pyx/graph/graph.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) 2003-2004 Michael Schindler <m-schindler@users.sourceforge.net>
   7 # Copyright (C) 2002-2004 André Wobst <wobsta@users.sourceforge.net>
   8 #
   9 # This file is part of PyX (http://pyx.sourceforge.net/).
  10 #
  11 # PyX is free software; you can redistribute it and/or modify
  12 # it under the terms of the GNU General Public License as published by
  13 # the Free Software Foundation; either version 2 of the License, or
  14 # (at your option) any later version.
  15 #
  16 # PyX is distributed in the hope that it will be useful,
  17 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  18 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  19 # GNU General Public License for more details.
  20 #
  21 # You should have received a copy of the GNU General Public License
  22 # along with PyX; if not, write to the Free Software
  23 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  24
  25
  26 import math, re, string
  27 from pyx import canvas, path, trafo, unit
  28 from pyx.graph.axis import painter, axis
  29
  30
  31 goldenmean = 0.5 * (math.sqrt(5) + 1)
  32
  33
  34 class lineaxispos:
  35     """an axispos linear along a line with a fix direction for the ticks"""
  36
  37     def __init__(self, convert, x1, y1, x2, y2, fixtickdirection):
  38         """initializes the instance
  39         - only the convert method is needed from the axis
  40         - x1, y1, x2, y2 are PyX lengths (start and end position of the line)
  41         - fixtickdirection is a tuple tick direction (fixed along the line)"""
  42         self.convert = convert
  43         self.x1 = x1
  44         self.y1 = y1
  45         self.x2 = x2
  46         self.y2 = y2
  47         self.x1_pt = unit.topt(x1)
  48         self.y1_pt = unit.topt(y1)
  49         self.x2_pt = unit.topt(x2)
  50         self.y2_pt = unit.topt(y2)
  51         self.fixtickdirection = fixtickdirection
  52
  53     def vbasepath(self, v1=None, v2=None):
  54         if v1 is None:
  55             v1 = 0
  56         if v2 is None:
  57             v2 = 1
  58         return path.line_pt((1-v1)*self.x1_pt+v1*self.x2_pt,
  59                             (1-v1)*self.y1_pt+v1*self.y2_pt,
  60                             (1-v2)*self.x1_pt+v2*self.x2_pt,
  61                             (1-v2)*self.y1_pt+v2*self.y2_pt)
  62
  63     def basepath(self, x1=None, x2=None):
  64         if x1 is None:
  65             v1 = 0
  66         else:
  67             v1 = self.convert(x1)
  68         if x2 is None:
  69             v2 = 1
  70         else:
  71             v2 = self.convert(x2)
  72         return path.line_pt((1-v1)*self.x1_pt+v1*self.x2_pt,
  73                             (1-v1)*self.y1_pt+v1*self.y2_pt,
  74                             (1-v2)*self.x1_pt+v2*self.x2_pt,
  75                             (1-v2)*self.y1_pt+v2*self.y2_pt)
  76
  77     def gridpath(self, x):
  78         raise RuntimeError("gridpath not available")
  79
  80     def vgridpath(self, v):
  81         raise RuntimeError("gridpath not available")
  82
  83     def vtickpoint_pt(self, v):
  84         return (1-v)*self.x1_pt+v*self.x2_pt, (1-v)*self.y1_pt+v*self.y2_pt
  85
  86     def vtickpoint(self, v):
  87         return (1-v)*self.x1+v*self.x2, (1-v)*self.y1+v*self.y2
  88
  89     def tickpoint_pt(self, x):
  90         v = self.convert(x)
  91         return (1-v)*self.x1_pt+v*self.x2_pt, (1-v)*self.y1_pt+v*self.y2_pt
  92
  93     def tickpoint(self, x):
  94         v = self.convert(x)
  95         return (1-v)*self.x1+v*self.x2, (1-v)*self.y1+v*self.y2
  96
  97     def tickdirection(self, x):
  98         return self.fixtickdirection
  99
 100     def vtickdirection(self, v):
 101         return self.fixtickdirection
 102
 103
 104 class lineaxisposlinegrid(lineaxispos):
 105     """an axispos linear along a line with a fix direction for the ticks
 106     with support for grid lines for a rectangular graphs"""
