/[escript]/trunk/pycad/py_src/transformations.py
ViewVC logotype

Contents of /trunk/pycad/py_src/transformations.py

Parent Directory Parent Directory | Revision Log Revision Log


Revision 999 - (show annotations)
Tue Feb 27 08:12:37 2007 UTC (12 years, 7 months ago) by gross
File MIME type: text/x-python
File size: 4474 byte(s)
start to put some pycad documentation into the users guide
1 # $Id:$
2 """
3 transformations
4
5 @var __author__: name of author
6 @var __copyright__: copyrights
7 @var __license__: licence agreement
8 @var __url__: url entry point on documentation
9 @var __version__: version
10 @var __date__: date of the version
11 @var DEG: unit of degree
12 @var RAD: unit of radiant
13 """
14
15 __author__="Lutz Gross, l.gross@uq.edu.au"
16 __copyright__=""" Copyright (c) 2006 by ACcESS MNRF
17 http://www.access.edu.au
18 Primary Business: Queensland, Australia"""
19 __license__="""Licensed under the Open Software License version 3.0
20 http://www.opensource.org/licenses/osl-3.0.php"""
21 __url__="http://www.iservo.edu.au/esys/escript"
22 __version__="$Revision:$"
23 __date__="$Date:$"
24
25 import numarray
26 import math
27
28 _TYPE=numarray.Float64
29 DEG=math.pi/180.
30 RAD=1.
31 class Transformation(object):
32 """
33 general class to define an affine transformation x->Ax+b
34 """
35 def __init__(self):
36 """
37 create a linear transformation
38 """
39 pass
40 def __call__(self,x=numarray.zeros((3,))):
41 """
42 applies transformation to x
43 """
44 raise NotImplementeError()
45 class Translation(Transformation):
46 """
47 defines a translation x->x+b
48 """
49 def __init__(self,b=numarray.zeros((3,),type=_TYPE)):
50 """
51 create linear transformation x->x+b
52 """
53 super(Translation, self).__init__()
54 self.__b=numarray.array(b,_TYPE)
55 def __call__(self,x=numarray.zeros((3,))):
56 """
57 applies translation to x
58 """
59 return numarray.array(x,_TYPE)+self.__b
60
61 class Rotatation(Transformation):
62 """
63 defines a rotation
64 """
65 def __init__(self,axis=numarray.ones((3,),type=_TYPE),point=numarray.zeros((3,),type=_TYPE),angle=0.*RAD):
66 """
67 creates a rotation using an axis and a point on the axis
68 """
69 self.__axis=numarray.array(axis,type=_TYPE)
70 self.__point=numarray.array(point,type=_TYPE)
71 lax=numarray.dot(self.__axis,self.__axis)
72 if not lax>0:
73 raise ValueError("points must be distinct.")
74 self.__axis/=math.sqrt(lax)
75 self.__angle=float(angle)
76 def __call__(self,x=numarray.zeros((3,))):
77 """
78 applies rotatation to x
79 """
80 x=numarray.array(x,_TYPE)
81 z=x-self.__point
82 z0=numarray.dot(z,self.__axis)
83 z_per=z-z0*self.__axis
84 lz_per=numarray.dot(z_per,z_per)
85 if lz_per>0:
86 axis1=z_per/math.sqrt(lz_per)
87 axis2=_cross(axis1,self.__axis)
88 lax2=numarray.dot(axis2,axis2)
89 if lax2>0:
90 axis2/=math.sqrt(lax2)
91 return z0*self.__axis+math.sqrt(lz_per)*(math.cos(self.__angle)*axis1-math.sin(self.__angle)*axis2)+self.__point
92 else:
93 return x
94 else:
95 return x
96 def _cross(x, y):
97 """
98 Returns the cross product of x and y
99 """
100 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)
101
102 class Dilation(Transformation):
103 """
104 defines a dilation
105 """
106 def __init__(self,factor=1.,center=numarray.zeros((3,),type=_TYPE)):
107 """
108 creates a dilation with a center an a given expansion/contraction factor
109 """
110 if not abs(factor)>0:
111 raise ValueError("factor must be non-zero.")
112 self.__factor=factor
113 self.__center=numarray.array(center,type=_TYPE)
114 def __call__(self,x=numarray.zeros((3,))):
115 """
116 applies dilation to x
117 """
118 x=numarray.array(x,_TYPE)
119 return self.__factor*(x-self.__center)+self.__center
120
121 class Reflection(Transformation):
122 """
123 defines a reflection on a plain
124 """
125 def __init__(self,normal=numarray.ones((3,),type=_TYPE),offset=0.):
126 """
127 defines a reflection on a plain defined in normal form
128 """
129 self.__normal=numarray.array(normal,type=_TYPE)
130 ln=math.sqrt(numarray.dot(self.__normal,self.__normal))
131 if not ln>0.:
132 raise ValueError("normal must have positive length.")
133 self.__normal/=ln
134 if isinstance(offset,float) or isinstance(offset,int):
135 self.__offset=offset/ln
136 else:
137 self.__offset=numarray.dot(numarray.array(offset,type=_TYPE),self.__normal)
138 def __call__(self,x=numarray.zeros((3,))):
139 """
140 applies reflection to x
141 """
142 x=numarray.array(x,_TYPE)
143 return x - 2*(numarray.dot(x,self.__normal)-self.__offset)*self.__normal

  ViewVC Help
Powered by ViewVC 1.1.26