pyx/path.py

   1 # -*- encoding: utf-8 -*-
   2 #
   3 #
   4 # Copyright (C) 2002-2006 Jörg Lehmann <joergl@users.sourceforge.net>
   5 # Copyright (C) 2003-2005 Michael Schindler <m-schindler@users.sourceforge.net>
   6 # Copyright (C) 2002-2011 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 from math import cos, sin, tan, acos, pi, radians, degrees
  26 import trafo, unit
  27 from normpath import NormpathException, normpath, normsubpath, normline_pt, normcurve_pt
  28 import bbox as bboxmodule
  29
  30 # set is available as an external interface to the normpath.set method
  31 from normpath import set
  32 # normpath's invalid is available as an external interface
  33 from normpath import invalid
  34
  35 # use new style classes when possible
  36 __metaclass__ = type
  37
  38 class _marker: pass
  39
  40 ################################################################################
  41
  42 # specific exception for path-related problems
  43 class PathException(Exception): pass
  44
  45 ################################################################################
  46 # Bezier helper functions
  47 ################################################################################
  48
  49 def _bezierpolyrange(x0, x1, x2, x3):
  50     tc = [0, 1]
  51
  52     a = x3 - 3*x2 + 3*x1 - x0
  53     b = 2*x0 - 4*x1 + 2*x2
  54     c = x1 - x0
  55
  56     s = b*b - 4*a*c
  57     if s >= 0:
  58         if b >= 0:
  59             q = -0.5*(b+math.sqrt(s))
  60         else:
  61             q = -0.5*(b-math.sqrt(s))
  62
  63         try:
  64             t = q*1.0/a
  65         except ZeroDivisionError:
  66             pass
  67         else:
  68             if 0 < t < 1:
  69                 tc.append(t)
  70
  71         try:
  72             t = c*1.0/q
  73         except ZeroDivisionError:
  74             pass
  75         else:
  76             if 0 < t < 1:
  77                 tc.append(t)
  78
  79     p = [(((a*t + 1.5*b)*t + 3*c)*t + x0) for t in tc]
  80
  81     return min(*p), max(*p)
  82
  83
  84 def _arctobcurve(x_pt, y_pt, r_pt, phi1, phi2):
  85     """generate the best bezier curve corresponding to an arc segment"""
  86
  87     dphi = phi2-phi1
  88
  89     if dphi==0: return None
  90
  91     # the two endpoints should be clear
  92     x0_pt, y0_pt = x_pt+r_pt*cos(phi1), y_pt+r_pt*sin(phi1)
  93     x3_pt, y3_pt = x_pt+r_pt*cos(phi2), y_pt+r_pt*sin(phi2)
  94
  95     # optimal relative distance along tangent for second and third
  96     # control point
  97     l = r_pt*4*(1-cos(dphi/2))/(3*sin(dphi/2))
  98
  99     x1_pt, y1_pt = x0_pt-l*sin(phi1), y0_pt+l*cos(phi1)
 100     x2_pt, y2_pt = x3_pt+l*sin(phi2), y3_pt-l*cos(phi2)
 101
 102     return normcurve_pt(x0_pt, y0_pt, x1_pt, y1_pt, x2_pt, y2_pt, x3_pt, y3_pt)
 103
 104
 105 def _arctobezierpath(x_pt, y_pt, r_pt, phi1, phi2, dphimax=45):
 106     apath = []
 107
 108     phi1 = radians(phi1)
 109     phi2 = radians(phi2)
 110     dphimax = radians(dphimax)
 111
 112     if phi2<phi1:
 113         # guarantee that phi2>phi1 ...
 114         phi2 = phi2 + (math.floor((phi1-phi2)/(2*pi))+1)*2*pi
 115     elif phi2>phi1+2*pi:
 116         # ... or remove unnecessary multiples of 2*pi
 117         phi2 = phi2 - (math.floor((phi2-phi1)/(2*pi))-1)*2*pi
 118
 119     if r_pt == 0 or phi1-phi2 == 0: return []
 120
 121     subdivisions = abs(int((1.0*(phi1-phi2))/dphimax))+1
 122
 123     dphi = (1.0*(phi2-phi1))/subdivisions
 124
 125     for i in range(subdivisions):
 126         apath.append(_arctobcurve(x_pt, y_pt, r_pt, phi1+i*dphi, phi1+(i+1)*dphi))
 127
 128     return apath
 129
 130 def _arcpoint(x_pt, y_pt, r_pt, angle):
 131     """return starting point of arc segment"""
 132     return x_pt+r_pt*cos(radians(angle)), y_pt+r_pt*sin(radians(angle))
 133
 134 def _arcbboxdata(x_pt, y_pt, r_pt, angle1, angle2):
 135     phi1 = radians(angle1)
 136     phi2 = radians(angle2)
 137
 138     # starting end end point of arc segment
 139     sarcx_pt, sarcy_pt = _arcpoint(x_pt, y_pt, r_pt, angle1)
 140     earcx_pt, earcy_pt = _arcpoint(x_pt, y_pt, r_pt, angle2)
 141
 142     # Now, we have to determine the corners of the bbox for the
 143     # arc segment, i.e. global maxima/mimima of cos(phi) and sin(phi)
 144     # in the interval [phi1, phi2]. These can either be located
 145     # on the borders of this interval or in the interior.
 146
 147     if phi2 < phi1:
 148         # guarantee that phi2>phi1
 149         phi2 = phi2 + (math.floor((phi1-phi2)/(2*pi))+1)*2*pi
 150
 151     # next minimum of cos(phi) looking from phi1 in counterclockwise
 152     # direction: 2*pi*floor((phi1-pi)/(2*pi)) + 3*pi
 153
 154     if phi2 < (2*math.floor((phi1-pi)/(2*pi))+3)*pi:
 155         minarcx_pt = min(sarcx_pt, earcx_pt)
 156     else:
 157         minarcx_pt = x_pt-r_pt
 158
 159     # next minimum of sin(phi) looking from phi1 in counterclockwise
 160     # direction: 2*pi*floor((phi1-3*pi/2)/(2*pi)) + 7/2*pi
 161
 162     if phi2 < (2*math.floor((phi1-3.0*pi/2)/(2*pi))+7.0/2)*pi:
 163         minarcy_pt = min(sarcy_pt, earcy_pt)
 164     else:
 165         minarcy_pt = y_pt-r_pt
 166
 167     # next maximum of cos(phi) looking from phi1 in counterclockwise
 168     # direction: 2*pi*floor((phi1)/(2*pi))+2*pi
 169
 170     if phi2 < (2*math.floor((phi1)/(2*pi))+2)*pi:
 171         maxarcx_pt = max(sarcx_pt, earcx_pt)
 172     else:
 173         maxarcx_pt = x_pt+r_pt
 174
 175     # next maximum of sin(phi) looking from phi1 in counterclockwise
 176     # direction: 2*pi*floor((phi1-pi/2)/(2*pi)) + 1/2*pi
 177
 178     if phi2 < (2*math.floor((phi1-pi/2)/(2*pi))+5.0/2)*pi:
 179         maxarcy_pt = max(sarcy_pt, earcy_pt)
 180     else:
 181         maxarcy_pt = y_pt+r_pt
 182
 183     return minarcx_pt, minarcy_pt, maxarcx_pt, maxarcy_pt
 184
 185
 186 ################################################################################
 187 # path context and pathitem base class
 188 ################################################################################
 189
 190 class context:
 191
 192     """context for pathitem"""
 193
 194     def __init__(self, x_pt, y_pt, subfirstx_pt, subfirsty_pt):
 195         """initializes a context for path items
 196
 197         x_pt, y_pt are the currentpoint. subfirstx_pt, subfirsty_pt
 198         are the starting point of the current subpath. There are no
 199         invalid contexts, i.e. all variables need to be set to integer
 200         or float numbers.