 107
 108     __implements__ = painter._Iaxispos
 109
 110     def __init__(self, convert, x1, y1, x2, y2, fixtickdirection, startgridlength, endgridlength):
 111         """initializes the instance
 112         - only the convert method is needed from the axis
 113         - x1, y1, x2, y2 are PyX lengths (start and end position of the line)
 114         - fixtickdirection is a tuple tick direction (fixed along the line)
 115         - startgridlength and endgridlength are PyX lengths for the starting
 116           and end point of the grid, respectively; the gridpath is a line along
 117           the fixtickdirection"""
 118         lineaxispos.__init__(self, convert, x1, y1, x2, y2, fixtickdirection)
 119         self.startgridlength = startgridlength
 120         self.endgridlength = endgridlength
 121         self.startgridlength_pt = unit.topt(self.startgridlength)
 122         self.endgridlength_pt = unit.topt(self.endgridlength)
 123
 124     def gridpath(self, x):
 125         v = self.convert(x)
 126         return path.line_pt((1-v)*self.x1_pt+v*self.x2_pt+self.fixtickdirection[0]*self.startgridlength_pt,
 127                           (1-v)*self.y1_pt+v*self.y2_pt+self.fixtickdirection[1]*self.startgridlength_pt,
 128                           (1-v)*self.x1_pt+v*self.x2_pt+self.fixtickdirection[0]*self.endgridlength_pt,
 129                           (1-v)*self.y1_pt+v*self.y2_pt+self.fixtickdirection[1]*self.endgridlength_pt)
 130
 131     def vgridpath(self, v):
 132         return path.line_pt((1-v)*self.x1_pt+v*self.x2_pt+self.fixtickdirection[0]*self.startgridlength_pt,
 133                           (1-v)*self.y1_pt+v*self.y2_pt+self.fixtickdirection[1]*self.startgridlength_pt,
 134                           (1-v)*self.x1_pt+v*self.x2_pt+self.fixtickdirection[0]*self.endgridlength_pt,
 135                           (1-v)*self.y1_pt+v*self.y2_pt+self.fixtickdirection[1]*self.endgridlength_pt)
 136
 137
 138 class graphxy(canvas.canvas):
 139
 140     axisnames = "x", "y"
 141
 142     def plot(self, data, styles=None):
 143         if self.haslayout:
 144             raise RuntimeError("layout setup was already performed")
 145         try:
 146             for d in data:
 147                 pass
 148         except:
 149             usedata = [data]
 150         else:
 151             usedata = data
 152         if styles is None:
 153             raise RuntimeError() # TODO: default styles handling ...
 154             for d in usedata:
 155                 if style is None:
 156                     style = d.defaultstyle
 157                 elif style != d.defaultstyle:
 158                     raise RuntimeError("defaultstyles differ")
 159         for d in usedata:
 160             d.setstyles(self, styles)
 161             self.plotdata.append(d)
 162         return data
 163
 164     def pos_pt(self, x, y, xaxis=None, yaxis=None):
 165         if xaxis is None:
 166             xaxis = self.axes["x"]
 167         if yaxis is None:
 168             yaxis = self.axes["y"]
 169         return self.xpos_pt + xaxis.convert(x)*self.width_pt, self.ypos_pt + yaxis.convert(y)*self.height_pt
 170
 171     def pos(self, x, y, xaxis=None, yaxis=None):
 172         if xaxis is None:
 173             xaxis = self.axes["x"]
 174         if yaxis is None:
 175             yaxis = self.axes["y"]
 176         return self.xpos + xaxis.convert(x)*self.width, self.ypos + yaxis.convert(y)*self.height
 177
 178     def vpos_pt(self, vx, vy):
 179         return self.xpos_pt + vx*self.width_pt, self.ypos_pt + vy*self.height_pt
 180
 181     def vpos(self, vx, vy):
 182         return self.xpos + vx*self.width, self.ypos + vy*self.height
 183
 184     def vgeodesic(self, vx1, vy1, vx2, vy2):
 185         """returns a geodesic path between two points in graph coordinates"""
 186         return path.line_pt(self.xpos_pt + vx1*self.width_pt,
 187                             self.ypos_pt + vy1*self.height_pt,
