pyx/trafo.py

   1 #!/usr/bin/env python
   2 #
   3 #
   4 # Copyright (C) 2002 Jörg Lehmann <joergl@users.sourceforge.net>
   5 # Copyright (C) 2002 André Wobst <wobsta@users.sourceforge.net>
   6 #
   7 # This file is part of PyX (http://pyx.sourceforge.net/).
   8 #
   9 # PyX is free software; you can redistribute it and/or modify
  10 # it under the terms of the GNU General Public License as published by
  11 # the Free Software Foundation; either version 2 of the License, or
  12 # (at your option) any later version.
  13 #
  14 # PyX is distributed in the hope that it will be useful,
  15 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  16 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  17 # GNU General Public License for more details.
  18 #
  19 # You should have received a copy of the GNU General Public License
  20 # along with PyX; if not, write to the Free Software
  21 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  22
  23 import unit, canvas
  24
  25 # TODO:
  26 # - switch to affine space description (i.e. represent transformation by
  27 #   3x3 matrix (cf. PLRM Sect. 4.3.3)? Cooler!
  28 #
  29
  30 # some helper routines
  31
  32 def _rmatrix(angle):
  33     from math import pi, cos, sin
  34     phi = 2*pi*angle/360
  35
  36     return  (( cos(phi), sin(phi)),
  37              (-sin(phi), cos(phi)))
  38
  39 def _mmatrix(angle):
  40     from math import pi, cos, sin
  41     phi = 2*pi*angle/360
  42
  43     return ( (cos(phi)*cos(phi)-sin(phi)*sin(phi), -2*sin(phi)*cos(phi)                ),
  44              (-2*sin(phi)*cos(phi),                sin(phi)*sin(phi)-cos(phi)*cos(phi) ) )
  45
  46 def _det(matrix):
  47     return matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0]
  48
  49 # Exception
  50
  51 class UndefinedResultError(ArithmeticError):
  52     pass
  53
  54 # transformation: affine transformations
  55
  56 class transformation:
  57     def __init__(self, matrix=((1,0),(0,1)), vector=(0,0)):
  58         if _det(matrix)==0:
  59             raise UndefinedResultError, "transformation matrix must not be singular"
  60         else:
  61             self.matrix=matrix
  62         self.vector=tuple(map(lambda x: unit.length(x), vector))
  63
  64     def __mul__(self, other):
  65         if isinstance(other, transformation):
  66             matrix = ( ( self.matrix[0][0]*other.matrix[0][0] + self.matrix[0][1]*other.matrix[1][0],
  67                          self.matrix[0][0]*other.matrix[0][1] + self.matrix[0][1]*other.matrix[1][1] ),
  68                        ( self.matrix[1][0]*other.matrix[0][0] + self.matrix[1][1]*other.matrix[1][0],
  69                          self.matrix[1][0]*other.matrix[0][1] + self.matrix[1][1]*other.matrix[1][1] )
  70                      )
  71
  72             vector = ( self.matrix[0][0]*other.vector[0] + self.matrix[1][0]*other.vector[1] + self.vector[0],
  73                        self.matrix[0][1]*other.vector[0] + self.matrix[1][1]*other.vector[1] + self.vector[1] )
  74
  75             # print " ( %s * %s => %s ) "% (self, other, transformation(angle=angle, vector=vector))
  76
  77             return transformation(matrix=matrix, vector=vector)
  78         else:
  79             raise NotImplementedError, "can only multiply two transformations"
  80     def __rmul__(self, other):                          # TODO: not needed!?
  81         return other.__mul__(self)
  82
  83     def apply(self, point):
  84         return (self.matrix[0][0]*point[0] + self.matrix[1][0]*point[1]+self.vector[0],
  85                 self.matrix[0][1]*point[0] + self.matrix[1][1]*point[1]+self.vector[1])
  86
  87     def matrix():
  88         return self.matrix
  89
  90     def vector(self):
  91         return self.vector
  92
  93     def angle(self):
  94         return self.angle
  95
  96     def translate(self,x,y):
  97         return transformation(vector=(x,y))*self
  98
  99     def rotate(self,angle):
 100         return transformation(matrix=_rmatrix(angle))*self
 101
 102     def mirror(self,angle):
 103         return transformation(matrix=_mmatrix(angle))*self
 104
 105     def scale(self, x, y=None):
 106         return transformation(matrix=((x, 0), (0,y or x)))*self
 107
 108     def inverse(self):
 109         det = _det(self.matrix)                         # shouldn't be zero, but
 110         try:
 111           matrix = ( ( self.matrix[1][1]/det, -self.matrix[0][1]/det),
 112                      (-self.matrix[1][0]/det,  self.matrix[0][0]/det)
 113                    )
 114         except ZeroDivisionError:
 115            raise UndefinedResultError, "transformation matrix must not be singular"
 116         return transformation(matrix=matrix) * transformation(vector=(-self.vector[0],-self.vector[1]))
 117
 118     def bbox(self, acanvas):
 119         # assert 0, "this shouldn't be called!"
