pyx/box.py

   1 #!/usr/bin/env python
   2 # -*- coding: ISO-8859-1 -*-
   3 #
   4 #
   5 # Copyright (C) 2002-2003 Jörg Lehmann <joergl@users.sourceforge.net>
   6 # Copyright (C) 2002-2003 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  23
  24
  25 import types, math
  26 import bbox, path, unit, trafo, helper
  27
  28
  29 class BoxCrossError(Exception): pass
  30
  31 class _polygon:
  32
  33     def __init__(self, corners=None, center=None):
  34         self.corners = corners
  35         self.center = center
  36         if self.center is None:
  37             self._ensurecenter()
  38
  39     def _ensurecenter(self):
  40         if self.center is None:
  41             self.center = [0,0]
  42             for corn in self.corners:
  43                 self.center = [self.center[0] + corn[0], self.center[1] + corn[1]]
  44             self.center = [self.center[0]/len(self.corners), self.center[1]/len(self.corners)]
  45
  46     def path(self, centerradius=None, bezierradius=None, beziersoftness=1):
  47         pathels = []
  48         if centerradius is not None and self.center is not None:
  49             r = unit.topt(unit.length(centerradius, default_type="v"))
  50             pathels.append(path._arc(self.center[0], self.center[1], r, 0, 360))
  51             pathels.append(path.closepath())
  52         if bezierradius is None:
  53             pathels.append(path._moveto(self.corners[0][0], self.corners[0][1]))
  54             for x, y in self.corners[1:]:
  55                 pathels.append(path._lineto(x, y))
  56             pathels.append(path.closepath())
  57         else:
  58             # curved box plotting by Michael Schindler
  59             l = len(self.corners)
  60             if helper.issequence(beziersoftness):
  61                 if not (len(beziersoftness) == l): raise ValueError
  62             else:
  63                 beziersoftness = [float(beziersoftness)]*l
  64             if helper.issequence(bezierradius):
  65                 r = list(bezierradius)
  66                 if len(bezierradius) == l:
  67                     for oner, i in zip(r, range(l)):
  68                         if helper.issequence(oner):
  69                             if len(oner) == 2:
  70                                 r[i] = [unit.topt(oner[0]), unit.topt(oner[1])]
  71                             else: raise ValueError
  72                         else:
  73                             r[i] = [unit.topt(oner)]*2
  74                 else: raise ValueError
  75             else:
  76                 r = [[unit.topt(bezierradius)]*2]*l
  77             for i in range(l):
  78                 c = self.corners[i]
  79                 def normed(*v):
  80                     n = math.sqrt(v[0] * v[0] + v[1] * v[1])
  81                     return v[0] / n, v[1] / n
  82                 d1 = normed(self.corners[(i - 1 + l) % l][0] - c[0],
  83                             self.corners[(i - 1 + l) % l][1] - c[1])
  84                 d2 = normed(self.corners[(i + 1 + l) % l][0] - c[0],
  85                             self.corners[(i + 1 + l) % l][1] - c[1])
  86                 dc = normed(d1[0] + d2[0], d1[1] + d2[1])
  87                 f = 0.3192 * beziersoftness[i]
  88                 g = (15.0 * f + math.sqrt(-15.0*f*f + 24.0*f))/12.0
  89                 f1 = c[0] + f * d1[0] * r[i][0], c[1] + f * d1[1] * r[i][0]
  90                 f2 = c[0] + f * d2[0] * r[i][1], c[1] + f * d2[1] * r[i][1]
  91                 g1 = c[0] + g * d1[0] * r[i][0], c[1] + g * d1[1] * r[i][0]
  92                 g2 = c[0] + g * d2[0] * r[i][1], c[1] + g * d2[1] * r[i][1]
  93                 d1 = c[0] +     d1[0] * r[i][0], c[1] +     d1[1] * r[i][0]
  94                 d2 = c[0] +     d2[0] * r[i][1], c[1] +     d2[1] * r[i][1]
  95                 e  = 0.5 * (f1[0] + f2[0]), 0.5 * (f1[1] + f2[1])
  96                 if i:
  97                     pathels.append(path._lineto(*d1))
  98                 else:
  99                     pathels.append(path._moveto(*d1))