 188                             self.xpos_pt + vx2*self.width_pt,
 189                             self.ypos_pt + vy2*self.height_pt)
 190
 191     def vgeodesic_el(self, vx1, vy1, vx2, vy2):
 192         """returns a geodesic path element between two points in graph coordinates"""
 193         return path.lineto_pt(self.xpos_pt + vx2*self.width_pt,
 194                               self.ypos_pt + vy2*self.height_pt)
 195
 196     def vcap_pt(self, direction, length_pt, vx, vy):
 197         """returns an error cap path for a given direction, lengths and
 198         point in graph coordinates"""
 199         if direction == "x":
 200             return path.line_pt(self.xpos_pt + vx*self.width_pt - 0.5*length_pt,
 201                                 self.ypos_pt + vy*self.height_pt,
 202                                 self.xpos_pt + vx*self.width_pt + 0.5*length_pt,
 203                                 self.ypos_pt + vy*self.height_pt)
 204         elif direction == "y":
 205             return path.line_pt(self.xpos_pt + vx*self.width_pt,
 206                                 self.ypos_pt + vy*self.height_pt - 0.5*length_pt,
 207                                 self.xpos_pt + vx*self.width_pt,
 208                                 self.ypos_pt + vy*self.height_pt + 0.5*length_pt)
 209         else:
 210             raise ValueError("direction invalid")
 211
 212     def keynum(self, key):
 213         try:
 214             while key[0] in string.letters:
 215                 key = key[1:]
 216             return int(key)
 217         except IndexError:
 218             return 1
 219
 220     def removedomethod(self, method):
 221         hadmethod = 0
 222         while 1:
 223             try:
 224                 self.domethods.remove(method)
 225                 hadmethod = 1
 226             except ValueError:
 227                 return hadmethod
 228
 229     def dolayout(self):
 230         if not self.removedomethod(self.dolayout): return
 231
 232         # count the usage of styles and perform selects
 233         # TODO: move it into the styles
 234         styletotal = {}
 235         for data in self.plotdata:
 236             for style in data.styles:
 237                 try:
 238                     styletotal[id(style)] += 1
 239                 except:
 240                     styletotal[id(style)] = 1
 241         styleindex = {}
 242         for data in self.plotdata:
 243             for style in data.styles:
 244                 try:
 245                     styleindex[id(style)] += 1
 246                 except:
 247                     styleindex[id(style)] = 0
 248             index = styleindex[id(data.styles[0])]
 249             total = styletotal[id(data.styles[0])]
 250             for style in data.styles[1:]:
 251                 if index != styleindex[id(style)] or total != styletotal[id(style)]:
 252                     raise RuntimeError("inconsistent style modification not yet supported")
 253             data.selectstyle(self, index, total)
 254
 255         # adjust the axes ranges
 256         for step in range(3):
 257             for data in self.plotdata:
 258                 data.adjustaxes(self, step)
 259
 260         # finish all axes
 261         XPattern = re.compile(r"%s([2-9]|[1-9][0-9]+)?$" % self.axisnames[0])
 262         YPattern = re.compile(r"%s([2-9]|[1-9][0-9]+)?$" % self.axisnames[1])
 263         xaxisextents = [0, 0]
 264         yaxisextents = [0, 0]
 265         needxaxisdist = [0, 0]
 266         needyaxisdist = [0, 0]
 267         items = list(self.axes.items())
 268         items.sort() #TODO: alphabetical sorting breaks for axis numbers bigger than 9
 269         # TODO: linked axes are not taken into account (consider x being a link to x2)
 270         for key, axis in items:
 271             num = self.keynum(key)
 272             num2 = 1 - num % 2 # x1 -> 0, x2 -> 1, x3 -> 0, x4 -> 1, ...
 273             num3 = 2 * (num % 2) - 1 # x1 -> 1, x2 -> -1, x3 -> 1, x4 -> -1, ...
