pyx/trafo.py

   1 # -*- coding: ISO-8859-1 -*-
   2 #
   3 #
   4 # Copyright (C) 2002-2006 Jörg Lehmann <joergl@users.sourceforge.net>
   5 # Copyright (C) 2002-2004 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 import attr, canvasitem, deformer, unit
  25 import bbox as bboxmodule
  26
  27 # global epsilon (used to judge whether a matrix is singular)
  28 _epsilon = (1e-5)**2
  29
  30 def set(epsilon=None):
  31     global _epsilon
  32     if epsilon is not None:
  33         _epsilon = epsilon
  34
  35
  36 # some helper routines
  37
  38 def _rmatrix(angle):
  39     phi = math.pi*angle/180.0
  40
  41     return  ((math.cos(phi), -math.sin(phi)),
  42              (math.sin(phi),  math.cos(phi)))
  43
  44 def _rvector(angle, x, y):
  45     phi = math.pi*angle/180.0
  46
  47     return  ((1-math.cos(phi))*x + math.sin(phi)    *y,
  48               -math.sin(phi)   *x + (1-math.cos(phi))*y)
  49
  50
  51 def _mmatrix(angle):
  52     phi = math.pi*angle/180.0
  53
  54     return ( (math.cos(phi)*math.cos(phi)-math.sin(phi)*math.sin(phi),
  55               -2*math.sin(phi)*math.cos(phi)                ),
  56              (-2*math.sin(phi)*math.cos(phi),
  57               math.sin(phi)*math.sin(phi)-math.cos(phi)*math.cos(phi) ) )
  58
  59 class _marker: pass
  60
  61 # Exception
  62
  63 class TrafoException(Exception):
  64     pass
  65
  66 # trafo: affine transformations
  67
  68 class trafo_pt(canvasitem.canvasitem, deformer.deformer):
  69
  70     """affine transformation (coordinates in constructor in pts)
  71
  72     Note that though the coordinates in the constructor are in
  73     pts (which is useful for internal purposes), all other
  74     methods only accept units in the standard user notation.
  75
  76     """
  77
  78     def __init__(self, matrix=((1, 0), (0, 1)), vector=(0, 0), epsilon=_marker):
  79         """Return trafo with given transformation matrix and vector. If epsilon
  80         is passed it is used instead of the global epsilon defined in the module to
  81         check whether the matrix is singular or not. Use epsilon=None to turn of this
  82         checking.
  83         """
  84         if epsilon is _marker:
  85             epsilon = _epsilon
  86         self.epsilon = epsilon
  87         if epsilon is not None and abs(matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0]) < epsilon:
  88             raise TrafoException("transformation matrix must not be singular")
  89         else:
  90             self.matrix = matrix
  91         self.vector = vector
  92
  93     def __mul__(self, other):
  94         if isinstance(other, trafo_pt):
  95             if self.epsilon is None or other.epsilon is None:
  96                 epsilon = None
  97             elif self.epsilon <= other.epsilon:
  98                 epsilon = self.epsilon
  99             else:
 100                 epsilon = other.epsilon
 101             matrix = ( ( self.matrix[0][0]*other.matrix[0][0] +
 102                          self.matrix[0][1]*other.matrix[1][0],
 103                          self.matrix[0][0]*other.matrix[0][1] +
 104                          self.matrix[0][1]*other.matrix[1][1] ),
 105                        ( self.matrix[1][0]*other.matrix[0][0] +
 106                          self.matrix[1][1]*other.matrix[1][0],
 107                          self.matrix[1][0]*other.matrix[0][1] +
 108                          self.matrix[1][1]*other.matrix[1][1] )
 109                      )
 110
 111             vector = ( self.matrix[0][0]*other.vector[0] +