 201         """
 202         self.x_pt = x_pt
 203         self.y_pt = y_pt
 204         self.subfirstx_pt = subfirstx_pt
 205         self.subfirsty_pt = subfirsty_pt
 206
 207
 208 class pathitem:
 209
 210     """element of a PS style path"""
 211
 212     def __str__(self):
 213         raise NotImplementedError()
 214
 215     def createcontext(self):
 216         """creates a context from the current pathitem
 217
 218         Returns a context instance. Is called, when no context has yet
 219         been defined, i.e. for the very first pathitem. Most of the
 220         pathitems do not provide this method. Note, that you should pass
 221         the context created by createcontext to updatebbox and updatenormpath
 222         of successive pathitems only; use the context-free createbbox and
 223         createnormpath for the first pathitem instead.
 224         """
 225         raise PathException("path must start with moveto or the like (%r)" % self)
 226
 227     def createbbox(self):
 228         """creates a bbox from the current pathitem
 229
 230         Returns a bbox instance. Is called, when a bbox has to be
 231         created instead of updating it, i.e. for the very first
 232         pathitem. Most pathitems do not provide this method.
 233         updatebbox must not be called for the created instance and the
 234         same pathitem.
 235         """
 236         raise PathException("path must start with moveto or the like (%r)" % self)
 237
 238     def createnormpath(self, epsilon=_marker):
 239         """create a normpath from the current pathitem
 240
 241         Return a normpath instance. Is called, when a normpath has to
 242         be created instead of updating it, i.e. for the very first
 243         pathitem. Most pathitems do not provide this method.
 244         updatenormpath must not be called for the created instance and
 245         the same pathitem.
 246         """
 247         raise PathException("path must start with moveto or the like (%r)" % self)
 248
 249     def updatebbox(self, bbox, context):
 250         """updates the bbox to contain the pathitem for the given
 251         context
 252
 253         Is called for all subsequent pathitems in a path to complete
 254         the bbox information. Both, the bbox and context are updated
 255         inplace. Does not return anything.
 256         """
 257         raise NotImplementedError()
 258
 259     def updatenormpath(self, normpath, context):
 260         """update the normpath to contain the pathitem for the given
 261         context
 262
 263         Is called for all subsequent pathitems in a path to complete
 264         the normpath. Both the normpath and the context are updated
 265         inplace. Most pathitem implementations will use
 266         normpath.normsubpath[-1].append to add normsubpathitem(s).
 267         Does not return anything.
 268         """
 269         raise NotImplementedError()
 270
 271     def outputPS(self, file, writer):
 272         """write PS representation of pathitem to file"""
 273
 274
 275
 276 ################################################################################
 277 # various pathitems
 278 ################################################################################
 279 # Each one comes in two variants:
 280 #  - one with suffix _pt. This one requires the coordinates
 281 #    to be already in pts (mainly used for internal purposes)
 282 #  - another which accepts arbitrary units
 283
 284
 285 class closepath(pathitem):
 286
 287     """Connect subpath back to its starting point"""
 288
 289     __slots__ = ()
 290
 291     def __str__(self):
 292         return "closepath()"
 293
 294     def updatebbox(self, bbox, context):
 295         context.x_pt = context.subfirstx_pt
 296         context.y_pt = context.subfirsty_pt
 297
 298     def updatenormpath(self, normpath, context):
 299         normpath.normsubpaths[-1].close()
 300         context.x_pt = context.subfirstx_pt
 301         context.y_pt = context.subfirsty_pt
 302
 303     def outputPS(self, file, writer):
 304         file.write("closepath\n")
 305
 306
 307 class pdfmoveto_pt(normline_pt):
 308
 309     def outputPDF(self, file, writer):
 310         pass
 311
 312
 313 class moveto_pt(pathitem):
 314
 315     """Start a new subpath and set current point to (x_pt, y_pt) (coordinates in pts)"""
 316
 317     __slots__ = "x_pt", "y_pt"
 318
 319     def __init__(self, x_pt, y_pt):
 320         self.x_pt = x_pt
 321         self.y_pt = y_pt
 322
 323     def __str__(self):
 324         return "moveto_pt(%g, %g)" % (self.x_pt, self.y_pt)
 325
 326     def createcontext(self):
 327         return context(self.x_pt, self.y_pt, self.x_pt, self.y_pt)
 328
 329     def createbbox(self):
 330         return bboxmodule.bbox_pt(self.x_pt, self.y_pt, self.x_pt, self.y_pt)
 331
 332     def createnormpath(self, epsilon=_marker):
 333         if epsilon is _marker:
 334             return normpath([normsubpath([normline_pt(self.x_pt, self.y_pt, self.x_pt, self.y_pt)])])
 335         elif epsilon is None:
 336             return normpath([normsubpath([pdfmoveto_pt(self.x_pt, self.y_pt, self.x_pt, self.y_pt)],
 337                                          epsilon=epsilon)])
 338         else:
 339             return normpath([normsubpath([normline_pt(self.x_pt, self.y_pt, self.x_pt, self.y_pt)],
 340                                          epsilon=epsilon)])
 341
 342     def updatebbox(self, bbox, context):
 343         bbox.includepoint_pt(self.x_pt, self.y_pt)
 344         context.x_pt = context.subfirstx_pt = self.x_pt
 345         context.y_pt = context.subfirsty_pt = self.y_pt
 346
 347     def updatenormpath(self, normpath, context):
 348         if normpath.normsubpaths[-1].epsilon is not None:
 349             normpath.append(normsubpath([normline_pt(self.x_pt, self.y_pt, self.x_pt, self.y_pt)],
 350                                         epsilon=normpath.normsubpaths[-1].epsilon))
 351         else:
 352             normpath.append(normsubpath(epsilon=normpath.normsubpaths[-1].epsilon))
 353         context.x_pt = context.subfirstx_pt = self.x_pt