 274             if XPattern.match(key):
 275                 if needxaxisdist[num2]:
 276                     xaxisextents[num2] += self.axesdist
 277                 self.axespos[key] = lineaxisposlinegrid(self.axes[key].convert,
 278                                                         self.xpos,
 279                                                         self.ypos + num2*self.height - num3*xaxisextents[num2],
 280                                                         self.xpos + self.width,
 281                                                         self.ypos + num2*self.height - num3*xaxisextents[num2],
 282                                                         (0, num3),
 283                                                         xaxisextents[num2], xaxisextents[num2] + self.height)
 284                 if num == 1:
 285                     self.xbasepath = self.axespos[key].basepath
 286                     self.xvbasepath = self.axespos[key].vbasepath
 287                     self.xgridpath = self.axespos[key].gridpath
 288                     self.xvgridpath = self.axespos[key].vgridpath
 289                     self.xtickpoint_pt = self.axespos[key].tickpoint_pt
 290                     self.xtickpoint = self.axespos[key].tickpoint
 291                     self.xvtickpoint_pt = self.axespos[key].vtickpoint_pt
 292                     self.xvtickpoint = self.axespos[key].tickpoint
 293                     self.xtickdirection = self.axespos[key].tickdirection
 294                     self.xvtickdirection = self.axespos[key].vtickdirection
 295             elif YPattern.match(key):
 296                 if needyaxisdist[num2]:
 297                     yaxisextents[num2] += self.axesdist
 298                 self.axespos[key] = lineaxisposlinegrid(self.axes[key].convert,
 299                                                         self.xpos + num2*self.width - num3*yaxisextents[num2],
 300                                                         self.ypos,
 301                                                         self.xpos + num2*self.width - num3*yaxisextents[num2],
 302                                                         self.ypos + self.height,
 303                                                         (num3, 0),
 304                                                         yaxisextents[num2], yaxisextents[num2] + self.width)
 305                 if num == 1:
 306                     self.ybasepath = self.axespos[key].basepath
 307                     self.yvbasepath = self.axespos[key].vbasepath
 308                     self.ygridpath = self.axespos[key].gridpath
 309                     self.yvgridpath = self.axespos[key].vgridpath
 310                     self.ytickpoint_pt = self.axespos[key].tickpoint_pt
 311                     self.ytickpoint = self.axespos[key].tickpoint
 312                     self.yvtickpoint_pt = self.axespos[key].vtickpoint_pt
 313                     self.yvtickpoint = self.axespos[key].tickpoint
 314                     self.ytickdirection = self.axespos[key].tickdirection
 315                     self.yvtickdirection = self.axespos[key].vtickdirection
 316             else:
 317                 raise ValueError("Axis key '%s' not allowed" % key)
 318             axis.finish(self.axespos[key])
 319             if XPattern.match(key):
 320                 xaxisextents[num2] += axis.axiscanvas.extent
 321                 needxaxisdist[num2] = 1
 322             if YPattern.match(key):
 323                 yaxisextents[num2] += axis.axiscanvas.extent
 324                 needyaxisdist[num2] = 1
 325         self.haslayout = 1
 326
 327     def dobackground(self):
 328         self.dolayout()
 329         if not self.removedomethod(self.dobackground): return
 330         if self.backgroundattrs is not None:
 331             self.draw(path.rect_pt(self.xpos_pt, self.ypos_pt, self.width_pt, self.height_pt),
 332                       self.backgroundattrs)
 333
 334     def doaxes(self):
 335         self.dolayout()
