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 math
  24 import base, bbox, 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 def _det(matrix):
  50     return matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0]
  51
  52 # Exception
  53
  54 class UndefinedResultError(ArithmeticError):
  55     pass
  56
  57 # trafo: affine transformations
  58
  59 class _trafo(base.PSOp):
  60
  61     """affine transformation (coordinates in constructor in pts)
  62
  63     Note that though the coordinates in the constructor are in
  64     pts (which is useful for internal purposes), all other
  65     methods only accept units in the standard user notation.
  66
  67     """
  68
  69     def __init__(self, matrix=((1,0),(0,1)), vector=(0,0)):
  70         if _det(matrix)==0:
  71             raise UndefinedResultError, "transformation matrix must not be singular"
  72         else:
  73             self.matrix=matrix
  74         self.vector = vector
  75
  76     def __mul__(self, other):
  77         if isinstance(other, _trafo):
  78             matrix = ( ( self.matrix[0][0]*other.matrix[0][0] +
  79                          self.matrix[0][1]*other.matrix[1][0],
  80                          self.matrix[0][0]*other.matrix[0][1] +
  81                          self.matrix[0][1]*other.matrix[1][1] ),
  82                        ( self.matrix[1][0]*other.matrix[0][0] +
  83                          self.matrix[1][1]*other.matrix[1][0],
  84                          self.matrix[1][0]*other.matrix[0][1] +
  85                          self.matrix[1][1]*other.matrix[1][1] )
  86                      )
  87
  88             vector = ( self.matrix[0][0]*other.vector[0] +
  89                        self.matrix[0][1]*other.vector[1] +
  90                        self.vector[0],
  91                        self.matrix[1][0]*other.vector[0] +
  92                        self.matrix[1][1]*other.vector[1] +
  93                        self.vector[1] )
  94
  95             return _trafo(matrix=matrix, vector=vector)
  96         else:
  97             raise NotImplementedError, "can only multiply two transformations"
  98
  99     def __str__(self):
 100         return "[%f %f %f %f %f %f]" % \
 101                ( self.matrix[0][0], self.matrix[1][0],
 102                  self.matrix[0][1], self.matrix[1][1],
 103                  self.vector[0], self.vector[1] )
 104
 105     def write(self, file):
 106         file.write("[%f %f %f %f %f %f] concat\n" % \
 107                     ( self.matrix[0][0], self.matrix[1][0],
 108                       self.matrix[0][1], self.matrix[1][1],
 109                       self.vector[0], self.vector[1] ) )
 110
 111     def bbox(self):
 112         return bbox.bbox()
 113
 114     def _apply(self, x, y):
 115         """apply transformation to point (x,y) (coordinates in pts)"""
 116         return (self.matrix[0][0]*x +
 117                 self.matrix[0][1]*y +
 118                 self.vector[0],
 119                 self.matrix[1][0]*x +
 120                 self.matrix[1][1]*y +
 121                 self.vector[1])
 122
 123     def apply(self, x, y):
 124         # before the transformation, we first have to convert to
 125         # our internal unit (i.e. pts)
 126         tx, ty = self._apply(unit.topt(x), unit.topt(y))
 127
 128         # the end result can be converted back to general lengths
 129         return (unit.t_pt(tx), unit.t_pt(ty))
 130
 131     def inverse(self):
 132         det = _det(self.matrix)                       # shouldn't be zero, but
 133         try:
 134           matrix = ( ( self.matrix[1][1]/det, -self.matrix[0][1]/det),
 135                      (-self.matrix[1][0]/det,  self.matrix[0][0]/det)
 136                    )
 137         except ZeroDivisionError:
 138            raise UndefinedResultError, "transformation matrix must not be singular"
 139         return _trafo(matrix=matrix) * \
 140                _trafo(vector=(-self.vector[0], -self.vector[1]))
 141
 142     def mirrored(self, angle):
 143         return mirror(angle)*self
 144
 145     def _rotated(self, angle, x=None, y=None):
 146         return _rotate(angle, x, y)*self
 147
 148     def rotated(self, angle, x=None, y=None):