 100                 pathels.append(path._curveto(*(g1 + f1 + e)))
 101                 pathels.append(path._curveto(*(f2 + g2 + d2)))
 102             pathels.append(path.closepath())
 103         return path.path(*pathels)
 104
 105     def transform(self, *trafos):
 106         for trafo in trafos:
 107             if self.center is not None:
 108                 self.center = trafo._apply(*self.center)
 109             self.corners = [trafo._apply(*point) for point in self.corners]
 110
 111     def reltransform(self, *trafos):
 112         if self.center is not None:
 113             trafos = ([trafo._translate(-self.center[0], -self.center[1])] +
 114                       list(trafos) +
 115                       [trafo._translate(self.center[0], self.center[1])])
 116         self.transform(*trafos)
 117
 118     def successivepointnumbers(self):
 119         return [i and (i - 1, i) or (len(self.corners) - 1, 0) for i in range(len(self.corners))]
 120
 121     def successivepoints(self):
 122         return [(self.corners[i], self.corners[j]) for i, j in self.successivepointnumbers()]
 123
 124     def _circlealignlinevector(self, a, dx, dy, ex, ey, fx, fy, epsilon=1e-10):
 125         cx, cy = self.center
 126         gx, gy = ex - fx, ey - fy # direction vector
 127         if gx*gx + gy*gy < epsilon: # zero line length
 128             return None             # no solution -> return None
 129         rsplit = (dx*gx + dy*gy) * 1.0 / (gx*gx + gy*gy)
 130         bx, by = dx - gx * rsplit, dy - gy * rsplit
 131         if bx*bx + by*by < epsilon: # zero projection
 132             return None             # no solution -> return None
 133         if bx*gy - by*gx < 0: # half space
 134             return None       # no solution -> return None
 135         sfactor = math.sqrt((dx*dx + dy*dy) / (bx*bx + by*by))
 136         bx, by = a * bx * sfactor, a * by * sfactor
 137         alpha = ((bx+cx-ex)*dy - (by+cy-ey)*dx) * 1.0 / (gy*dx - gx*dy)
 138         if alpha > 0 - epsilon and alpha < 1 + epsilon:
 139                 beta = ((ex-bx-cx)*gy - (ey-by-cy)*gx) * 1.0 / (gx*dy - gy*dx)
 140                 return beta*dx, beta*dy # valid solution -> return align tuple
 141         # crossing point at the line, but outside a valid range
 142         if alpha < 0:
 143             return 0 # crossing point outside e
 144         return 1 # crossing point outside f
 145
 146     def _linealignlinevector(self, a, dx, dy, ex, ey, fx, fy, epsilon=1e-10):
 147         cx, cy = self.center
 148         gx, gy = ex - fx, ey - fy # direction vector
 149         if gx*gx + gy*gy < epsilon: # zero line length
 150             return None             # no solution -> return None
 151         if gy*dx - gx*dy < -epsilon: # half space
 152             return None              # no solution -> return None
 153         if dx*gx + dy*gy > epsilon or dx*gx + dy*gy < -epsilon:
 154             if dx*gx + dy*gy < 0: # angle bigger 90 degree
 155                 return 0 # use point e
 156             return 1 # use point f
 157         # a and g are othorgonal
 158         alpha = ((a*dx+cx-ex)*dy - (a*dy+cy-ey)*dx) * 1.0 / (gy*dx - gx*dy)
 159         if alpha > 0 - epsilon and alpha < 1 + epsilon:
 160             beta = ((ex-a*dx-cx)*gy - (ey-a*dy-cy)*gx) * 1.0 / (gx*dy - gy*dx)
 161             return beta*dx, beta*dy # valid solution -> return align tuple
 162         # crossing point at the line, but outside a valid range
 163         if alpha < 0:
 164             return 0 # crossing point outside e
 165         return 1 # crossing point outside f
 166
 167     def _circlealignpointvector(self, a, dx, dy, px, py, epsilon=1e-10):
 168         if a*a < epsilon:
 169             return None
 170         cx, cy = self.center
 171         p = 2 * ((px-cx)*dx + (py-cy)*dy)
 172         q = ((px-cx)*(px-cx) + (py-cy)*(py-cy) - a*a)
 173         if p*p/4 - q < 0:
 174             return None
 175         if a > 0:
 176             alpha = - p / 2 + math.sqrt(p*p/4 - q)
 177         else:
 178             alpha = - p / 2 - math.sqrt(p*p/4 - q)
 179         return alpha*dx, alpha*dy
 180
 181     def _linealignpointvector(self, a, dx, dy, px, py):
 182         cx, cy = self.center
 183         beta = (a*dx+cx-px)*dy - (a*dy+cy-py)*dx
 184         return a*dx - beta*dy - px + cx, a*dy + beta*dx - py + cy
 185
 186     def _alignvector(self, a, dx, dy, alignlinevector, alignpointvector):
 187         n = math.sqrt(dx * dx + dy * dy)
 188         dx, dy = dx / n, dy / n
 189         linevectors = map(lambda (p1, p2), self=self, a=a, dx=dx, dy=dy, alignlinevector=alignlinevector:
 190                                 alignlinevector(a, dx, dy, *(p1 + p2)), self.successivepoints())
 191         for linevector in linevectors:
 192             if type(linevector) is types.TupleType:
 193                 return linevector
 194         for i, j in self.successivepointnumbers():
 195             l1, l2 = linevectors[i], linevectors[j]
 196             if (l1 is not None or l2 is not None) and (l1 == 1 or l1 is None) and (l2 == 0 or l2 is None):
 197                 return alignpointvector(a, dx, dy, *self.successivepoints()[j][0])
 198         return a*dx, a*dy
 199
 200     def _circlealignvector(self, a, dx, dy):
 201         return self._alignvector(a, dx, dy, self._circlealignlinevector, self._circlealignpointvector)
 202
 203     def _linealignvector(self, a, dx, dy):
 204         return self._alignvector(a, dx, dy, self._linealignlinevector, self._linealignpointvector)
 205
 206     def circlealignvector(self, a, dx, dy):
 207         return map(unit.t_pt, self._circlealignvector(unit.topt(a), dx, dy))
 208
 209     def linealignvector(self, a, dx, dy):
 210         return map(unit.t_pt, self._linealignvector(unit.topt(a), dx, dy))
 211
 212     def _circlealign(self, *args):
 213         self.transform(trafo._translate(*self._circlealignvector(*args)))
 214         return self
 215
 216     def _linealign(self, *args):
 217         self.transform(trafo._translate(*self._linealignvector(*args)))
 218         return self
 219
 220     def circlealign(self, *args):
 221         self.transform(trafo.translate(*self.circlealignvector(*args)))
 222         return self
 223
 224     def linealign(self, *args):
 225         self.transform(trafo.translate(*self.linealignvector(*args)))
 226         return self
 227
 228     def _extent(self, dx, dy):
 229         n = math.sqrt(dx * dx + dy * dy)
 230         dx, dy = dx / n, dy / n
 231         oldcenter = self.center
 232         if self.center is None:
 233             self.center = 0, 0
 234         x1, y1 = self._linealignvector(0, dx, dy)
 235         x2, y2 = self._linealignvector(0, -dx, -dy)
 236         self.center = oldcenter
 237         return (x1-x2)*dx + (y1-y2)*dy
 238
 239     def extent(self, dx, dy):
 240         return unit.t_pt(self._extent(dx, dy))
 241
 242     def _pointdistance(self, x, y):
 243         result = None
 244         for p1, p2 in self.successivepoints():
 245             gx, gy = p2[0] - p1[0], p2[1] - p1[1]
 246             if gx * gx + gy * gy < 1e-10:
 247                 dx, dy = p1[0] - x, p1[1] - y
 248             else:
 249                 a = (gx * (x - p1[0]) + gy * (y - p1[1])) / (gx * gx + gy * gy)
 250                 if a < 0:
 251                     dx, dy = p1[0] - x, p1[1] - y
 252                 elif a > 1:
 253                     dx, dy = p2[0] - x, p2[1] - y
 254                 else:
 255                     dx, dy = x - p1[0] - a * gx, y - p1[1] - a * gy
 256             new = math.sqrt(dx * dx + dy * dy)
 257             if result is None or new < result:
 258                 result = new
 259         return result
 260
 261     def pointdistance(self, x, y):
 262         return unit.t_pt(self._pointdistance(unit.topt(x), unit.topt(y)))
 263
 264     def _boxdistance(self, other, epsilon=1e-10):
 265         # XXX: boxes crossing and distance calculation is O(N^2)
 266         for p1, p2 in self.successivepoints():
 267             for p3, p4 in other.successivepoints():
