pyx/metapost/path.py

   1 # -*- coding: ISO-8859-1 -*-
   2 #
   3 # Copyright (C) 2011 Michael Schindler <m-schindler@users.sourceforge.net>
   4 #
   5 # This file is part of PyX (http://pyx.sourceforge.net/).
   6 #
   7 # PyX is free software; you can redistribute it and/or modify
   8 # it under the terms of the GNU General Public License as published by
   9 # the Free Software Foundation; either version 2 of the License, or
  10 # (at your option) any later version.
  11 #
  12 # PyX is distributed in the hope that it will be useful,
  13 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 # GNU General Public License for more details.
  16 #
  17 # You should have received a copy of the GNU General Public License
  18 # along with PyX; if not, write to the Free Software
  19 # Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA
  20
  21 from math import atan2, radians
  22 from pyx import unit, attr, normpath
  23 from pyx import path as pathmodule
  24
  25 from .mp_path import mp_endpoint, mp_explicit, mp_given, mp_curl, mp_open, mp_end_cycle, mp_make_choices
  26
  27 # global epsilon (default precision length of metapost, in pt)
  28 _epsilon = 1e-5
  29
  30 def set(epsilon=None):
  31     global _epsilon
  32     if epsilon is not None:
  33         _epsilon = epsilon
  34
  35 ################################################################################
  36 # Path knots
  37 ################################################################################
  38
  39 class _knot:
  40
  41     """Internal knot as used in MetaPost (mp.c)"""
  42
  43     def __init__(self, x_pt, y_pt, ltype, lx_pt, ly_pt, rtype, rx_pt, ry_pt):
  44         self.x_pt = x_pt
  45         self.y_pt = y_pt
  46         self.ltype = ltype
  47         self.lx_pt = lx_pt
  48         self.ly_pt = ly_pt
  49         self.rtype = rtype
  50         self.rx_pt = rx_pt
  51         self.ry_pt = ry_pt
  52         # this is a linked list:
  53         self.next = self
  54
  55     def set_left_tension(self, tens):
  56         self.ly_pt = tens
  57     def set_right_tension(self, tens):
  58         self.ry_pt = tens
  59     def set_left_curl(self, curl):
  60         self.lx_pt = curl
  61     def set_right_curl(self, curl):
  62         self.rx_pt = curl
  63     set_left_given = set_left_curl
  64     set_right_given = set_right_curl
  65
  66     def left_tension(self):
  67         return self.ly_pt
  68     def right_tension(self):
  69         return self.ry_pt
  70     def left_curl(self):
  71         return self.lx_pt
  72     def right_curl(self):
  73         return self.rx_pt
  74     left_given = left_curl
  75     right_given = right_curl
  76
  77     def linked_len(self):
  78         """returns the length of a circularly linked list of knots"""
  79         n = 1
  80         p = self.next
  81         while not p is self:
  82             n += 1
  83             p = p.next
  84         return n
  85
  86     def __repr__(self):
  87         result = ""
  88         # left
  89         if self.ltype == mp_endpoint:
  90             pass
  91         elif self.ltype == mp_explicit:
  92             result += "{explicit %s %s}" % (self.lx_pt, self.ly_pt)
  93         elif self.ltype == mp_given:
  94             result += "{given %g tens %g}" % (self.lx_pt, self.ly_pt)
  95         elif self.ltype == mp_curl:
  96             result += "{curl %g tens %g}" % (self.lx_pt, self.ly_pt)
  97         elif self.ltype == mp_open:
  98             result += "{open tens %g}" % (self.ly_pt)
  99         elif self.ltype == mp_end_cycle:
 100             result += "{cycle tens %g}" % (self.ly_pt)
 101         result += "(%g %g)" % (self.x_pt, self.y_pt)
 102         # right
 103         if self.rtype == mp_endpoint:
 104             pass
 105         elif self.rtype == mp_explicit:
 106             result += "{explicit %g %g}" % (self.rx_pt, self.ry_pt)
 107         elif self.rtype == mp_given:
 108             result += "{given %g tens %g}" % (self.rx_pt, self.ry_pt)
 109         elif self.rtype == mp_curl:
 110             result += "{curl %g tens %g}" % (self.rx_pt, self.ry_pt)
 111         elif self.rtype == mp_open:
 112             result += "{open tens %g}" % (self.ry_pt)
 113         elif self.rtype == mp_end_cycle:
 114             result += "{cycle tens %g}" % (self.ry_pt)
 115         return result
 116
 117 class beginknot_pt(_knot):
 118
 119     """A knot which interrupts a path, or which allows to continue it with a straight line"""
 120
 121     def __init__(self, x_pt, y_pt, curl=1, angle=None):
 122         if angle is None:
 123             type, value = mp_curl, curl
 124         else:
 125             type, value = mp_given, angle
 126         # tensions are modified by the adjacent curve, but default is 1
 127         _knot.__init__(self, x_pt, y_pt, mp_endpoint, None, None, type, value, 1)
 128
 129 class beginknot(beginknot_pt):
 130
 131     def __init__(self, x, y, curl=1, angle=None):
 132         if not (angle is None):
 133             angle = radians(angle)
 134         beginknot_pt.__init__(self, unit.topt(x), unit.topt(y), curl, angle)
 135
 136 startknot = beginknot
 137
 138 class endknot_pt(_knot):
 139
 140     """A knot which interrupts a path, or which allows to continue it with a straight line"""
 141
 142     def __init__(self, x_pt, y_pt, curl=1, angle=None):
 143         if angle is None:
 144             type, value = mp_curl, curl
 145         else:
 146             type, value = mp_given, angle
 147         # tensions are modified by the adjacent curve, but default is 1
 148         _knot.__init__(self, x_pt, y_pt, type, value, 1, mp_endpoint, None, None)
 149
 150 class endknot(endknot_pt):
 151
 152     def __init__(self, x, y, curl=1, angle=None):
 153         if not (angle is None):
 154             angle = radians(angle)
 155         endknot_pt.__init__(self, unit.topt(x), unit.topt(y), curl, angle)
 156
 157 class smoothknot_pt(_knot):
 158
 159     """A knot with continous tangent and "mock" curvature."""
