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             # make beziersoftnes a list of length l
  61             if helper.issequence(beziersoftness):
  62                 if not (len(beziersoftness) == l): raise ValueError
  63             else:
  64                 beziersoftness = [float(beziersoftness)]*l
  65             # make bezierradius a list (lenght l) of 2-tuples
  66             if helper.issequence(bezierradius):
  67                 r = list(bezierradius)
  68                 if len(bezierradius) == l:
  69                     for oner, i in zip(r, range(l)):
  70                         if helper.issequence(oner):
  71                             if len(oner) == 2:
  72                                 r[i] = [unit.topt(oner[0]), unit.topt(oner[1])]
  73                             else: raise ValueError
  74                         else:
  75                             r[i] = [unit.topt(oner)]*2
  76                 else: raise ValueError
  77             else:
  78                 r = [[unit.topt(bezierradius)]*2]*l
  79             for i in range(l):
  80                 c = self.corners[i]
  81                 def normed(*v):
  82                     n = math.sqrt(v[0] * v[0] + v[1] * v[1])
  83                     return v[0] / n, v[1] / n
  84                 d1 = normed(self.corners[(i - 1 + l) % l][0] - c[0],
  85                             self.corners[(i - 1 + l) % l][1] - c[1])
  86                 d2 = normed(self.corners[(i + 1 + l) % l][0] - c[0],
  87                             self.corners[(i + 1 + l) % l][1] - c[1])
  88                 dc = normed(d1[0] + d2[0], d1[1] + d2[1])
  89                 f = 0.3192 * beziersoftness[i]
  90                 g = (15.0 * f + math.sqrt(-15.0*f*f + 24.0*f))/12.0
  91                 f1 = c[0] + f * d1[0] * r[i][0], c[1] + f * d1[1] * r[i][0]
  92                 f2 = c[0] + f * d2[0] * r[i][1], c[1] + f * d2[1] * r[i][1]
  93                 g1 = c[0] + g * d1[0] * r[i][0], c[1] + g * d1[1] * r[i][0]
  94                 g2 = c[0] + g * d2[0] * r[i][1], c[1] + g * d2[1] * r[i][1]
  95                 d1 = c[0] +     d1[0] * r[i][0], c[1] +     d1[1] * r[i][0]
  96                 d2 = c[0] +     d2[0] * r[i][1], c[1] +     d2[1] * r[i][1]
  97                 e  = 0.5 * (f1[0] + f2[0]), 0.5 * (f1[1] + f2[1])
  98                 if i:
  99                     pathels.append(path._lineto(*d1))
 100                 else:
 101                     pathels.append(path._moveto(*d1))
 102                 pathels.append(path._curveto(*(g1 + f1 + e)))
 103                 pathels.append(path._curveto(*(f2 + g2 + d2)))
 104             pathels.append(path.closepath())
 105         return path.path(*pathels)
 106
 107     def transform(self, *trafos):
 108         for trafo in trafos:
 109             if self.center is not None:
 110                 self.center = trafo._apply(*self.center)
 111             self.corners = [trafo._apply(*point) for point in self.corners]
 112
 113     def reltransform(self, *trafos):
 114         if self.center is not None:
 115             trafos = ([trafo._translate(-self.center[0], -self.center[1])] +
 116                       list(trafos) +
 117                       [trafo._translate(self.center[0], self.center[1])])
 118         self.transform(*trafos)
 119
 120     def successivepointnumbers(self):
 121         return [i and (i - 1, i) or (len(self.corners) - 1, 0) for i in range(len(self.corners))]
 122
 123     def successivepoints(self):
 124         return [(self.corners[i], self.corners[j]) for i, j in self.successivepointnumbers()]
 125
 126     def _circlealignlinevector(self, a, dx, dy, ex, ey, fx, fy, epsilon=1e-10):