 149         return rotate(angle, x, y)*self
 150
 151     def _scaled(self, sx, sy=None, x=None, y=None):
 152         return _scale(sx, sy, x, y)*self
 153
 154     def scaled(self, sx, sy=None, x=None, y=None):
 155         return scale(sx, sy, x, y)*self
 156
 157     def _slanted(self, a, angle=0, x=None, y=None):
 158         return _slanted(a, angle, x, y)*self
 159
 160     def slanted(self, a, angle=0, x=None, y=None):
 161         return slanted(a, angle, x, y)*self
 162
 163     def _translated(self, x, y):
 164         return _translate(x,y)*self
 165
 166     def translated(self, x, y):
 167         return translate(x, y)*self
 168
 169
 170 class trafo(_trafo):
 171
 172     """affine transformation"""
 173
 174     def __init__(self, matrix=((1,0),(0,1)), vector=(0,0)):
 175         _trafo.__init__(self,
 176                         matrix,
 177                         (unit.topt(vector[0]), unit.topt(vector[1])))
 178
 179
 180 #
 181 # some standard transformations
 182 #
 183
 184 class mirror(trafo):
 185     def __init__(self,angle=0):
 186         trafo.__init__(self, matrix=_mmatrix(angle))
 187
 188
 189 class _rotate(_trafo):
 190     def __init__(self, angle, x=None, y=None):
 191         vector = 0, 0
 192         if x is not None or y is not None:
 193             if x is None or y is None:
 194                 raise (UndefinedResultError,
 195                        "either specify both x and y or none of them")
 196             vector=_rvector(angle, x, y)
 197
 198         _trafo.__init__(self,
 199                        matrix=_rmatrix(angle),
 200                        vector=vector)
 201
 202
 203 class rotate(_trafo):
 204     def __init__(self, angle, x=None, y=None):
 205         vector = 0, 0
 206         if x is not None or y is not None:
 207             if x is None or y is None:
 208                 raise (UndefinedResultError,
 209                        "either specify both x and y or none of them")
 210             vector=_rvector(angle, unit.topt(x), unit.topt(y))
 211
 212         _trafo.__init__(self,
 213                        matrix=_rmatrix(angle),
 214                        vector=vector)
 215
 216
 217 class _scale(_trafo):
 218     def __init__(self, sx, sy=None, x=None, y=None):
 219         sy = sy or sx
 220         if not sx or not sy:
 221             raise (UndefinedResultError,
 222                    "one scaling factor is 0")
 223         vector = 0, 0
 224         if x is not None or y is not None:
 225             if x is None or y is None:
 226                 raise (UndefinedResultError,
 227                        "either specify both x and y or none of them")
 228             vector = (1-sx)*x, (1-sy)*y
 229
 230         _trafo.__init__(self, matrix=((sx,0),(0,sy)), vector=vector)
 231
 232
 233 class scale(trafo):
 234     def __init__(self, sx, sy=None, x=None, y=None):
 235         sy = sy or sx
 236         if not sx or not sy:
 237             raise (UndefinedResultError,
 238                    "one scaling factor is 0")
 239         vector = 0, 0
 240         if x is not None or y is not None:
 241             if x is None or y is None:
 242                 raise (UndefinedResultError,
 243                        "either specify both x and y or none of them")
 244             vector = (1-sx)*x, (1-sy)*y
 245
 246         trafo.__init__(self, matrix=((sx,0),(0,sy)), vector=vector)
 247
 248
 249 class _slant(_trafo):
 250     def __init__(self, a, angle=0, x=None, y=None):
 251         t = ( _rotate(-angle, x, y)*
 252               trafo(matrix=((1, a), (0, 1)))*
 253               _rotate(angle, x, y) )
 254         _trafo.__init__(self, t.matrix, t.vector)
 255
 256
 257 class slant(trafo):
 258     def __init__(self, a, angle=0, x=None, y=None):
 259         t = ( rotate(-angle, x, y)*
 260               trafo(matrix=((1, a), (0, 1)))*
 261               rotate(angle, x, y) )
 262         trafo.__init__(self, t.matrix, t.vector)
 263
 264
 265 class _translate(_trafo):
 266     def __init__(self, x, y):
 267         _trafo.__init__(self, vector=(x, y))
 268
 269
 270 class translate(trafo):
 271     def __init__(self, x, y):
 272         trafo.__init__(self, vector=(x, y))