pyx/box.py

   1 #!/usr/bin/env python
   2 #
   3 #
   4 # Copyright (C) 2002-2003 Jörg Lehmann <joergl@users.sourceforge.net>
   5 # Copyright (C) 2002-2003 André Wobst <wobsta@users.sourceforge.net>
   6 #
   7 # This file is part of PyX (http://pyx.sourceforge.net/).
   8 #
   9 # PyX is free software; you can redistribute it and/or modify
  10 # it under the terms of the GNU General Public License as published by
  11 # the Free Software Foundation; either version 2 of the License, or
  12 # (at your option) any later version.
  13 #
  14 # PyX is distributed in the hope that it will be useful,
  15 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  16 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  17 # GNU General Public License for more details.
  18 #
  19 # You should have received a copy of the GNU General Public License
  20 # along with PyX; if not, write to the Free Software
  21 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  22
  23
  24 import types, re, math, string, sys
  25 import bbox, path, unit, trafo, helper
  26
  27
  28 class BoxCrossError(Exception): pass
  29
  30 class _polygon:
  31
  32     def __init__(self, corners=None, center=None):
  33         self.corners = corners
  34         self.center = center
  35         if self.center is None:
  36             self._ensurecenter()
  37
  38     def _ensurecenter(self):
  39         if self.center is None:
  40             self.center = [0,0]
  41             for corn in self.corners:
  42                 self.center = [self.center[0] + corn[0], self.center[1] + corn[1]]
  43             self.center = [self.center[0]/len(self.corners), self.center[1]/len(self.corners)]
  44
  45     def path(self, centerradius=None, bezierradius=None, beziersoftness=1):
  46         pathels = []
  47         if centerradius is not None and self.center is not None:
  48             r = unit.topt(unit.length(centerradius, default_type="v"))
  49             pathels.append(path._arc(self.center[0], self.center[1], r, 0, 360))
  50             pathels.append(path.closepath())
  51         if bezierradius is None:
  52             pathels.append(path._moveto(self.corners[0][0], self.corners[0][1]))
  53             for x, y in self.corners[1:]:
  54                 pathels.append(path._lineto(x, y))
  55             pathels.append(path.closepath())
  56         else:
  57             # curved box plotting by Michael Schindler
  58             l = len(self.corners)
  59             if helper.issequence(beziersoftness):
  60                 if not (len(beziersoftness) == l): raise ValueError
  61             else:
  62                 beziersoftness = [float(beziersoftness)]*l
  63             if helper.issequence(bezierradius):
  64                 r = list(bezierradius)
  65                 if len(bezierradius) == l:
  66                     for oner, i in zip(r, range(l)):
  67                         if helper.issequence(oner):
  68                             if len(oner) == 2:
  69                                 r[i] = [unit.topt(oner[0]), unit.topt(oner[1])]
  70                             else: raise ValueError
  71                         else:
  72                             r[i] = [unit.topt(oner)]*2
  73                 else: raise ValueError
  74             else:
  75                 r = [[unit.topt(bezierradius)]*2]*l
  76             for i in range(l):
  77                 c = self.corners[i]
  78                 def normed(*v):
  79                     n = math.sqrt(v[0] * v[0] + v[1] * v[1])
  80                     return v[0] / n, v[1] / n
  81                 d1 = normed(self.corners[(i - 1 + l) % l][0] - c[0],
  82                             self.corners[(i - 1 + l) % l][1] - c[1])
  83                 d2 = normed(self.corners[(i + 1 + l) % l][0] - c[0],
  84                             self.corners[(i + 1 + l) % l][1] - c[1])
  85                 dc = normed(d1[0] + d2[0], d1[1] + d2[1])
  86                 f = 0.3192 * beziersoftness[i]
  87                 g = (15.0 * f + math.sqrt(-15.0*f*f + 24.0*f))/12.0
  88                 f1 = c[0] + f * d1[0] * r[i][0], c[1] + f * d1[1] * r[i][0]
  89                 f2 = c[0] + f * d2[0] * r[i][1], c[1] + f * d2[1] * r[i][1]