 336         if not self.removedomethod(self.doaxes): return
 337         for axis in self.axes.values():
 338             self.insert(axis.axiscanvas)
 339
 340     def dodata(self):
 341         self.dolayout()
 342         if not self.removedomethod(self.dodata): return
 343         for data in self.plotdata:
 344             data.draw(self)
 345
 346     def dokey(self):
 347         self.dolayout()
 348         if not self.removedomethod(self.dokey): return
 349         if self.key is not None:
 350             c = self.key.paint(self.plotdata)
 351             bbox = c.bbox()
 352             def parentchildalign(pmin, pmax, cmin, cmax, pos, dist, inside):
 353                 ppos = pmin+0.5*(cmax-cmin)+dist+pos*(pmax-pmin-cmax+cmin-2*dist)
 354                 cpos = 0.5*(cmin+cmax)+(1-inside)*(1-2*pos)*(cmax-cmin+2*dist)
 355                 return ppos-cpos
 356             x = parentchildalign(self.xpos_pt, self.xpos_pt+self.width_pt,
 357                                  bbox.llx_pt, bbox.urx_pt,
 358                                  self.key.hpos, unit.topt(self.key.hdist), self.key.hinside)
 359             y = parentchildalign(self.ypos_pt, self.ypos_pt+self.height_pt,
 360                                  bbox.lly_pt, bbox.ury_pt,
 361                                  self.key.vpos, unit.topt(self.key.vdist), self.key.vinside)
 362             self.insert(c, [trafo.translate_pt(x, y)])
 363
 364     def finish(self):
 365         while len(self.domethods):
 366             self.domethods[0]()
 367
 368     def initwidthheight(self, width, height, ratio):
 369         if (width is not None) and (height is None):
 370              self.width = width
 371              self.height = (1.0/ratio) * self.width
 372         elif (height is not None) and (width is None):
 373              self.height = height
 374              self.width = ratio * self.height
 375         else:
 376              self.width = width
 377              self.height = height
 378         self.width_pt = unit.topt(self.width)
 379         self.height_pt = unit.topt(self.height)
 380         if self.width_pt <= 0: raise ValueError("width <= 0")
 381         if self.height_pt <= 0: raise ValueError("height <= 0")
 382
 383     def initaxes(self, axes, addlinkaxes=0):
 384         for key in self.axisnames:
 385             if not axes.has_key(key):
 386                 axes[key] = axis.linear()
 387             elif axes[key] is None:
 388                 del axes[key]
 389             if addlinkaxes:
 390                 if not axes.has_key(key + "2") and axes.has_key(key):
 391                     axes[key + "2"] = axes[key].createlinkaxis()
 392                 elif axes[key + "2"] is None:
 393                     del axes[key + "2"]
 394         self.axes = axes
 395
 396     def __init__(self, xpos=0, ypos=0, width=None, height=None, ratio=goldenmean,
 397                  key=None, backgroundattrs=None, axesdist=0.8*unit.v_cm, **axes):
 398         canvas.canvas.__init__(self)
 399         self.xpos = xpos
 400         self.ypos = ypos
 401         self.xpos_pt = unit.topt(self.xpos)
 402         self.ypos_pt = unit.topt(self.ypos)
 403         self.initwidthheight(width, height, ratio)
 404         self.initaxes(axes, 1)
 405         self.axescanvas = {}
 406         self.axespos = {}
 407         self.key = key
 408         self.backgroundattrs = backgroundattrs
 409         self.axesdist = axesdist
 410         self.plotdata = []
 411         self.domethods = [self.dolayout, self.dobackground, self.doaxes, self.dodata, self.dokey]
 412         self.haslayout = 0
 413         self.addkeys = []
 414
 415     def bbox(self):
 416         self.finish()
 417         return canvas.canvas.bbox(self)
 418
 419     def outputPS(self, file):
 420         self.finish()
 421         canvas.canvas.outputPS(self, file)
 422
 423
 424
 425 # some thoughts, but deferred right now
 426 #
 427 # class graphxyz(graphxy):
 428 #
 429 #     axisnames = "x", "y", "z"
 430 #
 431 #     def _vxtickpoint(self, axis, v):