 354         context.y_pt = context.subfirsty_pt = self.y_pt
 355
 356     def outputPS(self, file, writer):
 357         file.write("%g %g moveto\n" % (self.x_pt, self.y_pt) )
 358
 359
 360 class lineto_pt(pathitem):
 361
 362     """Append straight line to (x_pt, y_pt) (coordinates in pts)"""
 363
 364     __slots__ = "x_pt", "y_pt"
 365
 366     def __init__(self, x_pt, y_pt):
 367         self.x_pt = x_pt
 368         self.y_pt = y_pt
 369
 370     def __str__(self):
 371         return "lineto_pt(%g, %g)" % (self.x_pt, self.y_pt)
 372
 373     def updatebbox(self, bbox, context):
 374         bbox.includepoint_pt(self.x_pt, self.y_pt)
 375         context.x_pt = self.x_pt
 376         context.y_pt = self.y_pt
 377
 378     def updatenormpath(self, normpath, context):
 379         normpath.normsubpaths[-1].append(normline_pt(context.x_pt, context.y_pt,
 380                                                      self.x_pt, self.y_pt))
 381         context.x_pt = self.x_pt
 382         context.y_pt = self.y_pt
 383
 384     def outputPS(self, file, writer):
 385         file.write("%g %g lineto\n" % (self.x_pt, self.y_pt) )
 386
 387
 388 class curveto_pt(pathitem):
 389
 390     """Append curveto (coordinates in pts)"""
 391
 392     __slots__ = "x1_pt", "y1_pt", "x2_pt", "y2_pt", "x3_pt", "y3_pt"
 393
 394     def __init__(self, x1_pt, y1_pt, x2_pt, y2_pt, x3_pt, y3_pt):
 395         self.x1_pt = x1_pt
 396         self.y1_pt = y1_pt
 397         self.x2_pt = x2_pt
 398         self.y2_pt = y2_pt
 399         self.x3_pt = x3_pt
 400         self.y3_pt = y3_pt
 401
 402     def __str__(self):
 403         return "curveto_pt(%g, %g, %g, %g, %g, %g)" % (self.x1_pt, self.y1_pt,
 404                                                        self.x2_pt, self.y2_pt,
 405                                                        self.x3_pt, self.y3_pt)
 406
 407     def updatebbox(self, bbox, context):
 408         xmin_pt, xmax_pt = _bezierpolyrange(context.x_pt, self.x1_pt, self.x2_pt, self.x3_pt)
 409         ymin_pt, ymax_pt = _bezierpolyrange(context.y_pt, self.y1_pt, self.y2_pt, self.y3_pt)
 410         bbox.includepoint_pt(xmin_pt, ymin_pt)
 411         bbox.includepoint_pt(xmax_pt, ymax_pt)
 412         context.x_pt = self.x3_pt
 413         context.y_pt = self.y3_pt
 414
 415     def updatenormpath(self, normpath, context):
 416         normpath.normsubpaths[-1].append(normcurve_pt(context.x_pt, context.y_pt,
 417                                                       self.x1_pt, self.y1_pt,
 418                                                       self.x2_pt, self.y2_pt,
 419                                                       self.x3_pt, self.y3_pt))
 420         context.x_pt = self.x3_pt
 421         context.y_pt = self.y3_pt
 422
 423     def outputPS(self, file, writer):
 424         file.write("%g %g %g %g %g %g curveto\n" % (self.x1_pt, self.y1_pt,
 425                                                     self.x2_pt, self.y2_pt,
 426                                                     self.x3_pt, self.y3_pt))
 427
 428
 429 class rmoveto_pt(pathitem):
 430
 431     """Perform relative moveto (coordinates in pts)"""
 432
 433     __slots__ = "dx_pt", "dy_pt"
 434
 435     def __init__(self, dx_pt, dy_pt):
 436          self.dx_pt = dx_pt
 437          self.dy_pt = dy_pt
 438
 439     def __str__(self):
 440         return "rmoveto_pt(%g, %g)" % (self.dx_pt, self.dy_pt)
 441
 442     def updatebbox(self, bbox, context):
 443         bbox.includepoint_pt(context.x_pt + self.dx_pt, context.y_pt + self.dy_pt)
 444         context.x_pt += self.dx_pt
 445         context.y_pt += self.dy_pt
 446         context.subfirstx_pt = context.x_pt
 447         context.subfirsty_pt = context.y_pt
 448
 449     def updatenormpath(self, normpath, context):
 450         context.x_pt += self.dx_pt
 451         context.y_pt += self.dy_pt
 452         context.subfirstx_pt = context.x_pt
 453         context.subfirsty_pt = context.y_pt
 454         if normpath.normsubpaths[-1].epsilon is not None:
 455             normpath.append(normsubpath([normline_pt(context.x_pt, context.y_pt,
 456                                                      context.x_pt, context.y_pt)],
 457                                         epsilon=normpath.normsubpaths[-1].epsilon))
 458         else:
 459             normpath.append(normsubpath(epsilon=normpath.normsubpaths[-1].epsilon))
 460
 461     def outputPS(self, file, writer):
 462         file.write("%g %g rmoveto\n" % (self.dx_pt, self.dy_pt) )
 463
 464
 465 class rlineto_pt(pathitem):
 466
 467     """Perform relative lineto (coordinates in pts)"""
 468
 469     __slots__ = "dx_pt", "dy_pt"
 470
 471     def __init__(self, dx_pt, dy_pt):
 472         self.dx_pt = dx_pt
 473         self.dy_pt = dy_pt
 474
 475     def __str__(self):
 476         return "rlineto_pt(%g %g)" % (self.dx_pt, self.dy_pt)
 477
 478     def updatebbox(self, bbox, context):
 479         bbox.includepoint_pt(context.x_pt + self.dx_pt, context.y_pt + self.dy_pt)
 480         context.x_pt += self.dx_pt
 481         context.y_pt += self.dy_pt
 482
 483     def updatenormpath(self, normpath, context):
 484         normpath.normsubpaths[-1].append(normline_pt(context.x_pt, context.y_pt,
 485                                                      context.x_pt + self.dx_pt, context.y_pt + self.dy_pt))
 486         context.x_pt += self.dx_pt
 487         context.y_pt += self.dy_pt
 488
 489     def outputPS(self, file, writer):
 490         file.write("%g %g rlineto\n" % (self.dx_pt, self.dy_pt) )
 491
 492
 493 class rcurveto_pt(pathitem):
 494
 495     """Append rcurveto (coordinates in pts)"""
 496
 497     __slots__ = "dx1_pt", "dy1_pt", "dx2_pt", "dy2_pt", "dx3_pt", "dy3_pt"
 498
 499     def __init__(self, dx1_pt, dy1_pt, dx2_pt, dy2_pt, dx3_pt, dy3_pt):
 500         self.dx1_pt = dx1_pt
 501         self.dy1_pt = dy1_pt
 502         self.dx2_pt = dx2_pt
 503         self.dy2_pt = dy2_pt
 504         self.dx3_pt = dx3_pt
 505         self.dy3_pt = dy3_pt
 506
 507     def __str__(self):
 508         return "rcurveto_pt(%g, %g, %g, %g, %g, %g)" % (self.dx1_pt, self.dy1_pt,
 509                                                         self.dx2_pt, self.dy2_pt,