  90                 g1 = c[0] + g * d1[0] * r[i][0], c[1] + g * d1[1] * r[i][0]
  91                 g2 = c[0] + g * d2[0] * r[i][1], c[1] + g * d2[1] * r[i][1]
  92                 d1 = c[0] +     d1[0] * r[i][0], c[1] +     d1[1] * r[i][0]
  93                 d2 = c[0] +     d2[0] * r[i][1], c[1] +     d2[1] * r[i][1]
  94                 e  = 0.5 * (f1[0] + f2[0]), 0.5 * (f1[1] + f2[1])
  95                 if i:
  96                     pathels.append(path._lineto(*d1))
  97                 else:
  98                     pathels.append(path._moveto(*d1))
  99                 pathels.append(path._curveto(*(g1 + f1 + e)))
 100                 pathels.append(path._curveto(*(f2 + g2 + d2)))
 101             pathels.append(path.closepath())
 102         return path.path(*pathels)
 103
 104     def transform(self, *trafos):
 105         for trafo in trafos:
 106             if self.center is not None:
 107                 self.center = trafo._apply(*self.center)
 108             self.corners = [trafo._apply(*point) for point in self.corners]
 109
 110     def reltransform(self, *trafos):
 111         if self.center is not None:
 112             trafos = ([trafo._translate(-self.center[0], -self.center[1])] +
 113                       list(trafos) +
 114                       [trafo._translate(self.center[0], self.center[1])])
 115         self.transform(*trafos)
 116
 117     def successivepointnumbers(self):
 118         return [i and (i - 1, i) or (len(self.corners) - 1, 0) for i in range(len(self.corners))]
 119
 120     def successivepoints(self):
 121         return [(self.corners[i], self.corners[j]) for i, j in self.successivepointnumbers()]
 122
 123     def _circlealignlinevector(self, a, dx, dy, ex, ey, fx, fy, epsilon=1e-10):
 124         cx, cy = self.center
 125         gx, gy = ex - fx, ey - fy # direction vector
 126         if gx*gx + gy*gy < epsilon: # zero line length
 127             return None             # no solution -> return None
 128         rsplit = (dx*gx + dy*gy) * 1.0 / (gx*gx + gy*gy)
 129         bx, by = dx - gx * rsplit, dy - gy * rsplit
 130         if bx*bx + by*by < epsilon: # zero projection
 131             return None             # no solution -> return None
 132         if bx*gy - by*gx < 0: # half space
 133             return None       # no solution -> return None
 134         sfactor = math.sqrt((dx*dx + dy*dy) / (bx*bx + by*by))
 135         bx, by = a * bx * sfactor, a * by * sfactor
 136         alpha = ((bx+cx-ex)*dy - (by+cy-ey)*dx) * 1.0 / (gy*dx - gx*dy)
 137         if alpha > 0 - epsilon and alpha < 1 + epsilon:
 138                 beta = ((ex-bx-cx)*gy - (ey-by-cy)*gx) * 1.0 / (gx*dy - gy*dx)
 139                 return beta*dx, beta*dy # valid solution -> return align tuple
 140         # crossing point at the line, but outside a valid range
 141         if alpha < 0:
 142             return 0 # crossing point outside e
 143         return 1 # crossing point outside f
 144
 145     def _linealignlinevector(self, a, dx, dy, ex, ey, fx, fy, epsilon=1e-10):
 146         cx, cy = self.center
 147         gx, gy = ex - fx, ey - fy # direction vector
 148         if gx*gx + gy*gy < epsilon: # zero line length
 149             return None             # no solution -> return None
 150         if gy*dx - gx*dy < -epsilon: # half space
 151             return None              # no solution -> return None
 152         if dx*gx + dy*gy > epsilon or dx*gx + dy*gy < -epsilon:
 153             if dx*gx + dy*gy < 0: # angle bigger 90 degree
 154                 return 0 # use point e
 155             return 1 # use point f
 156         # a and g are othorgonal
 157         alpha = ((a*dx+cx-ex)*dy - (a*dy+cy-ey)*dx) * 1.0 / (gy*dx - gx*dy)
 158         if alpha > 0 - epsilon and alpha < 1 + epsilon:
 159             beta = ((ex-a*dx-cx)*gy - (ey-a*dy-cy)*gx) * 1.0 / (gx*dy - gy*dx)
 160             return beta*dx, beta*dy # valid solution -> return align tuple
 161         # crossing point at the line, but outside a valid range
 162         if alpha < 0:
 163             return 0 # crossing point outside e
 164         return 1 # crossing point outside f
 165
 166     def _circlealignpointvector(self, a, dx, dy, px, py, epsilon=1e-10):