 432 #         return self._vpos(v, axis.vypos, axis.vzpos)
 433 #
 434 #     def _vytickpoint(self, axis, v):
 435 #         return self._vpos(axis.vxpos, v, axis.vzpos)
 436 #
 437 #     def _vztickpoint(self, axis, v):
 438 #         return self._vpos(axis.vxpos, axis.vypos, v)
 439 #
 440 #     def vxtickdirection(self, axis, v):
 441 #         x1, y1 = self._vpos(v, axis.vypos, axis.vzpos)
 442 #         x2, y2 = self._vpos(v, 0.5, 0)
 443 #         dx, dy = x1 - x2, y1 - y2
 444 #         norm = math.hypot(dx, dy)
 445 #         return dx/norm, dy/norm
 446 #
 447 #     def vytickdirection(self, axis, v):
 448 #         x1, y1 = self._vpos(axis.vxpos, v, axis.vzpos)
 449 #         x2, y2 = self._vpos(0.5, v, 0)
 450 #         dx, dy = x1 - x2, y1 - y2
 451 #         norm = math.hypot(dx, dy)
 452 #         return dx/norm, dy/norm
 453 #
 454 #     def vztickdirection(self, axis, v):
 455 #         return -1, 0
 456 #         x1, y1 = self._vpos(axis.vxpos, axis.vypos, v)
 457 #         x2, y2 = self._vpos(0.5, 0.5, v)
 458 #         dx, dy = x1 - x2, y1 - y2
 459 #         norm = math.hypot(dx, dy)
 460 #         return dx/norm, dy/norm
 461 #
 462 #     def _pos(self, x, y, z, xaxis=None, yaxis=None, zaxis=None):
 463 #         if xaxis is None: xaxis = self.axes["x"]
 464 #         if yaxis is None: yaxis = self.axes["y"]
 465 #         if zaxis is None: zaxis = self.axes["z"]
 466 #         return self._vpos(xaxis.convert(x), yaxis.convert(y), zaxis.convert(z))
 467 #
 468 #     def pos(self, x, y, z, xaxis=None, yaxis=None, zaxis=None):
 469 #         if xaxis is None: xaxis = self.axes["x"]
 470 #         if yaxis is None: yaxis = self.axes["y"]
 471 #         if zaxis is None: zaxis = self.axes["z"]
 472 #         return self.vpos(xaxis.convert(x), yaxis.convert(y), zaxis.convert(z))
 473 #
 474 #     def _vpos(self, vx, vy, vz):
 475 #         x, y, z = (vx - 0.5)*self._depth, (vy - 0.5)*self._width, (vz - 0.5)*self._height
 476 #         d0 = float(self.a[0]*self.b[1]*(z-self.eye[2])
 477 #                  + self.a[2]*self.b[0]*(y-self.eye[1])
 478 #                  + self.a[1]*self.b[2]*(x-self.eye[0])
 479 #                  - self.a[2]*self.b[1]*(x-self.eye[0])
 480 #                  - self.a[0]*self.b[2]*(y-self.eye[1])
 481 #                  - self.a[1]*self.b[0]*(z-self.eye[2]))
 482 #         da = (self.eye[0]*self.b[1]*(z-self.eye[2])
 483 #             + self.eye[2]*self.b[0]*(y-self.eye[1])
 484 #             + self.eye[1]*self.b[2]*(x-self.eye[0])
 485 #             - self.eye[2]*self.b[1]*(x-self.eye[0])
 486 #             - self.eye[0]*self.b[2]*(y-self.eye[1])
 487 #             - self.eye[1]*self.b[0]*(z-self.eye[2]))
 488 #         db = (self.a[0]*self.eye[1]*(z-self.eye[2])
 489 #             + self.a[2]*self.eye[0]*(y-self.eye[1])
 490 #             + self.a[1]*self.eye[2]*(x-self.eye[0])
 491 #             - self.a[2]*self.eye[1]*(x-self.eye[0])
 492 #             - self.a[0]*self.eye[2]*(y-self.eye[1])
 493 #             - self.a[1]*self.eye[0]*(z-self.eye[2]))
 494 #         return da/d0 + self._xpos, db/d0 + self._ypos
 495 #
 496 #     def vpos(self, vx, vy, vz):
 497 #         tx, ty = self._vpos(vx, vy, vz)
 498 #         return unit.t_pt(tx), unit.t_pt(ty)
 499 #
 500 #     def xbaseline(self, axis, x1, x2, xaxis=None):
 501 #         if xaxis is None: xaxis = self.axes["x"]
 502 #         return self.vxbaseline(axis, xaxis.convert(x1), xaxis.convert(x2))
 503 #
 504 #     def ybaseline(self, axis, y1, y2, yaxis=None):
 505 #         if yaxis is None: yaxis = self.axes["y"]
 506 #         return self.vybaseline(axis, yaxis.convert(y1), yaxis.convert(y2))
 507 #
 508 #     def zbaseline(self, axis, z1, z2, zaxis=None):
 509 #         if zaxis is None: zaxis = self.axes["z"]
 510 #         return self.vzbaseline(axis, zaxis.convert(z1), zaxis.convert(z2))
 511 #
 512 #     def vxbaseline(self, axis, v1, v2):
 513 #         return (path._line(*(self._vpos(v1, 0, 0) + self._vpos(v2, 0, 0))) +
