pyx/trafo.py

   1 #!/usr/bin/env python
   2 # -*- coding: ISO-8859-1 -*-
   3 #
   4 #
   5 # Copyright (C) 2002-2004 Jörg Lehmann <joergl@users.sourceforge.net>
   6 # Copyright (C) 2002-2004 André Wobst <wobsta@users.sourceforge.net>
   7 #
   8 # This file is part of PyX (http://pyx.sourceforge.net/).
   9 #
  10 # PyX is free software; you can redistribute it and/or modify
  11 # it under the terms of the GNU General Public License as published by
  12 # the Free Software Foundation; either version 2 of the License, or
  13 # (at your option) any later version.
  14 #
  15 # PyX is distributed in the hope that it will be useful,
  16 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  17 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  18 # GNU General Public License for more details.
  19 #
  20 # You should have received a copy of the GNU General Public License
  21 # along with PyX; if not, write to the Free Software
  22 # Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA
  23
  24 import math
  25 import attr, canvas, deformer, unit
  26
  27 # some helper routines
  28
  29 def _rmatrix(angle):
  30     phi = math.pi*angle/180.0
  31
  32     return  ((math.cos(phi), -math.sin(phi)),
  33              (math.sin(phi),  math.cos(phi)))
  34
  35 def _rvector(angle, x, y):
  36     phi = math.pi*angle/180.0
  37
  38     return  ((1-math.cos(phi))*x + math.sin(phi)    *y,
  39               -math.sin(phi)   *x + (1-math.cos(phi))*y)
  40
  41
  42 def _mmatrix(angle):
  43     phi = math.pi*angle/180.0
  44
  45     return ( (math.cos(phi)*math.cos(phi)-math.sin(phi)*math.sin(phi),
  46               -2*math.sin(phi)*math.cos(phi)                ),
  47              (-2*math.sin(phi)*math.cos(phi),
  48               math.sin(phi)*math.sin(phi)-math.cos(phi)*math.cos(phi) ) )
  49
  50 def _det(matrix):
  51     return matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0]
  52
  53 # Exception
  54
  55 class UndefinedResultError(ArithmeticError):
  56     pass
  57
  58 # trafo: affine transformations
  59
  60 class trafo_pt(canvas.canvasitem, deformer.deformer):
  61
  62     """affine transformation (coordinates in constructor in pts)
  63
  64     Note that though the coordinates in the constructor are in
  65     pts (which is useful for internal purposes), all other
  66     methods only accept units in the standard user notation.
  67
  68     """
  69
  70     def __init__(self, matrix=((1,0),(0,1)), vector=(0,0)):
  71         if _det(matrix)==0:
  72             raise UndefinedResultError, "transformation matrix must not be singular"
  73         else:
  74             self.matrix=matrix
  75         self.vector = vector
  76
  77     def __mul__(self, other):
  78         if isinstance(other, trafo_pt):
  79             matrix = ( ( self.matrix[0][0]*other.matrix[0][0] +
  80                          self.matrix[0][1]*other.matrix[1][0],
  81                          self.matrix[0][0]*other.matrix[0][1] +
  82                          self.matrix[0][1]*other.matrix[1][1] ),
  83                        ( self.matrix[1][0]*other.matrix[0][0] +
  84                          self.matrix[1][1]*other.matrix[1][0],
  85                          self.matrix[1][0]*other.matrix[0][1] +
  86                          self.matrix[1][1]*other.matrix[1][1] )
  87                      )
  88
  89             vector = ( self.matrix[0][0]*other.vector[0] +
  90                        self.matrix[0][1]*other.vector[1] +
  91                        self.vector[0],
  92                        self.matrix[1][0]*other.vector[0] +
  93                        self.matrix[1][1]*other.vector[1] +
  94                        self.vector[1] )
  95
  96             return trafo_pt(matrix=matrix, vector=vector)
  97         else:
  98             raise NotImplementedError, "can only multiply two transformations"
  99
 100     def __str__(self):
 101         return "[%f %f %f %f %f %f]" % \
 102                ( self.matrix[0][0], self.matrix[1][0],
 103                  self.matrix[0][1], self.matrix[1][1],
 104                  self.vector[0], self.vector[1] )
 105
 106     def outputPS(self, file, writer, context):
 107         file.write("[%f %f %f %f %f %f] concat\n" % \
 108                     ( self.matrix[0][0], self.matrix[1][0],
 109                       self.matrix[0][1], self.matrix[1][1],
 110                       self.vector[0], self.vector[1] ) )
 111
 112     def outputPDF(self, file, writer, context):
 113         file.write("%f %f %f %f %f %f cm\n" % \
 114                     ( self.matrix[0][0], self.matrix[1][0],
 115                       self.matrix[0][1], self.matrix[1][1],
 116                       self.vector[0], self.vector[1] ) )
 117
 118     def bbox(self):
 119         return None
 120
 121     def _apply(self, x, y):
 122         """apply transformation to point (x,y) (coordinates in pts)"""
 123         return (self.matrix[0][0]*x +
 124                 self.matrix[0][1]*y +
 125                 self.vector[0],
 126                 self.matrix[1][0]*x +
 127                 self.matrix[1][1]*y +
 128                 self.vector[1])
 129
 130     def apply(self, x, y):
 131         # for the transformation we have to convert to points