 112                        self.matrix[0][1]*other.vector[1] +
 113                        self.vector[0],
 114                        self.matrix[1][0]*other.vector[0] +
 115                        self.matrix[1][1]*other.vector[1] +
 116                        self.vector[1] )
 117
 118             return trafo_pt(matrix=matrix, vector=vector, epsilon=epsilon)
 119         else:
 120             raise NotImplementedError("can only multiply two transformations")
 121
 122     def __str__(self):
 123         return "[%f %f %f %f %f %f]" % \
 124                ( self.matrix[0][0], self.matrix[1][0],
 125                  self.matrix[0][1], self.matrix[1][1],
 126                  self.vector[0], self.vector[1] )
 127
 128     def processPS(self, file, writer, context, registry, bbox):
 129         file.write("[%f %f %f %f %f %f] concat\n" % \
 130                     ( self.matrix[0][0], self.matrix[1][0],
 131                       self.matrix[0][1], self.matrix[1][1],
 132                       self.vector[0], self.vector[1] ) )
 133
 134     def processPDF(self, file, writer, context, registry, bbox):
 135         file.write("%f %f %f %f %f %f cm\n" % \
 136                     ( self.matrix[0][0], self.matrix[1][0],
 137                       self.matrix[0][1], self.matrix[1][1],
 138                       self.vector[0], self.vector[1] ) )
 139
 140     def bbox(self):
 141         return bboxmodule.empty()
 142
 143     def apply_pt(self, x_pt, y_pt):
 144         """apply transformation to point (x_pt, y_pt) in pts"""
 145         return ( self.matrix[0][0]*x_pt + self.matrix[0][1]*y_pt + self.vector[0],
 146                  self.matrix[1][0]*x_pt + self.matrix[1][1]*y_pt + self.vector[1] )
 147
 148     def apply(self, x, y):
 149         # for the transformation we have to convert to points
 150         tx, ty = self.apply_pt(unit.topt(x), unit.topt(y))
 151         return tx * unit.t_pt, ty * unit.t_pt
 152
 153     def deform(self, path):
 154         return path.transformed(self)
 155
 156     def inverse(self):
 157         det = 1.0*(self.matrix[0][0]*self.matrix[1][1] - self.matrix[0][1]*self.matrix[1][0])
 158         matrix = ( ( self.matrix[1][1]/det, -self.matrix[0][1]/det),
 159                    (-self.matrix[1][0]/det,  self.matrix[0][0]/det) )
 160         return ( trafo_pt(matrix=matrix, epsilon=self.epsilon) *
 161                  trafo_pt(vector=(-self.vector[0], -self.vector[1]), epsilon=self.epsilon) )
 162
 163     def mirrored(self, angle):
 164         return mirror(angle, epsilon=self.epsilon) * self
 165
 166     def rotated_pt(self, angle, x=None, y=None):
 167         return rotate_pt(angle, x, y, epsilon=self.epsilon) * self
 168
 169     def rotated(self, angle, x=None, y=None):
 170         return rotate(angle, x, y, epsilon=self.epsilon) * self
 171
 172     def scaled_pt(self, sx, sy=None, x=None, y=None):
 173         return scale_pt(sx, sy, x, y, epsilon=self.epsilon) * self
 174
 175     def scaled(self, sx, sy=None, x=None, y=None):
 176         return scale(sx, sy, x, y, epsilon=self.epsilon) * self
 177
 178     def slanted_pt(self, a, angle=0, x=None, y=None):
 179         return slant_pt(a, angle, x, y, epsilon=self.epsilon) * self
 180
 181     def slanted(self, a, angle=0, x=None, y=None):
 182         return slant(a, angle, x, y, epsilon=self.epsilon) * self
 183
 184     def translated_pt(self, x, y):
 185         return translate_pt(x, y, epsilon=self.epsilon) * self
 186
 187     def translated(self, x, y):
 188         return translate(x, y, epsilon=self.epsilon) * self
 189