 514 #                 path._line(*(self._vpos(v1, 0, 1) + self._vpos(v2, 0, 1))) +
 515 #                 path._line(*(self._vpos(v1, 1, 1) + self._vpos(v2, 1, 1))) +
 516 #                 path._line(*(self._vpos(v1, 1, 0) + self._vpos(v2, 1, 0))))
 517 #
 518 #     def vybaseline(self, axis, v1, v2):
 519 #         return (path._line(*(self._vpos(0, v1, 0) + self._vpos(0, v2, 0))) +
 520 #                 path._line(*(self._vpos(0, v1, 1) + self._vpos(0, v2, 1))) +
 521 #                 path._line(*(self._vpos(1, v1, 1) + self._vpos(1, v2, 1))) +
 522 #                 path._line(*(self._vpos(1, v1, 0) + self._vpos(1, v2, 0))))
 523 #
 524 #     def vzbaseline(self, axis, v1, v2):
 525 #         return (path._line(*(self._vpos(0, 0, v1) + self._vpos(0, 0, v2))) +
 526 #                 path._line(*(self._vpos(0, 1, v1) + self._vpos(0, 1, v2))) +
 527 #                 path._line(*(self._vpos(1, 1, v1) + self._vpos(1, 1, v2))) +
 528 #                 path._line(*(self._vpos(1, 0, v1) + self._vpos(1, 0, v2))))
 529 #
 530 #     def xgridpath(self, x, xaxis=None):
 531 #         assert 0
 532 #         if xaxis is None: xaxis = self.axes["x"]
 533 #         v = xaxis.convert(x)
 534 #         return path._line(self._xpos+v*self._width, self._ypos,
 535 #                           self._xpos+v*self._width, self._ypos+self._height)
 536 #
 537 #     def ygridpath(self, y, yaxis=None):
 538 #         assert 0
 539 #         if yaxis is None: yaxis = self.axes["y"]
 540 #         v = yaxis.convert(y)
 541 #         return path._line(self._xpos, self._ypos+v*self._height,
 542 #                           self._xpos+self._width, self._ypos+v*self._height)
 543 #
 544 #     def zgridpath(self, z, zaxis=None):
 545 #         assert 0
 546 #         if zaxis is None: zaxis = self.axes["z"]
 547 #         v = zaxis.convert(z)
 548 #         return path._line(self._xpos, self._zpos+v*self._height,
 549 #                           self._xpos+self._width, self._zpos+v*self._height)
 550 #
 551 #     def vxgridpath(self, v):
 552 #         return path.path(path._moveto(*self._vpos(v, 0, 0)),
 553 #                          path._lineto(*self._vpos(v, 0, 1)),
 554 #                          path._lineto(*self._vpos(v, 1, 1)),
 555 #                          path._lineto(*self._vpos(v, 1, 0)),
 556 #                          path.closepath())
 557 #
 558 #     def vygridpath(self, v):
 559 #         return path.path(path._moveto(*self._vpos(0, v, 0)),
 560 #                          path._lineto(*self._vpos(0, v, 1)),
 561 #                          path._lineto(*self._vpos(1, v, 1)),
 562 #                          path._lineto(*self._vpos(1, v, 0)),
 563 #                          path.closepath())
 564 #
 565 #     def vzgridpath(self, v):
 566 #         return path.path(path._moveto(*self._vpos(0, 0, v)),
 567 #                          path._lineto(*self._vpos(0, 1, v)),
 568 #                          path._lineto(*self._vpos(1, 1, v)),
 569 #                          path._lineto(*self._vpos(1, 0, v)),
 570 #                          path.closepath())
 571 #
 572 #     def _addpos(self, x, y, dx, dy):
 573 #         assert 0
 574 #         return x+dx, y+dy
 575 #
 576 #     def _connect(self, x1, y1, x2, y2):
 577 #         assert 0
 578 #         return path._lineto(x2, y2)
 579 #
 580 #     def doaxes(self):
 581 #         self.dolayout()
 582 #         if not self.removedomethod(self.doaxes): return
 583 #         axesdist_pt = unit.topt(self.axesdist)
 584 #         XPattern = re.compile(r"%s([2-9]|[1-9][0-9]+)?$" % self.axisnames[0])
 585 #         YPattern = re.compile(r"%s([2-9]|[1-9][0-9]+)?$" % self.axisnames[1])
 586 #         ZPattern = re.compile(r"%s([2-9]|[1-9][0-9]+)?$" % self.axisnames[2])
 587 #         items = list(self.axes.items())
 588 #         items.sort() #TODO: alphabetical sorting breaks for axis numbers bigger than 9
 589 #         for key, axis in items:
 590 #             num = self.keynum(key)
 591 #             num2 = 1 - num % 2 # x1 -> 0, x2 -> 1, x3 -> 0, x4 -> 1, ...