 167         if a*a < epsilon:
 168             return None
 169         cx, cy = self.center
 170         p = 2 * ((px-cx)*dx + (py-cy)*dy)
 171         q = ((px-cx)*(px-cx) + (py-cy)*(py-cy) - a*a)
 172         if p*p/4 - q < 0:
 173             return None
 174         if a > 0:
 175             alpha = - p / 2 + math.sqrt(p*p/4 - q)
 176         else:
 177             alpha = - p / 2 - math.sqrt(p*p/4 - q)
 178         return alpha*dx, alpha*dy
 179
 180     def _linealignpointvector(self, a, dx, dy, px, py):
 181         cx, cy = self.center
 182         beta = (a*dx+cx-px)*dy - (a*dy+cy-py)*dx
 183         return a*dx - beta*dy - px + cx, a*dy + beta*dx - py + cy
 184
 185     def _alignvector(self, a, dx, dy, alignlinevector, alignpointvector):
 186         n = math.sqrt(dx * dx + dy * dy)
 187         dx, dy = dx / n, dy / n
 188         linevectors = map(lambda (p1, p2), self=self, a=a, dx=dx, dy=dy, alignlinevector=alignlinevector:
 189                                 alignlinevector(a, dx, dy, *(p1 + p2)), self.successivepoints())
 190         for linevector in linevectors:
 191             if type(linevector) is types.TupleType:
 192                 return linevector
 193         for i, j in self.successivepointnumbers():
 194             l1, l2 = linevectors[i], linevectors[j]
 195             if (l1 is not None or l2 is not None) and (l1 == 1 or l1 is None) and (l2 == 0 or l2 is None):
 196                 return alignpointvector(a, dx, dy, *self.successivepoints()[j][0])
 197         return a*dx, a*dy
 198
 199     def _circlealignvector(self, a, dx, dy):
 200         return self._alignvector(a, dx, dy, self._circlealignlinevector, self._circlealignpointvector)
 201
 202     def _linealignvector(self, a, dx, dy):
 203         return self._alignvector(a, dx, dy, self._linealignlinevector, self._linealignpointvector)
 204
 205     def circlealignvector(self, a, dx, dy):
 206         return map(unit.t_pt, self._circlealignvector(unit.topt(a), dx, dy))
 207
 208     def linealignvector(self, a, dx, dy):
 209         return map(unit.t_pt, self._linealignvector(unit.topt(a), dx, dy))
 210
 211     def _circlealign(self, *args):
 212         self.transform(trafo._translate(*self._circlealignvector(*args)))
 213         return self
 214
 215     def _linealign(self, *args):
 216         self.transform(trafo._translate(*self._linealignvector(*args)))
 217         return self
 218
 219     def circlealign(self, *args):
 220         self.transform(trafo.translate(*self.circlealignvector(*args)))
 221         return self
 222
 223     def linealign(self, *args):
 224         self.transform(trafo.translate(*self.linealignvector(*args)))
 225         return self
 226
 227     def _extent(self, dx, dy):
 228         n = math.sqrt(dx * dx + dy * dy)
 229         dx, dy = dx / n, dy / n
 230         oldcenter = self.center
 231         if self.center is None:
 232             self.center = 0, 0
 233         x1, y1 = self._linealignvector(0, dx, dy)
 234         x2, y2 = self._linealignvector(0, -dx, -dy)
 235         self.center = oldcenter
 236         return (x1-x2)*dx + (y1-y2)*dy
 237
 238     def extent(self, dx, dy):
 239         return unit.t_pt(self._extent(dx, dy))
 240
 241     def _pointdistance(self, x, y):
 242         result = None
 243         for p1, p2 in self.successivepoints():
 244             gx, gy = p2[0] - p1[0], p2[1] - p1[1]
 245             if gx * gx + gy * gy < 1e-10:
 246                 dx, dy = p1[0] - x, p1[1] - y
 247             else:
 248                 a = (gx * (x - p1[0]) + gy * (y - p1[1])) / (gx * gx + gy * gy)
 249                 if a < 0:
 250                     dx, dy = p1[0] - x, p1[1] - y
 251                 elif a > 1:
 252                     dx, dy = p2[0] - x, p2[1] - y
 253                 else:
 254                     dx, dy = x - p1[0] - a * gx, y - p1[1] - a * gy
 255             new = math.sqrt(dx * dx + dy * dy)
 256             if result is None or new < result:
 257                 result = new
 258         return result
 259
 260     def pointdistance(self, x, y):
 261         return unit.t_pt(self._pointdistance(unit.topt(x), unit.topt(y)))
 262
 263     def _boxdistance(self, other, epsilon=1e-10):
