies dilation to x |
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""" |
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x=numarray.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 plain |
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""" |
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def __init__(self,normal=numarray.ones((3,),type=_TYPE),offset=0.): |
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""" |
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defines a reflection on a plain defined in normal form |
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""" |
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self.__normal=numarray.array(normal,type=_TYPE) |
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ln=math.sqrt(numarray.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=numarray.dot(numarray.array(offset,type=_TYPE),self.__normal) |
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def __call__(self,x=numarray.zeros((3,))): |
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""" |
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applies reflection to x |
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""" |
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x=numarray.array(x,_TYPE) |
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return x - 2*(numarray.dot(x,self.__normal)-self.__offset)*self.__normal |
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