trafo.py

   1 # -*- encoding: utf-8 -*-
   2 #
   3 #
   4 # Copyright (C) 2002-2011 Jörg Lehmann <joergl@users.sourceforge.net>
   5 # Copyright (C) 2002-2011 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA
  22
  23 import math
  24 from . import attr, baseclasses, unit
  25
  26 # some helper routines
  27
  28 def _rmatrix(angle):
  29     phi = math.pi*angle/180.0
  30
  31     return  ((math.cos(phi), -math.sin(phi)),
  32              (math.sin(phi),  math.cos(phi)))
  33
  34 def _rvector(angle, x, y):
  35     phi = math.pi*angle/180.0
  36
  37     return  ((1-math.cos(phi))*x + math.sin(phi)    *y,
  38               -math.sin(phi)   *x + (1-math.cos(phi))*y)
  39
  40
  41 def _mmatrix(angle):
  42     phi = math.pi*angle/180.0
  43
  44     return ( (math.cos(phi)*math.cos(phi)-math.sin(phi)*math.sin(phi),
  45               -2*math.sin(phi)*math.cos(phi)                ),
  46              (-2*math.sin(phi)*math.cos(phi),
  47               math.sin(phi)*math.sin(phi)-math.cos(phi)*math.cos(phi) ) )
  48
  49
  50 # trafo: affine transformations
  51
  52 class trafo_pt(baseclasses.deformer):
  53
  54     """affine transformation (coordinates in constructor in pts)
  55
  56     Note that though the coordinates in the constructor are in
  57     pts (which is useful for internal purposes), all other
  58     methods only accept units in the standard user notation.
  59
  60     """
  61
  62     def __init__(self, matrix=((1, 0), (0, 1)), vector=(0, 0)):
  63         """Return trafo with given transformation matrix and vector.
  64         """
  65         self.matrix = matrix
  66         self.vector = vector
  67
  68     def __mul__(self, other):
  69         if isinstance(other, trafo_pt):
  70             matrix = ( ( self.matrix[0][0]*other.matrix[0][0] +
  71                          self.matrix[0][1]*other.matrix[1][0],
  72                          self.matrix[0][0]*other.matrix[0][1] +
  73                          self.matrix[0][1]*other.matrix[1][1] ),
  74                        ( self.matrix[1][0]*other.matrix[0][0] +
  75                          self.matrix[1][1]*other.matrix[1][0],
  76                          self.matrix[1][0]*other.matrix[0][1] +
  77                          self.matrix[1][1]*other.matrix[1][1] )
  78                      )
  79
  80             vector = ( self.matrix[0][0]*other.vector[0] +
  81                        self.matrix[0][1]*other.vector[1] +
  82                        self.vector[0],
  83                        self.matrix[1][0]*other.vector[0] +
  84                        self.matrix[1][1]*other.vector[1] +
  85                        self.vector[1] )
  86
  87             return trafo_pt(matrix=matrix, vector=vector)
  88         else:
  89             raise NotImplementedError("can only multiply two transformations")
  90
  91     def __str__(self):
  92         return "[%f %f %f %f %f %f]" % \
  93                ( self.matrix[0][0], self.matrix[1][0],
  94                  self.matrix[0][1], self.matrix[1][1],
  95                  self.vector[0], self.vector[1] )
  96
  97     def processPS(self, file, writer, context, registry):
  98         file.write("[%f %f %f %f %f %f] concat\n" % \
  99                     ( self.matrix[0][0], self.matrix[1][0],
 100                       self.matrix[0][1], self.matrix[1][1],
 101                       self.vector[0], self.vector[1] ) )
 102
 103     def processPDF(self, file, writer, context, registry):
 104         file.write("%f %f %f %f %f %f cm\n" % \
 105                     ( self.matrix[0][0], self.matrix[1][0],
 106                       self.matrix[0][1], self.matrix[1][1],
 107                       self.vector[0], self.vector[1] ) )
 108
 109     def apply_pt(self, x_pt, y_pt):
 110         """apply transformation to point (x_pt, y_pt) in pts"""
 111         return ( self.matrix[0][0]*x_pt + self.matrix[0][1]*y_pt + self.vector[0],
 112                  self.matrix[1][0]*x_pt + self.matrix[1][1]*y_pt + self.vector[1] )
 113
 114     def apply(self, x, y):
 115         # for the transformation we have to convert to points
 116         tx, ty = self.apply_pt(unit.topt(x), unit.topt(y))
 117         return tx * unit.t_pt, ty * unit.t_pt
 118
 119     def deform(self, path):
 120         return path.transformed(self)
 121
 122     def inverse(self):