 190
 191 class trafo(trafo_pt):
 192
 193     """affine transformation"""
 194
 195     def __init__(self, matrix=((1,0), (0,1)), vector=(0, 0), epsilon=_marker):
 196         trafo_pt.__init__(self,
 197                           matrix, (unit.topt(vector[0]), unit.topt(vector[1])),
 198                           epsilon=epsilon)
 199
 200 #
 201 # some standard transformations
 202 #
 203
 204 class mirror(trafo):
 205     def __init__(self, angle=0, epsilon=_marker):
 206         trafo.__init__(self, matrix=_mmatrix(angle), epsilon=epsilon)
 207
 208
 209 class rotate_pt(trafo_pt):
 210     def __init__(self, angle, x=None, y=None, epsilon=_marker):
 211         vector = 0, 0
 212         if x is not None or y is not None:
 213             if x is None or y is None:
 214                 raise TrafoException("either specify both x and y or none of them")
 215             vector=_rvector(angle, x, y)
 216
 217         trafo_pt.__init__(self, matrix=_rmatrix(angle), vector=vector, epsilon=epsilon)
 218
 219
 220 class rotate(trafo_pt):
 221     def __init__(self, angle, x=None, y=None, epsilon=_marker):
 222         vector = 0, 0
 223         if x is not None or y is not None:
 224             if x is None or y is None:
 225                 raise TrafoException("either specify both x and y or none of them")
 226             vector=_rvector(angle, unit.topt(x), unit.topt(y))
 227
 228         trafo_pt.__init__(self, matrix=_rmatrix(angle), vector=vector, epsilon=epsilon)
 229
 230
 231 class scale_pt(trafo_pt):
 232     def __init__(self, sx, sy=None, x=None, y=None, epsilon=_marker):
 233         if sy is None:
 234             sy = sx
 235         vector = 0, 0
 236         if x is not None or y is not None:
 237             if x is None or y is None:
 238                 raise TrafoException("either specify both x and y or none of them")
 239             vector = (1-sx)*x, (1-sy)*y
 240         trafo_pt.__init__(self, matrix=((sx, 0), (0, sy)), vector=vector, epsilon=epsilon)
 241
 242
 243 class scale(trafo):
 244     def __init__(self, sx, sy=None, x=None, y=None, epsilon=_marker):
 245         if sy is None:
 246             sy = sx
 247         vector = 0, 0
 248         if x is not None or y is not None:
 249             if x is None or y is None:
 250                 raise TrafoException("either specify both x and y or none of them")
 251             vector = (1-sx)*x, (1-sy)*y
 252         trafo.__init__(self, matrix=((sx, 0), (0, sy)), vector=vector, epsilon=epsilon)
 253
 254
 255 class slant_pt(trafo_pt):
 256     def __init__(self, a, angle=0, x=None, y=None, epsilon=_marker):
 257         t = ( rotate_pt(-angle, x, y, epsilon=epsilon) *
 258               trafo(matrix=((1, a), (0, 1)), epsilon=epsilon) *
 259               rotate_pt(angle, x, y, epsilon=epsilon) )
 260         trafo_pt.__init__(self, t.matrix, t.vector, epsilon=epsilon)
 261
 262
 263 class slant(trafo):
 264     def __init__(self, a, angle=0, x=None, y=None, epsilon=_marker):
 265         t = ( rotate(-angle, x, y, epsilon=epsilon) *
 266               trafo(matrix=((1, a), (0, 1)), epsilon=epsilon) *
 267               rotate(angle, x, y, epsilon=epsilon) )
 268         trafo.__init__(self, t.matrix, t.vector, epsilon=epsilon)
 269
 270
 271 class translate_pt(trafo_pt):
 272     def __init__(self, x, y, epsilon=_marker):
 273         trafo_pt.__init__(self, vector=(x, y), epsilon=epsilon)
 274
 275
 276 class translate(trafo):
 277     def __init__(self, x, y, epsilon=_marker):
 278         trafo.__init__(self, vector=(x, y), epsilon=epsilon)