 510                                                         self.dx3_pt, self.dy3_pt)
 511
 512     def updatebbox(self, bbox, context):
 513         xmin_pt, xmax_pt = _bezierpolyrange(context.x_pt,
 514                                             context.x_pt+self.dx1_pt,
 515                                             context.x_pt+self.dx2_pt,
 516                                             context.x_pt+self.dx3_pt)
 517         ymin_pt, ymax_pt = _bezierpolyrange(context.y_pt,
 518                                             context.y_pt+self.dy1_pt,
 519                                             context.y_pt+self.dy2_pt,
 520                                             context.y_pt+self.dy3_pt)
 521         bbox.includepoint_pt(xmin_pt, ymin_pt)
 522         bbox.includepoint_pt(xmax_pt, ymax_pt)
 523         context.x_pt += self.dx3_pt
 524         context.y_pt += self.dy3_pt
 525
 526     def updatenormpath(self, normpath, context):
 527         normpath.normsubpaths[-1].append(normcurve_pt(context.x_pt, context.y_pt,
 528                                                       context.x_pt + self.dx1_pt, context.y_pt + self.dy1_pt,
 529                                                       context.x_pt + self.dx2_pt, context.y_pt + self.dy2_pt,
 530                                                       context.x_pt + self.dx3_pt, context.y_pt + self.dy3_pt))
 531         context.x_pt += self.dx3_pt
 532         context.y_pt += self.dy3_pt
 533
 534     def outputPS(self, file, writer):
 535         file.write("%g %g %g %g %g %g rcurveto\n" % (self.dx1_pt, self.dy1_pt,
 536                                                      self.dx2_pt, self.dy2_pt,
 537                                                      self.dx3_pt, self.dy3_pt))
 538
 539
 540 class arc_pt(pathitem):
 541
 542     """Append counterclockwise arc (coordinates in pts)"""
 543
 544     __slots__ = "x_pt", "y_pt", "r_pt", "angle1", "angle2"
 545
 546     def __init__(self, x_pt, y_pt, r_pt, angle1, angle2):
 547         self.x_pt = x_pt
 548         self.y_pt = y_pt
 549         self.r_pt = r_pt
 550         self.angle1 = angle1
 551         self.angle2 = angle2
 552
 553     def __str__(self):
 554         return "arc_pt(%g, %g, %g, %g, %g)" % (self.x_pt, self.y_pt, self.r_pt,
 555                                                self.angle1, self.angle2)
 556
 557     def createcontext(self):
 558         x_pt, y_pt = _arcpoint(self.x_pt, self.y_pt, self.r_pt, self.angle2)
 559         return context(x_pt, y_pt, x_pt, y_pt)
 560
 561     def createbbox(self):
 562         return bboxmodule.bbox_pt(*_arcbboxdata(self.x_pt, self.y_pt, self.r_pt,
 563                                                 self.angle1, self.angle2))
 564
 565     def createnormpath(self, epsilon=_marker):
 566         if epsilon is _marker:
 567             return normpath([normsubpath(_arctobezierpath(self.x_pt, self.y_pt, self.r_pt, self.angle1, self.angle2))])
 568         else:
 569             return normpath([normsubpath(_arctobezierpath(self.x_pt, self.y_pt, self.r_pt, self.angle1, self.angle2),
 570                                          epsilon=epsilon)])
 571
 572     def updatebbox(self, bbox, context):
 573         minarcx_pt, minarcy_pt, maxarcx_pt, maxarcy_pt = _arcbboxdata(self.x_pt, self.y_pt, self.r_pt,
 574                                                                       self.angle1, self.angle2)
 575         bbox.includepoint_pt(minarcx_pt, minarcy_pt)
 576         bbox.includepoint_pt(maxarcx_pt, maxarcy_pt)
 577         context.x_pt, context.y_pt = _arcpoint(self.x_pt, self.y_pt, self.r_pt, self.angle2)
 578
 579     def updatenormpath(self, normpath, context):
 580         if normpath.normsubpaths[-1].closed:
 581             normpath.append(normsubpath([normline_pt(context.x_pt, context.y_pt,
 582                                                          *_arcpoint(self.x_pt, self.y_pt, self.r_pt, self.angle1))],
 583                                         epsilon=normpath.normsubpaths[-1].epsilon))
 584         else:
 585             normpath.normsubpaths[-1].append(normline_pt(context.x_pt, context.y_pt,
 586                                                          *_arcpoint(self.x_pt, self.y_pt, self.r_pt, self.angle1)))
 587         normpath.normsubpaths[-1].extend(_arctobezierpath(self.x_pt, self.y_pt, self.r_pt, self.angle1, self.angle2))
 588         context.x_pt, context.y_pt = _arcpoint(self.x_pt, self.y_pt, self.r_pt, self.angle2)
 589
 590     def outputPS(self, file, writer):
 591         file.write("%g %g %g %g %g arc\n" % (self.x_pt, self.y_pt,
 592                                              self.r_pt,
 593                                              self.angle1,
 594                                              self.angle2))
 595
 596
 597 class arcn_pt(pathitem):
 598
 599     """Append clockwise arc (coordinates in pts)"""
 600
 601     __slots__ = "x_pt", "y_pt", "r_pt", "angle1", "angle2"
 602
 603     def __init__(self, x_pt, y_pt, r_pt, angle1, angle2):
 604         self.x_pt = x_pt
 605         self.y_pt = y_pt
 606         self.r_pt = r_pt
 607         self.angle1 = angle1
 608         self.angle2 = angle2
 609
 610     def __str__(self):
 611         return "arcn_pt(%g, %g, %g, %g, %g)" % (self.x_pt, self.y_pt, self.r_pt,
 612                                                 self.angle1, self.angle2)
 613
 614     def createcontext(self):
 615         x_pt, y_pt = _arcpoint(self.x_pt, self.y_pt, self.r_pt, self.angle2)
 616         return context(x_pt, y_pt, x_pt, y_pt)
 617
 618     def createbbox(self):
 619         return bboxmodule.bbox_pt(*_arcbboxdata(self.x_pt, self.y_pt, self.r_pt,
 620                                                 self.angle2, self.angle1))
 621
 622     def createnormpath(self, epsilon=_marker):
 623         if epsilon is _marker:
 624             return normpath([normsubpath(_arctobezierpath(self.x_pt, self.y_pt, self.r_pt, self.angle2, self.angle1))]).reversed()
 625         else:
 626             return normpath([normsubpath(_arctobezierpath(self.x_pt, self.y_pt, self.r_pt, self.angle2, self.angle1),
 627                                          epsilon=epsilon)]).reversed()