 123         det = 1.0*(self.matrix[0][0]*self.matrix[1][1] - self.matrix[0][1]*self.matrix[1][0])
 124         matrix = ( ( self.matrix[1][1]/det, -self.matrix[0][1]/det),
 125                    (-self.matrix[1][0]/det,  self.matrix[0][0]/det) )
 126         return ( trafo_pt(matrix=matrix) *
 127                  trafo_pt(vector=(-self.vector[0], -self.vector[1])) )
 128
 129     def mirrored(self, angle):
 130         return mirror(angle) * self
 131
 132     def rotated_pt(self, angle, x=None, y=None):
 133         return rotate_pt(angle, x, y) * self
 134
 135     def rotated(self, angle, x=None, y=None):
 136         return rotate(angle, x, y) * self
 137
 138     def scaled_pt(self, sx, sy=None, x=None, y=None):
 139         return scale_pt(sx, sy, x, y) * self
 140
 141     def scaled(self, sx, sy=None, x=None, y=None):
 142         return scale(sx, sy, x, y) * self
 143
 144     def slanted_pt(self, a, angle=0, x=None, y=None):
 145         return slant_pt(a, angle, x, y) * self
 146
 147     def slanted(self, a, angle=0, x=None, y=None):
 148         return slant(a, angle, x, y) * self
 149
 150     def translated_pt(self, x, y):
 151         return translate_pt(x, y) * self
 152
 153     def translated(self, x, y):
 154         return translate(x, y) * self
 155
 156
 157 class trafo(trafo_pt):
 158
 159     """affine transformation"""
 160
 161     def __init__(self, matrix=((1,0), (0,1)), vector=(0, 0)):
 162         trafo_pt.__init__(self,
 163                           matrix, (unit.topt(vector[0]), unit.topt(vector[1])))
 164
 165 #
 166 # some standard transformations
 167 #
 168
 169 identity = trafo()
 170
 171 class mirror(trafo):
 172     def __init__(self, angle=0):
 173         trafo.__init__(self, matrix=_mmatrix(angle))
 174
 175
 176 class rotate_pt(trafo_pt):
 177     def __init__(self, angle, x=None, y=None):
 178         vector = 0, 0
 179         if x is not None or y is not None:
 180             if x is None or y is None:
 181                 raise TrafoException("either specify both x and y or none of them")
 182             vector=_rvector(angle, x, y)
 183
 184         trafo_pt.__init__(self, matrix=_rmatrix(angle), vector=vector)
 185
 186
 187 class rotate(trafo_pt):
 188     def __init__(self, angle, x=None, y=None):
 189         vector = 0, 0
 190         if x is not None or y is not None:
 191             if x is None or y is None:
 192                 raise TrafoException("either specify both x and y or none of them")
 193             vector=_rvector(angle, unit.topt(x), unit.topt(y))
 194
 195         trafo_pt.__init__(self, matrix=_rmatrix(angle), vector=vector)
 196
 197
 198 class scale_pt(trafo_pt):
 199     def __init__(self, sx, sy=None, x=None, y=None):
 200         if sy is None:
 201             sy = sx
 202         vector = 0, 0
 203         if x is not None or y is not None:
 204             if x is None or y is None:
 205                 raise TrafoException("either specify both x and y or none of them")
 206             vector = (1-sx)*x, (1-sy)*y
 207         trafo_pt.__init__(self, matrix=((sx, 0), (0, sy)), vector=vector)
 208
 209
 210 class scale(trafo):
 211     def __init__(self, sx, sy=None, x=None, y=None):
 212         if sy is None:
 213             sy = sx
 214         vector = 0, 0
 215         if x is not None or y is not None:
 216             if x is None or y is None:
 217                 raise TrafoException("either specify both x and y or none of them")
 218             vector = (1-sx)*x, (1-sy)*y
 219         trafo.__init__(self, matrix=((sx, 0), (0, sy)), vector=vector)
 220
 221
 222 class slant_pt(trafo_pt):
 223     def __init__(self, a, angle=0, x=None, y=None):
 224         t = ( rotate_pt(-angle, x, y) *
 225               trafo(matrix=((1, a), (0, 1))) *
 226               rotate_pt(angle, x, y) )
 227         trafo_pt.__init__(self, t.matrix, t.vector)
 228
 229
 230 class slant(trafo):
 231     def __init__(self, a, angle=0, x=None, y=None):
 232         t = ( rotate(-angle, x, y) *
 233               trafo(matrix=((1, a), (0, 1))) *
 234               rotate(angle, x, y) )
 235         trafo.__init__(self, t.matrix, t.vector)
 236
 237
 238 class translate_pt(trafo_pt):
 239     def __init__(self, x, y):
 240         trafo_pt.__init__(self, vector=(x, y))
 241
 242
 243 class translate(trafo):
 244     def __init__(self, x, y):
 245         trafo.__init__(self, vector=(x, y))