 264         # XXX: boxes crossing and distance calculation is O(N^2)
 265         for p1, p2 in self.successivepoints():
 266             for p3, p4 in other.successivepoints():
 267                 a = (p4[1] - p3[1]) * (p3[0] - p1[0]) - (p4[0] - p3[0]) * (p3[1] - p1[1])
 268                 b = (p2[1] - p1[1]) * (p3[0] - p1[0]) - (p2[0] - p1[0]) * (p3[1] - p1[1])
 269                 c = (p2[0] - p1[0]) * (p4[1] - p3[1]) - (p2[1] - p1[1]) * (p4[0] - p3[0])
 270                 if (abs(c) > 1e-10 and
 271                     a / c > -epsilon and a / c < 1 + epsilon and
 272                     b / c > -epsilon and b / c < 1 + epsilon):
 273                     raise BoxCrossError
 274         result = None
 275         for x, y in other.corners:
 276             new = self._pointdistance(x, y)
 277             if result is None or new < result:
 278                 result = new
 279         for x, y in self.corners:
 280             new = other._pointdistance(x, y)
 281             if result is None or new < result:
 282                 result = new
 283         return result
 284
 285     def boxdistance(self, other):
 286         return unit.t_pt(self._boxdistance(other))
 287
 288     def bbox(self):
 289         return bbox._bbox(min([x[0] for x in self.corners]),
 290                           min([x[1] for x in self.corners]),
 291                           max([x[0] for x in self.corners]),
 292                           max([x[1] for x in self.corners]))
 293
 294
 295 def _genericalignequal(method, polygons, a, dx, dy):
 296     vec = None
 297     for p in polygons:
 298         v = method(p, a, dx, dy)
 299         if vec is None or vec[0] * dx + vec[1] * dy < v[0] * dx + v[1] * dy:
 300             vec = v
 301     for p in polygons:
 302         p.transform(trafo._translate(*vec))
 303
 304
 305 def _circlealignequal(polygons, *args):
 306     _genericalignequal(_polygon._circlealignvector, polygons, *args)
 307
 308 def _linealignequal(polygons, *args):
 309     _genericalignequal(_polygon._linealignvector, polygons, *args)
 310
 311 def circlealignequal(polygons, a, *args):
 312     _circlealignequal(polygons, unit.topt(a), *args)
 313
 314 def linealignequal(polygons, a, *args):
 315     _linealignequal(polygons, unit.topt(a), *args)
 316
 317
 318 def _tile(polygons, a, dx, dy):
 319     maxextent = polygons[0]._extent(dx, dy)
 320     for p in polygons[1:]:
 321         extent = p._extent(dx, dy)
 322         if extent > maxextent:
 323             maxextent = extent
 324     d = 0
 325     for p in polygons:
 326         p.transform(trafo._translate(d*dx, d*dy))
 327         d += maxextent + a
 328
 329
 330 def tile(polygons, a, dx, dy):
 331     _tile(polygons, unit.topt(a), dx, dy)
 332
 333
 334 class polygon(_polygon):
 335
 336     def __init__(self, corners=None, center=None, **args):
 337         corners = [[unit.topt(x) for x in corner] for corner in corners]
 338         if center is not None:
 339             center = map(unit.topt, center)
 340         _polygon.__init__(self, corners=corners, center=center, **args)
 341
 342
 343 class _rect(_polygon):
 344
 345     def __init__(self, x, y, width, height, relcenter=(0, 0), abscenter=(0, 0),
 346                        corners=helper.nodefault, center=helper.nodefault, **args):
 347         if corners != helper.nodefault or center != helper.nodefault:
 348             raise ValueError
 349         _polygon.__init__(self, corners=((x, y),
 350                                          (x + width, y),
 351                                          (x + width, y + height),
 352                                          (x, y + height)),
 353                                 center=(x + relcenter[0] * width + abscenter[0],
 354                                         y + relcenter[1] * height + abscenter[1]),
 355                                 **args)
 356
 357
 358 class rect(_rect):
 359
 360     def __init__(self, x, y, width, height, relcenter=(0, 0), abscenter=(0, 0), **args):
 361         _rect.__init__(self, unit.topt(x), unit.topt(y), unit.topt(width), unit.topt(height),
 362                              relcenter=relcenter, abscenter=(unit.topt(abscenter[0]), unit.topt(abscenter[1])), **args)
 363