 628
 629     def updatebbox(self, bbox, context):
 630         minarcx_pt, minarcy_pt, maxarcx_pt, maxarcy_pt = _arcbboxdata(self.x_pt, self.y_pt, self.r_pt,
 631                                                                       self.angle2, self.angle1)
 632         bbox.includepoint_pt(minarcx_pt, minarcy_pt)
 633         bbox.includepoint_pt(maxarcx_pt, maxarcy_pt)
 634         context.x_pt, context.y_pt = _arcpoint(self.x_pt, self.y_pt, self.r_pt, self.angle2)
 635
 636     def updatenormpath(self, normpath, context):
 637         if normpath.normsubpaths[-1].closed:
 638             normpath.append(normsubpath([normline_pt(context.x_pt, context.y_pt,
 639                                                          *_arcpoint(self.x_pt, self.y_pt, self.r_pt, self.angle1))],
 640                                         epsilon=normpath.normsubpaths[-1].epsilon))
 641         else:
 642             normpath.normsubpaths[-1].append(normline_pt(context.x_pt, context.y_pt,
 643                                                          *_arcpoint(self.x_pt, self.y_pt, self.r_pt, self.angle1)))
 644         bpathitems = _arctobezierpath(self.x_pt, self.y_pt, self.r_pt, self.angle2, self.angle1)
 645         bpathitems.reverse()
 646         for bpathitem in bpathitems:
 647             normpath.normsubpaths[-1].append(bpathitem.reversed())
 648         context.x_pt, context.y_pt = _arcpoint(self.x_pt, self.y_pt, self.r_pt, self.angle2)
 649
 650     def outputPS(self, file, writer):
 651         file.write("%g %g %g %g %g arcn\n" % (self.x_pt, self.y_pt,
 652                                               self.r_pt,
 653                                               self.angle1,
 654                                               self.angle2))
 655
 656
 657 class arct_pt(pathitem):
 658
 659     """Append tangent arc (coordinates in pts)"""
 660
 661     __slots__ = "x1_pt", "y1_pt", "x2_pt", "y2_pt", "r_pt"
 662
 663     def __init__(self, x1_pt, y1_pt, x2_pt, y2_pt, r_pt):
 664         self.x1_pt = x1_pt
 665         self.y1_pt = y1_pt
 666         self.x2_pt = x2_pt
 667         self.y2_pt = y2_pt
 668         self.r_pt = r_pt
 669
 670     def __str__(self):
 671         return "arct_pt(%g, %g, %g, %g, %g)" % (self.x1_pt, self.y1_pt,
 672                                                 self.x2_pt, self.y2_pt,
 673                                                 self.r_pt)
 674
 675     def _pathitems(self, x_pt, y_pt):
 676         """return pathitems corresponding to arct for given currentpoint x_pt, y_pt.
 677
 678         The return is a list containing line_pt, arc_pt, a arcn_pt instances.
 679
 680         This is a helper routine for updatebbox and updatenormpath,
 681         which will delegate the work to the constructed pathitem.
 682         """
 683
 684         # direction of tangent 1
 685         dx1_pt, dy1_pt = self.x1_pt-x_pt, self.y1_pt-y_pt
 686         l1_pt = math.hypot(dx1_pt, dy1_pt)
 687         dx1, dy1 = dx1_pt/l1_pt, dy1_pt/l1_pt
 688
 689         # direction of tangent 2
 690         dx2_pt, dy2_pt = self.x2_pt-self.x1_pt, self.y2_pt-self.y1_pt
 691         l2_pt = math.hypot(dx2_pt, dy2_pt)
 692         dx2, dy2 = dx2_pt/l2_pt, dy2_pt/l2_pt
 693
 694         # intersection angle between two tangents in the range (-pi, pi).
 695         # We take the orientation from the sign of the vector product.
 696         # Negative (positive) angles alpha corresponds to a turn to the right (left)
 697         # as seen from currentpoint.
 698         if dx1*dy2-dy1*dx2 > 0:
 699             alpha = acos(dx1*dx2+dy1*dy2)
 700         else:
 701             alpha = -acos(dx1*dx2+dy1*dy2)
 702
 703         try:
 704             # two tangent points
 705             xt1_pt = self.x1_pt - dx1*self.r_pt*tan(abs(alpha)/2)
 706             yt1_pt = self.y1_pt - dy1*self.r_pt*tan(abs(alpha)/2)
 707             xt2_pt = self.x1_pt + dx2*self.r_pt*tan(abs(alpha)/2)
 708             yt2_pt = self.y1_pt + dy2*self.r_pt*tan(abs(alpha)/2)
 709
 710             # direction point 1 -> center of arc
 711             dmx_pt = 0.5*(xt1_pt+xt2_pt) - self.x1_pt
 712             dmy_pt = 0.5*(yt1_pt+yt2_pt) - self.y1_pt
 713             lm_pt = math.hypot(dmx_pt, dmy_pt)
 714             dmx, dmy = dmx_pt/lm_pt, dmy_pt/lm_pt
 715
 716             # center of arc
 717             mx_pt = self.x1_pt + dmx*self.r_pt/cos(alpha/2)
 718             my_pt = self.y1_pt + dmy*self.r_pt/cos(alpha/2)
 719
 720             # angle around which arc is centered
 721             phi = degrees(math.atan2(-dmy, -dmx))
 722
 723             # half angular width of arc
 724             deltaphi = degrees(alpha)/2
 725
 726             line = lineto_pt(*_arcpoint(mx_pt, my_pt, self.r_pt, phi-deltaphi))
 727             if alpha > 0:
 728                 return [line, arc_pt(mx_pt, my_pt, self.r_pt, phi-deltaphi, phi+deltaphi)]
 729             else:
 730                 return [line, arcn_pt(mx_pt, my_pt, self.r_pt, phi-deltaphi, phi+deltaphi)]
 731
 732         except ZeroDivisionError:
 733             # in the degenerate case, we just return a line as specified by the PS
 734             # language reference
 735             return [lineto_pt(self.x1_pt, self.y1_pt)]
 736
 737     def updatebbox(self, bbox, context):
 738         for pathitem in self._pathitems(context.x_pt, context.y_pt):
 739             pathitem.updatebbox(bbox, context)
 740
 741     def updatenormpath(self, normpath, context):
 742         for pathitem in self._pathitems(context.x_pt, context.y_pt):
 743             pathitem.updatenormpath(normpath, context)
 744
 745     def outputPS(self, file, writer):
 746         file.write("%g %g %g %g %g arct\n" % (self.x1_pt, self.y1_pt,
 747                                               self.x2_pt, self.y2_pt,
 748                                               self.r_pt))
 749
 750 #
 751 # now the pathitems that convert from user coordinates to pts
 752 #
 753
 754 class moveto(moveto_pt):
 755
 756     """Set current point to (x, y)"""
 757
 758     __slots__ = "x_pt", "y_pt"
 759
 760     def __init__(self, x, y):
 761         moveto_pt.__init__(self, unit.topt(x), unit.topt(y))
 762