 127         cx, cy = self.center
 128         gx, gy = ex - fx, ey - fy # direction vector
 129         if gx*gx + gy*gy < epsilon: # zero line length
 130             return None             # no solution -> return None
 131         rsplit = (dx*gx + dy*gy) * 1.0 / (gx*gx + gy*gy)
 132         bx, by = dx - gx * rsplit, dy - gy * rsplit
 133         if bx*bx + by*by < epsilon: # zero projection
 134             return None             # no solution -> return None
 135         if bx*gy - by*gx < 0: # half space
 136             return None       # no solution -> return None
 137         sfactor = math.sqrt((dx*dx + dy*dy) / (bx*bx + by*by))
 138         bx, by = a * bx * sfactor, a * by * sfactor
 139         alpha = ((bx+cx-ex)*dy - (by+cy-ey)*dx) * 1.0 / (gy*dx - gx*dy)
 140         if alpha > 0 - epsilon and alpha < 1 + epsilon:
 141                 beta = ((ex-bx-cx)*gy - (ey-by-cy)*gx) * 1.0 / (gx*dy - gy*dx)
 142                 return beta*dx, beta*dy # valid solution -> return align tuple
 143         # crossing point at the line, but outside a valid range
 144         if alpha < 0:
 145             return 0 # crossing point outside e
 146         return 1 # crossing point outside f
 147
 148     def _linealignlinevector(self, a, dx, dy, ex, ey, fx, fy, epsilon=1e-10):
 149         cx, cy = self.center
 150         gx, gy = ex - fx, ey - fy # direction vector
 151         if gx*gx + gy*gy < epsilon: # zero line length
 152             return None             # no solution -> return None
 153         if gy*dx - gx*dy < -epsilon: # half space
 154             return None              # no solution -> return None
 155         if dx*gx + dy*gy > epsilon or dx*gx + dy*gy < -epsilon:
 156             if dx*gx + dy*gy < 0: # angle bigger 90 degree
 157                 return 0 # use point e
 158             return 1 # use point f
 159         # a and g are othorgonal
 160         alpha = ((a*dx+cx-ex)*dy - (a*dy+cy-ey)*dx) * 1.0 / (gy*dx - gx*dy)
 161         if alpha > 0 - epsilon and alpha < 1 + epsilon:
 162             beta = ((ex-a*dx-cx)*gy - (ey-a*dy-cy)*gx) * 1.0 / (gx*dy - gy*dx)
 163             return beta*dx, beta*dy # valid solution -> return align tuple
 164         # crossing point at the line, but outside a valid range
 165         if alpha < 0:
 166             return 0 # crossing point outside e
 167         return 1 # crossing point outside f
 168
 169     def _circlealignpointvector(self, a, dx, dy, px, py, epsilon=1e-10):
 170         if a*a < epsilon:
 171             return None
 172         cx, cy = self.center
 173         p = 2 * ((px-cx)*dx + (py-cy)*dy)
 174         q = ((px-cx)*(px-cx) + (py-cy)*(py-cy) - a*a)
 175         if p*p/4 - q < 0:
 176             return None
 177         if a > 0:
 178             alpha = - p / 2 + math.sqrt(p*p/4 - q)
 179         else:
 180             alpha = - p / 2 - math.sqrt(p*p/4 - q)
 181         return alpha*dx, alpha*dy
 182
 183     def _linealignpointvector(self, a, dx, dy, px, py):
 184         cx, cy = self.center
 185         beta = (a*dx+cx-px)*dy - (a*dy+cy-py)*dx
 186         return a*dx - beta*dy - px + cx, a*dy + beta*dx - py + cy
 187
 188     def _alignvector(self, a, dx, dy, alignlinevector, alignpointvector):
 189         n = math.sqrt(dx * dx + dy * dy)
 190         dx, dy = dx / n, dy / n
 191         linevectors = map(lambda (p1, p2), self=self, a=a, dx=dx, dy=dy, alignlinevector=alignlinevector:
 192                                 alignlinevector(a, dx, dy, *(p1 + p2)), self.successivepoints())
 193         for linevector in linevectors:
 194             if type(linevector) is types.TupleType:
 195                 return linevector
 196         for i, j in self.successivepointnumbers():
 197             l1, l2 = linevectors[i], linevectors[j]
 198             if (l1 is not None or l2 is not None) and (l1 == 1 or l1 is None) and (l2 == 0 or l2 is None):
 199                 return alignpointvector(a, dx, dy, *self.successivepoints()[j][0])
 200         return a*dx, a*dy
 201
 202     def _circlealignvector(self, a, dx, dy):
 203         return self._alignvector(a, dx, dy, self._circlealignlinevector, self._circlealignpointvector)
 204
 205     def _linealignvector(self, a, dx, dy):
 206         return self._alignvector(a, dx, dy, self._linealignlinevector, self._linealignpointvector)
 207
 208     def circlealignvector(self, a, dx, dy):
 209         return map(unit.t_pt, self._circlealignvector(unit.topt(a), dx, dy))
 210
 211     def linealignvector(self, a, dx, dy):
 212         return map(unit.t_pt, self._linealignvector(unit.topt(a), dx, dy))
 213
 214     def _circlealign(self, *args):
 215         self.transform(trafo._translate(*self._circlealignvector(*args)))
 216         return self
 217
 218     def _linealign(self, *args):
 219         self.transform(trafo._translate(*self._linealignvector(*args)))
 220         return self
 221
 222     def circlealign(self, *args):
 223         self.transform(trafo.translate(*self.circlealignvector(*args)))
 224         return self
 225
 226     def linealign(self, *args):
 227         self.transform(trafo.translate(*self.linealignvector(*args)))
 228         return self
 229
 230     def _extent(self, dx, dy):
 231         n = math.sqrt(dx * dx + dy * dy)
 232         dx, dy = dx / n, dy / n
 233         oldcenter = self.center
 234         if self.center is None:
 235             self.center = 0, 0
 236         x1, y1 = self._linealignvector(0, dx, dy)
 237         x2, y2 = self._linealignvector(0, -dx, -dy)
 238         self.center = oldcenter
 239         return (x1-x2)*dx + (y1-y2)*dy
 240
 241     def extent(self, dx, dy):
 242         return unit.t_pt(self._extent(dx, dy))
 243
 244     def _pointdistance(self, x, y):
 245         result = None
 246         for p1, p2 in self.successivepoints():
 247             gx, gy = p2[0] - p1[0], p2[1] - p1[1]
 248             if gx * gx + gy * gy < 1e-10:
 249                 dx, dy = p1[0] - x, p1[1] - y
 250             else:
 251                 a = (gx * (x - p1[0]) + gy * (y - p1[1])) / (gx * gx + gy * gy)
 252                 if a < 0:
 253                     dx, dy = p1[0] - x, p1[1] - y
 254                 elif a > 1:
 255                     dx, dy = p2[0] - x, p2[1] - y
 256                 else:
 257                     dx, dy = x - p1[0] - a * gx, y - p1[1] - a * gy
 258             new = math.sqrt(dx * dx + dy * dy)
 259             if result is None or new < result:
 260                 result = new
 261         return result
 262
 263     def pointdistance(self, x, y):
 264         return unit.t_pt(self._pointdistance(unit.topt(x), unit.topt(y)))
 265
 266     def _boxdistance(self, other, epsilon=1e-10):
 267         # XXX: boxes crossing and distance calculation is O(N^2)
 268         for p1, p2 in self.successivepoints():
 269             for p3, p4 in other.successivepoints():
 270                 a = (p4[1] - p3[1]) * (p3[0] - p1[0]) - (p4[0] - p3[0]) * (p3[1] - p1[1])
 271                 b = (p2[1] - p1[1]) * (p3[0] - p1[0]) - (p2[0] - p1[0]) * (p3[1] - p1[1])
 272                 c = (p2[0] - p1[0]) * (p4[1] - p3[1]) - (p2[1] - p1[1]) * (p4[0] - p3[0])
 273                 if (abs(c) > 1e-10 and
 274                     a / c > -epsilon and a / c < 1 + epsilon and