 120         return canvas.bbox()
 121
 122     def write(self, canvas, file):
 123         file.write("[%f %f %f %f %f %f] concat\n" % \
 124                     ( self.matrix[0][0], self.matrix[0][1],
 125                       self.matrix[1][0], self.matrix[1][1],
 126                       canvas.unit.pt(self.vector[0]), canvas.unit.pt(self.vector[1])))
 127
 128
 129 class translate(transformation):
 130     def __init__(self,x,y):
 131         transformation.__init__(self, vector=(x,y))
 132
 133 class rotate(transformation):
 134     def __init__(self,angle):
 135         transformation.__init__(self, matrix=_rmatrix(angle))
 136
 137 class mirror(transformation):
 138     def __init__(self,angle=0):
 139         transformation.__init__(self, matrix=_mmatrix(angle))
 140
 141 class scale(transformation):
 142     def __init__(self,x,y=None):
 143         transformation.__init__(self, matrix=((x,0),(0,y or x)))
 144
 145
 146 if __name__=="__main__":
 147    # test for some invariants:
 148
 149    def checkforidentity(trafo):
 150        u=unit.unit()
 151        m = max(map(abs,[trafo.matrix[0][0]-1,
 152                         trafo.matrix[1][0],
 153                         trafo.matrix[0][1],
 154                         trafo.matrix[1][1]-1,
 155                         u.pt(trafo.vector[0]),
 156                         u.pt(trafo.vector[1])]))
 157
 158        assert m<1e-7, "tests for invariants failed"
 159
 160
 161    # transformation(angle=angle, vector=(x,y)) == translate(x,y) * rotate(angle)
 162    checkforidentity( translate(1,3) * rotate(15)  * transformation(matrix=_rmatrix(15),vector=(1,3)).inverse())
 163
 164    # t*t.inverse() == 1
 165    t = translate(-1,-1)*rotate(72)*translate(1,1)
 166    checkforidentity(t*t.inverse())
 167
 168    # -mirroring two times should yield identiy
 169    # -mirror(phi)=mirror(phi+180)
 170    checkforidentity( mirror(20)*mirror(20))
 171    checkforidentity( mirror(20).mirror(20))
 172    checkforidentity( mirror(20)*mirror(180+20))
 173
 174    # equivalent notations
 175    checkforidentity( translate(1,2).rotate(72).translate(-3,-1)*(translate(-3,-1)*rotate(72)*translate(1,2)).inverse() )
 176
 177    checkforidentity( rotate(40).rotate(120).rotate(90).rotate(110) )
 178
 179    checkforidentity( scale(2,3).scale(1/2.0, 1/3.0) )
 180
 181    def applyonbasis(t):
 182        u=unit.unit()
 183        ex = (1,0)
 184        ey = (0,1)
 185        print "%s:" % t
 186        t=eval(t)
 187        esx=t.apply(ex)
 188        esy=t.apply(ey)
 189        print "  (1,0) => (%f, %f)" % (u.m(esx[0])*100, u.m(esx[1])*100)
 190        print "  (0,1) => (%f, %f)" % (u.m(esy[0])*100, u.m(esy[1])*100)
 191
 192    applyonbasis("translate(1,0)")
 193    applyonbasis("translate(0,1)")
 194    applyonbasis("rotate(90)")
 195    applyonbasis("scale(0.5)")
 196    applyonbasis("translate(1,0)*rotate(90)")
 197    applyonbasis("translate(1,0)*scale(0.5)")
 198    applyonbasis("rotate(90)*translate(1,0)")
 199    applyonbasis("scale(0.5)*translate(1,0)")
 200    applyonbasis("translate(1,0)*rotate(90)*scale(0.5)")
 201    applyonbasis("translate(1,0)*scale(0.5)*rotate(90)")
 202    applyonbasis("rotate(90)*scale(0.5)*translate(1,0)")
 203    applyonbasis("scale(0.5)*rotate(90)*translate(1,0)")
 204
 205