 763
 764 class lineto(lineto_pt):
 765
 766     """Append straight line to (x, y)"""
 767
 768     __slots__ = "x_pt", "y_pt"
 769
 770     def __init__(self, x, y):
 771         lineto_pt.__init__(self, unit.topt(x), unit.topt(y))
 772
 773
 774 class curveto(curveto_pt):
 775
 776     """Append curveto"""
 777
 778     __slots__ = "x1_pt", "y1_pt", "x2_pt", "y2_pt", "x3_pt", "y3_pt"
 779
 780     def __init__(self, x1, y1, x2, y2, x3, y3):
 781         curveto_pt.__init__(self,
 782                             unit.topt(x1), unit.topt(y1),
 783                             unit.topt(x2), unit.topt(y2),
 784                             unit.topt(x3), unit.topt(y3))
 785
 786 class rmoveto(rmoveto_pt):
 787
 788     """Perform relative moveto"""
 789
 790     __slots__ = "dx_pt", "dy_pt"
 791
 792     def __init__(self, dx, dy):
 793         rmoveto_pt.__init__(self, unit.topt(dx), unit.topt(dy))
 794
 795
 796 class rlineto(rlineto_pt):
 797
 798     """Perform relative lineto"""
 799
 800     __slots__ = "dx_pt", "dy_pt"
 801
 802     def __init__(self, dx, dy):
 803         rlineto_pt.__init__(self, unit.topt(dx), unit.topt(dy))
 804
 805
 806 class rcurveto(rcurveto_pt):
 807
 808     """Append rcurveto"""
 809
 810     __slots__ = "dx1_pt", "dy1_pt", "dx2_pt", "dy2_pt", "dx3_pt", "dy3_pt"
 811
 812     def __init__(self, dx1, dy1, dx2, dy2, dx3, dy3):
 813         rcurveto_pt.__init__(self,
 814                              unit.topt(dx1), unit.topt(dy1),
 815                              unit.topt(dx2), unit.topt(dy2),
 816                              unit.topt(dx3), unit.topt(dy3))
 817
 818
 819 class arcn(arcn_pt):
 820
 821     """Append clockwise arc"""
 822
 823     __slots__ = "x_pt", "y_pt", "r_pt", "angle1", "angle2"
 824
 825     def __init__(self, x, y, r, angle1, angle2):
 826         arcn_pt.__init__(self, unit.topt(x), unit.topt(y), unit.topt(r), angle1, angle2)
 827
 828
 829 class arc(arc_pt):
 830
 831     """Append counterclockwise arc"""
 832
 833     __slots__ = "x_pt", "y_pt", "r_pt", "angle1", "angle2"
 834
 835     def __init__(self, x, y, r, angle1, angle2):
 836         arc_pt.__init__(self, unit.topt(x), unit.topt(y), unit.topt(r), angle1, angle2)
 837
 838
 839 class arct(arct_pt):
 840
 841     """Append tangent arc"""
 842
 843     __slots__ = "x1_pt", "y1_pt", "x2_pt", "y2_pt", "r_pt"
 844
 845     def __init__(self, x1, y1, x2, y2, r):
 846         arct_pt.__init__(self, unit.topt(x1), unit.topt(y1),
 847                          unit.topt(x2), unit.topt(y2), unit.topt(r))
 848
 849 #
 850 # "combined" pathitems provided for performance reasons
 851 #
 852
 853 class multilineto_pt(pathitem):
 854
 855     """Perform multiple linetos (coordinates in pts)"""
 856
 857     __slots__ = "points_pt"
 858
 859     def __init__(self, points_pt):
 860         self.points_pt = points_pt
 861
 862     def __str__(self):
 863         result = []
 864         for point_pt in self.points_pt:
 865             result.append("(%g, %g)" % point_pt )
 866         return "multilineto_pt([%s])" % (", ".join(result))
 867
 868     def updatebbox(self, bbox, context):
 869         for point_pt in self.points_pt:
 870             bbox.includepoint_pt(*point_pt)
 871         if self.points_pt:
 872             context.x_pt, context.y_pt = self.points_pt[-1]
 873
 874     def updatenormpath(self, normpath, context):
 875         x0_pt, y0_pt = context.x_pt, context.y_pt
 876         for point_pt in self.points_pt:
 877             normpath.normsubpaths[-1].append(normline_pt(x0_pt, y0_pt, *point_pt))
 878             x0_pt, y0_pt = point_pt
 879         context.x_pt, context.y_pt = x0_pt, y0_pt
 880
 881     def outputPS(self, file, writer):
 882         for point_pt in self.points_pt:
 883             file.write("%g %g lineto\n" % point_pt )
 884
 885
 886 class multicurveto_pt(pathitem):
 887
 888     """Perform multiple curvetos (coordinates in pts)"""
 889
 890     __slots__ = "points_pt"
 891
 892     def __init__(self, points_pt):
 893         self.points_pt = points_pt
 894
 895     def __str__(self):
 896         result = []
 897         for point_pt in self.points_pt:
 898             result.append("(%g, %g, %g, %g, %g, %g)" % point_pt )
 899         return "multicurveto_pt([%s])" % (", ".join(result))
 900
 901     def updatebbox(self, bbox, context):
 902         for point_pt in self.points_pt:
 903             bbox.includepoint_pt(*point_pt[0: 2])
 904             bbox.includepoint_pt(*point_pt[2: 4])
 905             bbox.includepoint_pt(*point_pt[4: 6])
 906         if self.points_pt:
 907             context.x_pt, context.y_pt = self.points_pt[-1][4:]
 908
 909     def updatenormpath(self, normpath, context):
 910         x0_pt, y0_pt = context.x_pt, context.y_pt
 911         for point_pt in self.points_pt:
 912             normpath.normsubpaths[-1].append(normcurve_pt(x0_pt, y0_pt, *point_pt))
 913             x0_pt, y0_pt = point_pt[4:]
 914         context.x_pt, context.y_pt = x0_pt, y0_pt
 915
 916     def outputPS(self, file, writer):
 917         for point_pt in self.points_pt:
 918             file.write("%g %g %g %g %g %g curveto\n" % point_pt)
 919
 920
 921 ################################################################################
 922 # path: PS style path
 923 ################################################################################
 924
 925 class path:
 926
 927     """PS style path"""
 928
 929     __slots__ = "pathitems", "_normpath"
 930
 931     def __init__(self, *pathitems):
 932         """construct a path from pathitems *args"""
 933
 934         for apathitem in pathitems:
 935             assert isinstance(apathitem, pathitem), "only pathitem instances allowed"
 936
 937         self.pathitems = list(pathitems)
 938         # normpath cache (when no epsilon is set)
 939         self._normpath = None
 940
 941     def __add__(self, other):
 942         """create new path out of self and other"""
 943         return path(*(self.pathitems + other.path().pathitems))
 944
 945     def __iadd__(self, other):
 946         """add other inplace
 947
 948         If other is a normpath instance, it is converted to a path before
 949         being added.