 275                     b / c > -epsilon and b / c < 1 + epsilon):
 276                     raise BoxCrossError
 277         result = None
 278         for x, y in other.corners:
 279             new = self._pointdistance(x, y)
 280             if result is None or new < result:
 281                 result = new
 282         for x, y in self.corners:
 283             new = other._pointdistance(x, y)
 284             if result is None or new < result:
 285                 result = new
 286         return result
 287
 288     def boxdistance(self, other):
 289         return unit.t_pt(self._boxdistance(other))
 290
 291     def bbox(self):
 292         return bbox._bbox(min([x[0] for x in self.corners]),
 293                           min([x[1] for x in self.corners]),
 294                           max([x[0] for x in self.corners]),
 295                           max([x[1] for x in self.corners]))
 296
 297
 298 def _genericalignequal(method, polygons, a, dx, dy):
 299     vec = None
 300     for p in polygons:
 301         v = method(p, a, dx, dy)
 302         if vec is None or vec[0] * dx + vec[1] * dy < v[0] * dx + v[1] * dy:
 303             vec = v
 304     for p in polygons:
 305         p.transform(trafo._translate(*vec))
 306
 307
 308 def _circlealignequal(polygons, *args):
 309     _genericalignequal(_polygon._circlealignvector, polygons, *args)
 310
 311 def _linealignequal(polygons, *args):
 312     _genericalignequal(_polygon._linealignvector, polygons, *args)
 313
 314 def circlealignequal(polygons, a, *args):
 315     _circlealignequal(polygons, unit.topt(a), *args)
 316
 317 def linealignequal(polygons, a, *args):
 318     _linealignequal(polygons, unit.topt(a), *args)
 319
 320
 321 def _tile(polygons, a, dx, dy):
 322     maxextent = polygons[0]._extent(dx, dy)
 323     for p in polygons[1:]:
 324         extent = p._extent(dx, dy)
 325         if extent > maxextent:
 326             maxextent = extent
 327     d = 0
 328     for p in polygons:
 329         p.transform(trafo._translate(d*dx, d*dy))
 330         d += maxextent + a
 331
 332
 333 def tile(polygons, a, dx, dy):
 334     _tile(polygons, unit.topt(a), dx, dy)
 335
 336
 337 class polygon(_polygon):
 338
 339     def __init__(self, corners=None, center=None, **args):
 340         corners = [[unit.topt(x) for x in corner] for corner in corners]
 341         if center is not None:
 342             center = map(unit.topt, center)
 343         _polygon.__init__(self, corners=corners, center=center, **args)
 344
 345
 346 class _rect(_polygon):
 347
 348     def __init__(self, x, y, width, height, relcenter=(0, 0), abscenter=(0, 0),
 349                        corners=helper.nodefault, center=helper.nodefault, **args):
 350         if corners != helper.nodefault or center != helper.nodefault:
 351             raise ValueError
 352         _polygon.__init__(self, corners=((x, y),
 353                                          (x + width, y),
 354                                          (x + width, y + height),
 355                                          (x, y + height)),
 356                                 center=(x + relcenter[0] * width + abscenter[0],
 357                                         y + relcenter[1] * height + abscenter[1]),
 358                                 **args)
 359
 360
 361 class rect(_rect):
 362
 363     def __init__(self, x, y, width, height, relcenter=(0, 0), abscenter=(0, 0), **args):
 364         _rect.__init__(self, unit.topt(x), unit.topt(y), unit.topt(width), unit.topt(height),
 365                              relcenter=relcenter, abscenter=(unit.topt(abscenter[0]), unit.topt(abscenter[1])), **args)
 366