 268                 a = (p4[1] - p3[1]) * (p3[0] - p1[0]) - (p4[0] - p3[0]) * (p3[1] - p1[1])
 269                 b = (p2[1] - p1[1]) * (p3[0] - p1[0]) - (p2[0] - p1[0]) * (p3[1] - p1[1])
 270                 c = (p2[0] - p1[0]) * (p4[1] - p3[1]) - (p2[1] - p1[1]) * (p4[0] - p3[0])
 271                 if (abs(c) > 1e-10 and
 272                     a / c > -epsilon and a / c < 1 + epsilon and
 273                     b / c > -epsilon and b / c < 1 + epsilon):
 274                     raise BoxCrossError
 275         result = None
 276         for x, y in other.corners:
 277             new = self._pointdistance(x, y)
 278             if result is None or new < result:
 279                 result = new
 280         for x, y in self.corners:
 281             new = other._pointdistance(x, y)
 282             if result is None or new < result:
 283                 result = new
 284         return result
 285
 286     def boxdistance(self, other):
 287         return unit.t_pt(self._boxdistance(other))
 288
 289     def bbox(self):
 290         return bbox._bbox(min([x[0] for x in self.corners]),
 291                           min([x[1] for x in self.corners]),
 292                           max([x[0] for x in self.corners]),
 293                           max([x[1] for x in self.corners]))
 294
 295
 296 def _genericalignequal(method, polygons, a, dx, dy):
 297     vec = None
 298     for p in polygons:
 299         v = method(p, a, dx, dy)
 300         if vec is None or vec[0] * dx + vec[1] * dy < v[0] * dx + v[1] * dy:
 301             vec = v
 302     for p in polygons:
 303         p.transform(trafo._translate(*vec))
 304
 305
 306 def _circlealignequal(polygons, *args):
 307     _genericalignequal(_polygon._circlealignvector, polygons, *args)
 308
 309 def _linealignequal(polygons, *args):
 310     _genericalignequal(_polygon._linealignvector, polygons, *args)
 311
 312 def circlealignequal(polygons, a, *args):
 313     _circlealignequal(polygons, unit.topt(a), *args)
 314
 315 def linealignequal(polygons, a, *args):
 316     _linealignequal(polygons, unit.topt(a), *args)
 317
 318
 319 def _tile(polygons, a, dx, dy):
 320     maxextent = polygons[0]._extent(dx, dy)
 321     for p in polygons[1:]:
 322         extent = p._extent(dx, dy)
 323         if extent > maxextent:
 324             maxextent = extent
 325     d = 0
 326     for p in polygons:
 327         p.transform(trafo._translate(d*dx, d*dy))
 328         d += maxextent + a
 329
 330
 331 def tile(polygons, a, dx, dy):
 332     _tile(polygons, unit.topt(a), dx, dy)
 333
 334
 335 class polygon(_polygon):
 336
 337     def __init__(self, corners=None, center=None, **args):
 338         corners = [[unit.topt(x) for x in corner] for corner in corners]
 339         if center is not None:
 340             center = map(unit.topt, center)
 341         _polygon.__init__(self, corners=corners, center=center, **args)
 342
 343
 344 class _rect(_polygon):
 345
 346     def __init__(self, x, y, width, height, relcenter=(0, 0), abscenter=(0, 0),
 347                        corners=helper.nodefault, center=helper.nodefault, **args):
 348         if corners != helper.nodefault or center != helper.nodefault:
 349             raise ValueError
 350         _polygon.__init__(self, corners=((x, y),
 351                                          (x + width, y),
 352                                          (x + width, y + height),
 353                                          (x, y + height)),
 354                                 center=(x + relcenter[0] * width + abscenter[0],
 355                                         y + relcenter[1] * height + abscenter[1]),
 356                                 **args)
 357
 358
 359 class rect(_rect):
 360
 361     def __init__(self, x, y, width, height, relcenter=(0, 0), abscenter=(0, 0), **args):
 362         _rect.__init__(self, unit.topt(x), unit.topt(y), unit.topt(width), unit.topt(height),
 363                              relcenter=relcenter, abscenter=(unit.topt(abscenter[0]), unit.topt(abscenter[1])), **args)
 364