 950         """
 951         self.pathitems += other.path().pathitems
 952         self._normpath = None
 953         return self
 954
 955     def __getitem__(self, i):
 956         """return path item i"""
 957         return self.pathitems[i]
 958
 959     def __len__(self):
 960         """return the number of path items"""
 961         return len(self.pathitems)
 962
 963     def __str__(self):
 964         l = ", ".join(map(str, self.pathitems))
 965         return "path(%s)" % l
 966
 967     def append(self, apathitem):
 968         """append a path item"""
 969         assert isinstance(apathitem, pathitem), "only pathitem instance allowed"
 970         self.pathitems.append(apathitem)
 971         self._normpath = None
 972
 973     def arclen_pt(self):
 974         """return arc length in pts"""
 975         return self.normpath().arclen_pt()
 976
 977     def arclen(self):
 978         """return arc length"""
 979         return self.normpath().arclen()
 980
 981     def arclentoparam_pt(self, lengths_pt):
 982         """return the param(s) matching the given length(s)_pt in pts"""
 983         return self.normpath().arclentoparam_pt(lengths_pt)
 984
 985     def arclentoparam(self, lengths):
 986         """return the param(s) matching the given length(s)"""
 987         return self.normpath().arclentoparam(lengths)
 988
 989     def at_pt(self, params):
 990         """return coordinates of path in pts at param(s) or arc length(s) in pts"""
 991         return self.normpath().at_pt(params)
 992
 993     def at(self, params):
 994         """return coordinates of path at param(s) or arc length(s)"""
 995         return self.normpath().at(params)
 996
 997     def atbegin_pt(self):
 998         """return coordinates of the beginning of first subpath in path in pts"""
 999         return self.normpath().atbegin_pt()
1000
1001     def atbegin(self):
1002         """return coordinates of the beginning of first subpath in path"""
1003         return self.normpath().atbegin()
1004
1005     def atend_pt(self):
1006         """return coordinates of the end of last subpath in path in pts"""
1007         return self.normpath().atend_pt()
1008
1009     def atend(self):
1010         """return coordinates of the end of last subpath in path"""
1011         return self.normpath().atend()
1012
1013     def bbox(self):
1014         """return bbox of path"""
1015         if self.pathitems:
1016             bbox = self.pathitems[0].createbbox()
1017             context = self.pathitems[0].createcontext()
1018             for pathitem in self.pathitems[1:]:
1019                 pathitem.updatebbox(bbox, context)
1020             return bbox
1021         else:
1022             return bboxmodule.empty()
1023
1024     def begin(self):
1025         """return param corresponding of the beginning of the path"""
1026         return self.normpath().begin()
1027
1028     def curveradius_pt(self, params):
1029         """return the curvature radius in pts at param(s) or arc length(s) in pts
1030
1031         The curvature radius is the inverse of the curvature. When the
1032         curvature is 0, None is returned. Note that this radius can be negative
1033         or positive, depending on the sign of the curvature."""
1034         return self.normpath().curveradius_pt(params)
1035
1036     def curveradius(self, params):
1037         """return the curvature radius at param(s) or arc length(s)
1038
1039         The curvature radius is the inverse of the curvature. When the
1040         curvature is 0, None is returned. Note that this radius can be negative
1041         or positive, depending on the sign of the curvature."""
1042         return self.normpath().curveradius(params)
1043
1044     def end(self):
1045         """return param corresponding of the end of the path"""
1046         return self.normpath().end()
1047
1048     def extend(self, pathitems):
1049         """extend path by pathitems"""
1050         for apathitem in pathitems:
1051             assert isinstance(apathitem, pathitem), "only pathitem instance allowed"
1052         self.pathitems.extend(pathitems)
1053         self._normpath = None
1054
1055     def intersect(self, other):
1056         """intersect self with other path
1057
1058         Returns a tuple of lists consisting of the parameter values
1059         of the intersection points of the corresponding normpath.
1060         """
1061         return self.normpath().intersect(other)
1062
1063     def join(self, other):
1064         """join other path/normpath inplace
1065
1066         If other is a normpath instance, it is converted to a path before
1067         being joined.
1068         """
1069         self.pathitems = self.joined(other).path().pathitems
1070         self._normpath = None
1071         return self
1072
1073     def joined(self, other):
1074         """return path consisting of self and other joined together"""
1075         return self.normpath().joined(other).path()
1076
1077     # << operator also designates joining
1078     __lshift__ = joined
1079
1080     def normpath(self, epsilon=_marker):
1081         """convert the path into a normpath"""
1082         # use cached value if existent and epsilon is _marker
1083         if self._normpath is not None and epsilon is _marker:
1084             return self._normpath
1085         if self.pathitems:
1086             if epsilon is _marker:
1087                 normpath = self.pathitems[0].createnormpath()
1088             else:
1089                 normpath = self.pathitems[0].createnormpath(epsilon)
1090             context = self.pathitems[0].createcontext()
1091             for pathitem in self.pathitems[1:]:
1092                 pathitem.updatenormpath(normpath, context)
1093         else:
1094             if epsilon is _marker:
1095                 normpath = normpath([])
1096             else:
1097                 normpath = normpath(epsilon=epsilon)
1098         if epsilon is _marker:
1099             self._normpath = normpath
1100         return normpath
1101
1102     def paramtoarclen_pt(self, params):
1103         """return arc lenght(s) in pts matching the given param(s)"""
1104         return self.normpath().paramtoarclen_pt(params)
1105
1106     def paramtoarclen(self, params):
1107         """return arc lenght(s) matching the given param(s)"""
1108         return self.normpath().paramtoarclen(params)
1109
1110     def path(self):
1111         """return corresponding path, i.e., self"""
1112         return self
1113
1114     def reversed(self):
1115         """return reversed normpath"""
1116         # TODO: couldn't we try to return a path instead of converting it
1117         #       to a normpath (but this might not be worth the trouble)
1118         return self.normpath().reversed()
1119
1120     def rotation_pt(self, params):
1121         """return rotation at param(s) or arc length(s) in pts"""
1122         return self.normpath().rotation(params)
1123
1124     def rotation(self, params):
1125         """return rotation at param(s) or arc length(s)"""
1126         return self.normpath().rotation(params)
1127
1128     def split_pt(self, params):
1129         """split normpath at param(s) or arc length(s) in pts and return list of normpaths"""
1130         return self.normpath().split(params)
1131
1132     def split(self, params):
1133         """split normpath at param(s) or arc length(s) and return list of normpaths"""
1134         return self.normpath().split(params)
1135
1136     def tangent_pt(self, params, length):
1137         """return tangent vector of path at param(s) or arc length(s) in pts
1138
1139         If length in pts is not None, the tangent vector will be scaled to
1140         the desired length.