 592 #             num3 = 1 - 2 * (num % 2) # x1 -> -1, x2 -> 1, x3 -> -1, x4 -> 1, ...
 593 #             if XPattern.match(key):
 594 #                 axis.vypos = 0
 595 #                 axis.vzpos = 0
 596 #                 axis._vtickpoint = self._vxtickpoint
 597 #                 axis.vgridpath = self.vxgridpath
 598 #                 axis.vbaseline = self.vxbaseline
 599 #                 axis.vtickdirection = self.vxtickdirection
 600 #             elif YPattern.match(key):
 601 #                 axis.vxpos = 0
 602 #                 axis.vzpos = 0
 603 #                 axis._vtickpoint = self._vytickpoint
 604 #                 axis.vgridpath = self.vygridpath
 605 #                 axis.vbaseline = self.vybaseline
 606 #                 axis.vtickdirection = self.vytickdirection
 607 #             elif ZPattern.match(key):
 608 #                 axis.vxpos = 0
 609 #                 axis.vypos = 0
 610 #                 axis._vtickpoint = self._vztickpoint
 611 #                 axis.vgridpath = self.vzgridpath
 612 #                 axis.vbaseline = self.vzbaseline
 613 #                 axis.vtickdirection = self.vztickdirection
 614 #             else:
 615 #                 raise ValueError("Axis key '%s' not allowed" % key)
 616 #             if axis.painter is not None:
 617 #                 axis.dopaint(self)
 618 # #            if XPattern.match(key):
 619 # #                self._xaxisextents[num2] += axis._extent
 620 # #                needxaxisdist[num2] = 1
 621 # #            if YPattern.match(key):
 622 # #                self._yaxisextents[num2] += axis._extent
 623 # #                needyaxisdist[num2] = 1
 624 #
 625 #     def __init__(self, tex, xpos=0, ypos=0, width=None, height=None, depth=None,
 626 #                  phi=30, theta=30, distance=1,
 627 #                  backgroundattrs=None, axesdist=0.8*unit.v_cm, **axes):
 628 #         canvas.canvas.__init__(self)
 629 #         self.tex = tex
 630 #         self.xpos = xpos
 631 #         self.ypos = ypos
 632 #         self._xpos = unit.topt(xpos)
 633 #         self._ypos = unit.topt(ypos)
 634 #         self._width = unit.topt(width)
 635 #         self._height = unit.topt(height)
 636 #         self._depth = unit.topt(depth)
 637 #         self.width = width
 638 #         self.height = height
 639 #         self.depth = depth
 640 #         if self._width <= 0: raise ValueError("width < 0")
 641 #         if self._height <= 0: raise ValueError("height < 0")
 642 #         if self._depth <= 0: raise ValueError("height < 0")
 643 #         self._distance = distance*math.sqrt(self._width*self._width+
 644 #                                             self._height*self._height+
 645 #                                             self._depth*self._depth)
 646 #         phi *= -math.pi/180
 647 #         theta *= math.pi/180
 648 #         self.a = (-math.sin(phi), math.cos(phi), 0)
 649 #         self.b = (-math.cos(phi)*math.sin(theta),
 650 #                   -math.sin(phi)*math.sin(theta),
 651 #                   math.cos(theta))
 652 #         self.eye = (self._distance*math.cos(phi)*math.cos(theta),
 653 #                     self._distance*math.sin(phi)*math.cos(theta),
 654 #                     self._distance*math.sin(theta))
 655 #         self.initaxes(axes)
 656 #         self.axesdist = axesdist
 657 #         self.backgroundattrs = backgroundattrs
 658 #
 659 #         self.data = []
 660 #         self.domethods = [self.dolayout, self.dobackground, self.doaxes, self.dodata]
 661 #         self.haslayout = 0
 662 #         self.defaultstyle = {}
 663 #
 664 #     def bbox(self):
 665 #         self.finish()
 666 #         return bbox._bbox(self._xpos - 200, self._ypos - 200, self._xpos + 200, self._ypos + 200)