 160
 161     def __init__(self, x_pt, y_pt):
 162         # tensions are modified by the adjacent curve, but default is 1
 163         _knot.__init__(self, x_pt, y_pt, mp_open, None, 1, mp_open, None, 1)
 164
 165 class smoothknot(smoothknot_pt):
 166
 167     def __init__(self, x, y):
 168         smoothknot_pt.__init__(self, unit.topt(x), unit.topt(y))
 169
 170 knot = smoothknot
 171
 172 class roughknot_pt(_knot):
 173
 174     """A knot with noncontinous tangent."""
 175
 176     def __init__(self, x_pt, y_pt, lcurl=1, rcurl=None, langle=None, rangle=None):
 177         """Specify either the relative curvatures, or tangent angles left (l)
 178         or right (r) of the point."""
 179         if langle is None:
 180             ltype, lvalue = mp_curl, lcurl
 181         else:
 182             ltype, lvalue = mp_given, langle
 183         if rcurl is not None:
 184             rtype, rvalue = mp_curl, rcurl
 185         elif rangle is not None:
 186             rtype, rvalue = mp_given, rangle
 187         else:
 188             rtype, rvalue = ltype, lvalue
 189         # tensions are modified by the adjacent curve, but default is 1
 190         _knot.__init__(self, x_pt, y_pt, ltype, lvalue, 1, rtype, rvalue, 1)
 191
 192 class roughknot(roughknot_pt):
 193
 194     def __init__(self, x, y, lcurl=1, rcurl=None, langle=None, rangle=None):
 195         if langle is not None:
 196             langle = radians(langle)
 197         if rangle is not None:
 198             rangle = radians(rangle)
 199         roughknot_pt.__init__(self, unit.topt(x), unit.topt(y), lcurl, rcurl, langle, rangle)
 200
 201 ################################################################################
 202 # Path links
 203 ################################################################################
 204
 205 class _link:
 206     def set_knots(self, left_knot, right_knot):
 207         """Sets the internal properties of the metapost knots"""
 208         pass
 209
 210 class line(_link):
 211
 212     """A straight line"""
 213
 214     def __init__(self, keepangles=False):
 215         """The option keepangles will guarantee a continuous tangent. The
 216         curvature may become discontinuous, however"""
 217         self.keepangles = keepangles
 218
 219     def set_knots(self, left_knot, right_knot):
 220         left_knot.rtype = mp_endpoint
 221         right_knot.ltype = mp_endpoint
 222         left_knot.rx_pt, left_knot.ry_pt = None, None
 223         right_knot.lx_pt, right_knot.ly_pt = None, None
 224         if self.keepangles:
 225             angle = atan2(right_knot.y_pt-left_knot.y_pt, right_knot.x_pt-left_knot.x_pt)
 226             left_knot.ltype = mp_given
 227             left_knot.set_left_given(angle)
 228             right_knot.rtype = mp_given
 229             right_knot.set_right_given(angle)
 230
 231
 232 class controlcurve_pt(_link):
 233
 234     """A cubic Bezier curve which has its control points explicity set"""
 235
 236     def __init__(self, lcontrol_pt, rcontrol_pt):
 237         """The control points at the beginning (l) and the end (r) must be
 238         coordinate pairs"""
 239         self.lcontrol_pt = lcontrol_pt
 240         self.rcontrol_pt = rcontrol_pt
 241
 242     def set_knots(self, left_knot, right_knot):
 243         left_knot.rtype = mp_explicit
 244         right_knot.ltype = mp_explicit
 245         left_knot.rx_pt, left_knot.ry_pt = self.lcontrol_pt
 246         right_knot.lx_pt, right_knot.ly_pt = self.rcontrol_pt
 247
 248 class controlcurve(controlcurve_pt):
 249
 250     def __init__(self, lcontrol, rcontrol):
 251         controlcurve_pt.__init__(self, (unit.topt(lcontrol[0]), unit.topt(lcontrol[1])),
 252                                        (unit.topt(rcontrol[0]), unit.topt(rcontrol[1])))
 253
 254
 255 class tensioncurve(_link):
 256
 257     """A yet unspecified cubic Bezier curve"""
 258
 259     def __init__(self, ltension=1, latleast=False, rtension=None, ratleast=None):
 260         """The tension parameters indicate the tensions at the beginning (l)
 261         and the end (r) of the curve. Set the parameters (l/r)atleast to True
 262         if you want to avoid inflection points."""