1141         """
1142         return self.normpath().tangent_pt(params, length)
1143
1144     def tangent(self, params, length=1):
1145         """return tangent vector of path at param(s) or arc length(s)
1146
1147         If length is not None, the tangent vector will be scaled to
1148         the desired length.
1149         """
1150         return self.normpath().tangent(params, length)
1151
1152     def trafo_pt(self, params):
1153         """return transformation at param(s) or arc length(s) in pts"""
1154         return self.normpath().trafo(params)
1155
1156     def trafo(self, params):
1157         """return transformation at param(s) or arc length(s)"""
1158         return self.normpath().trafo(params)
1159
1160     def transformed(self, trafo):
1161         """return transformed path"""
1162         return self.normpath().transformed(trafo)
1163
1164     def outputPS(self, file, writer):
1165         """write PS code to file"""
1166         for pitem in self.pathitems:
1167             pitem.outputPS(file, writer)
1168
1169     def outputPDF(self, file, writer):
1170         """write PDF code to file"""
1171         # PDF only supports normsubpathitems; we need to use a normpath
1172         # with epsilon equals None to prevent failure for paths shorter
1173         # than epsilon
1174         self.normpath(epsilon=None).outputPDF(file, writer)
1175
1176
1177 #
1178 # some special kinds of path, again in two variants
1179 #
1180
1181 class line_pt(path):
1182
1183     """straight line from (x1_pt, y1_pt) to (x2_pt, y2_pt) in pts"""
1184
1185     def __init__(self, x1_pt, y1_pt, x2_pt, y2_pt):
1186         path.__init__(self, moveto_pt(x1_pt, y1_pt), lineto_pt(x2_pt, y2_pt))
1187
1188
1189 class curve_pt(path):
1190
1191     """bezier curve with control points (x0_pt, y1_pt),..., (x3_pt, y3_pt) in pts"""
1192
1193     def __init__(self, x0_pt, y0_pt, x1_pt, y1_pt, x2_pt, y2_pt, x3_pt, y3_pt):
1194         path.__init__(self,
1195                       moveto_pt(x0_pt, y0_pt),
1196                       curveto_pt(x1_pt, y1_pt, x2_pt, y2_pt, x3_pt, y3_pt))
1197
1198
1199 class rect_pt(path):
1200
1201     """rectangle at position (x_pt, y_pt) with width_pt and height_pt in pts"""
1202
1203     def __init__(self, x_pt, y_pt, width_pt, height_pt):
1204         path.__init__(self, moveto_pt(x_pt, y_pt),
1205                             lineto_pt(x_pt+width_pt, y_pt),
1206                             lineto_pt(x_pt+width_pt, y_pt+height_pt),
1207                             lineto_pt(x_pt, y_pt+height_pt),
1208                             closepath())
1209
1210
1211 class circle_pt(path):
1212
1213     """circle with center (x_pt, y_pt) and radius_pt in pts"""
1214
1215     def __init__(self, x_pt, y_pt, radius_pt, arcepsilon=0.1):
1216         path.__init__(self, moveto_pt(x_pt+radius_pt, y_pt),
1217                             arc_pt(x_pt, y_pt, radius_pt, arcepsilon, 360-arcepsilon),
1218                             closepath())
1219
1220
1221 class ellipse_pt(path):
1222
1223     """ellipse with center (x_pt, y_pt) in pts,
1224     the two axes (a_pt, b_pt) in pts,
1225     and the angle angle of the first axis"""
1226
1227     def __init__(self, x_pt, y_pt, a_pt, b_pt, angle, **kwargs):
1228         t = trafo.scale(a_pt, b_pt, epsilon=None).rotated(angle).translated_pt(x_pt, y_pt)
1229         p = circle_pt(0, 0, 1, **kwargs).normpath(epsilon=None).transformed(t).path()
1230         path.__init__(self, *p.pathitems)
1231
1232
1233 class line(line_pt):
1234
1235     """straight line from (x1, y1) to (x2, y2)"""
1236
1237     def __init__(self, x1, y1, x2, y2):
1238         line_pt.__init__(self, unit.topt(x1), unit.topt(y1),
1239                                unit.topt(x2), unit.topt(y2))
1240
1241
1242 class curve(curve_pt):
1243
1244     """bezier curve with control points (x0, y1),..., (x3, y3)"""
1245
1246     def __init__(self, x0, y0, x1, y1, x2, y2, x3, y3):
1247         curve_pt.__init__(self, unit.topt(x0), unit.topt(y0),
1248                                 unit.topt(x1), unit.topt(y1),
1249                                 unit.topt(x2), unit.topt(y2),
1250                                 unit.topt(x3), unit.topt(y3))
1251
1252
1253 class rect(rect_pt):
1254
1255     """rectangle at position (x,y) with width and height"""
1256
1257     def __init__(self, x, y, width, height):
1258         rect_pt.__init__(self, unit.topt(x), unit.topt(y),
1259                                unit.topt(width), unit.topt(height))
1260
1261
1262 class circle(circle_pt):
1263
1264     """circle with center (x,y) and radius"""
1265
1266     def __init__(self, x, y, radius, **kwargs):
1267         circle_pt.__init__(self, unit.topt(x), unit.topt(y), unit.topt(radius), **kwargs)
1268
1269
1270 class ellipse(ellipse_pt):
1271
1272     """ellipse with center (x, y), the two axes (a, b),
1273     and the angle angle of the first axis"""
1274
1275     def __init__(self, x, y, a, b, angle, **kwargs):
1276         ellipse_pt.__init__(self, unit.topt(x), unit.topt(y), unit.topt(a), unit.topt(b), angle, **kwargs)