 132         tx, ty = self._apply(unit.topt(x), unit.topt(y))
 133         return tx * unit.t_pt, ty * unit.t_pt
 134
 135     def deform(self, path):
 136         return path.transformed(self)
 137
 138     def inverse(self):
 139         det = _det(self.matrix)                       # shouldn't be zero, but
 140         try:
 141           matrix = ( ( self.matrix[1][1]/det, -self.matrix[0][1]/det),
 142                      (-self.matrix[1][0]/det,  self.matrix[0][0]/det)
 143                    )
 144         except ZeroDivisionError:
 145            raise UndefinedResultError, "transformation matrix must not be singular"
 146         return trafo_pt(matrix=matrix) * \
 147                trafo_pt(vector=(-self.vector[0], -self.vector[1]))
 148
 149     def mirrored(self, angle):
 150         return mirror(angle)*self
 151
 152     def rotated_pt(self, angle, x=None, y=None):
 153         return rotate_pt(angle, x, y)*self
 154
 155     def rotated(self, angle, x=None, y=None):
 156         return rotate(angle, x, y)*self
 157
 158     def scaled_pt(self, sx, sy=None, x=None, y=None):
 159         return scale_pt(sx, sy, x, y)*self
 160
 161     def scaled(self, sx, sy=None, x=None, y=None):
 162         return scale(sx, sy, x, y)*self
 163
 164     def slanted_pt(self, a, angle=0, x=None, y=None):
 165         return slant_pt(a, angle, x, y)*self
 166
 167     def slanted(self, a, angle=0, x=None, y=None):
 168         return slant(a, angle, x, y)*self
 169
 170     def translated_pt(self, x, y):
 171         return translate_pt(x,y)*self
 172
 173     def translated(self, x, y):
 174         return translate(x, y)*self
 175
 176
 177 class trafo(trafo_pt):
 178
 179     """affine transformation"""
 180
 181     def __init__(self, matrix=((1,0),(0,1)), vector=(0,0)):
 182         trafo_pt.__init__(self,
 183                         matrix,
 184                         (unit.topt(vector[0]), unit.topt(vector[1])))
 185
 186
 187 #
 188 # some standard transformations
 189 #
 190
 191 class mirror(trafo):
 192     def __init__(self,angle=0):
 193         trafo.__init__(self, matrix=_mmatrix(angle))
 194
 195
 196 class rotate_pt(trafo_pt):
 197     def __init__(self, angle, x=None, y=None):
 198         vector = 0, 0
 199         if x is not None or y is not None:
 200             if x is None or y is None:
 201                 raise (UndefinedResultError,
 202                        "either specify both x and y or none of them")
 203             vector=_rvector(angle, x, y)
 204
 205         trafo_pt.__init__(self,
 206                        matrix=_rmatrix(angle),
 207                        vector=vector)
 208
 209
 210 class rotate(trafo_pt):
 211     def __init__(self, angle, x=None, y=None):
 212         vector = 0, 0
 213         if x is not None or y is not None:
 214             if x is None or y is None:
 215                 raise (UndefinedResultError,
 216                        "either specify both x and y or none of them")
 217             vector=_rvector(angle, unit.topt(x), unit.topt(y))
 218
 219         trafo_pt.__init__(self,
 220                        matrix=_rmatrix(angle),
 221                        vector=vector)
 222
 223
 224 class scale_pt(trafo_pt):
 225     def __init__(self, sx, sy=None, x=None, y=None):
 226         sy = sy or sx
 227         if not sx or not sy:
 228             raise (UndefinedResultError,
 229                    "one scaling factor is 0")
 230         vector = 0, 0
 231         if x is not None or y is not None:
 232             if x is None or y is None:
 233                 raise (UndefinedResultError,
 234                        "either specify both x and y or none of them")
 235             vector = (1-sx)*x, (1-sy)*y
 236
 237         trafo_pt.__init__(self, matrix=((sx,0),(0,sy)), vector=vector)
 238
 239
 240 class scale(trafo):
 241     def __init__(self, sx, sy=None, x=None, y=None):
 242         sy = sy or sx
 243         if not sx or not sy:
 244             raise (UndefinedResultError,
 245                    "one scaling factor is 0")
 246         vector = 0, 0
 247         if x is not None or y is not None:
 248             if x is None or y is None:
 249                 raise (UndefinedResultError,
 250                        "either specify both x and y or none of them")
 251             vector = (1-sx)*x, (1-sy)*y
 252
 253         trafo.__init__(self, matrix=((sx,0),(0,sy)), vector=vector)
 254
 255
 256 class slant_pt(trafo_pt):
 257     def __init__(self, a, angle=0, x=None, y=None):
 258         t = ( rotate_pt(-angle, x, y)*
 259               trafo(matrix=((1, a), (0, 1)))*
 260               rotate_pt(angle, x, y) )
 261         trafo_pt.__init__(self, t.matrix, t.vector)
 262
 263
 264 class slant(trafo):
 265     def __init__(self, a, angle=0, x=None, y=None):
 266         t = ( rotate(-angle, x, y)*
 267               trafo(matrix=((1, a), (0, 1)))*
 268               rotate(angle, x, y) )
 269         trafo.__init__(self, t.matrix, t.vector)
 270
 271
 272 class translate_pt(trafo_pt):
 273     def __init__(self, x, y):
 274         trafo_pt.__init__(self, vector=(x, y))
 275
 276
 277 class translate(trafo):
 278     def __init__(self, x, y):
 279         trafo.__init__(self, vector=(x, y))