 263         if rtension is None:
 264             rtension = ltension
 265         if ratleast is None:
 266             ratleast = latleast
 267         # make sure that tension >= 0.75 (p. 9 mpman.pdf)
 268         self.ltension = max(0.75, abs(ltension))
 269         self.rtension = max(0.75, abs(rtension))
 270         if latleast:
 271             self.ltension = -self.ltension
 272         if ratleast:
 273             self.rtension = -self.rtension
 274
 275     def set_knots(self, left_knot, right_knot):
 276         if left_knot.rtype <= mp_explicit or right_knot.ltype <= mp_explicit:
 277             raise Exception("metapost curve with given tension cannot have explicit knots")
 278         left_knot.set_right_tension(self.ltension)
 279         right_knot.set_left_tension(self.rtension)
 280
 281 curve = tensioncurve
 282
 283
 284 ################################################################################
 285 # Path creation class
 286 ################################################################################
 287
 288 class path(pathmodule.path):
 289
 290     """A MetaPost-like path, which finds an optimal way through given points.
 291
 292     At points, you can either specify a given tangent direction (angle in
 293     degrees) or a certain "curlyness" (relative to the curvature at the other
 294     end of a curve), or nothing. In the latter case, both the tangent and the
 295     "mock" curvature (an approximation to the real curvature, introduced by
 296     J.D. Hobby in MetaPost) will be continuous.
 297
 298     The shape of the cubic Bezier curves between two points is controlled by
 299     its "tension", unless you choose to set the control points manually."""
 300
 301     def __init__(self, elems, epsilon=None):
 302         """elems should contain metapost knots or links"""
 303         if epsilon is None:
 304             epsilon = _epsilon
 305         knots = []
 306         is_closed = True
 307         for i, elem in enumerate(elems):
 308             if isinstance(elem, _link):
 309                 elem.set_knots(elems[i-1], elems[(i+1)%len(elems)])
 310             elif isinstance(elem, _knot):
 311                 knots.append(elem)
 312                 if elem.ltype == mp_endpoint or elem.rtype == mp_endpoint:
 313                     is_closed = False
 314
 315         # link the knots among each other
 316         for i in range(len(knots)):
 317             knots[i-1].next = knots[i]
 318
 319         # determine the control points
 320         mp_make_choices(knots[0], epsilon)
 321
 322         pathmodule.path.__init__(self)
 323         # build up the path
 324         do_moveto = True
 325         do_lineto = False
 326         do_curveto = False
 327         prev = None
 328         for i, elem in enumerate(elems):
 329             if isinstance(elem, _link):
 330                 do_moveto = False
 331                 if isinstance(elem, line):
 332                     do_lineto, do_curveto = True, False
 333                 else:
 334                     do_lineto, do_curveto = False, True
 335             elif isinstance(elem, _knot):
 336                 if do_moveto:
 337                     self.append(pathmodule.moveto_pt(elem.x_pt, elem.y_pt))
 338                 if do_lineto:
 339                     self.append(pathmodule.lineto_pt(elem.x_pt, elem.y_pt))
 340                 elif do_curveto:
 341                     self.append(pathmodule.curveto_pt(prev.rx_pt, prev.ry_pt, elem.lx_pt, elem.ly_pt, elem.x_pt, elem.y_pt))
 342                 do_moveto = True
 343                 do_lineto = False
 344                 do_curveto = False
 345                 prev = elem
 346
 347         # close the path if necessary
 348         if knots[0].ltype == mp_explicit:
 349             elem = knots[0]
 350             if do_lineto and is_closed:
 351                 self.append(pathmodule.closepath())
 352             elif do_curveto:
 353                 self.append(pathmodule.curveto_pt(prev.rx_pt, prev.ry_pt, elem.lx_pt, elem.ly_pt, elem.x_pt, elem.y_pt))
 354                 if is_closed:
 355                     self.append(pathmodule.closepath())
 356