pyx/box.py

   1 # -*- encoding: utf-8 -*-
   2 #
   3 #
   4 # Copyright (C) 2002-2004 Jörg Lehmann <joergl@users.sourceforge.net>
   5 # Copyright (C) 2003-2004 Michael Schindler <m-schindler@users.sourceforge.net>
   6 # Copyright (C) 2002-2004 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
  25 import types, math
  26 import bbox, path, unit, trafo
  27
  28 class _marker: pass
  29
  30 class BoxCrossError(Exception): pass
  31
  32 class polygon_pt:
  33
  34     def __init__(self, corners=None, center=None):
  35         self.corners = corners
  36         self.center = center
  37         if self.center is None:
  38             self._ensurecenter()
  39
  40     def _ensurecenter(self):
  41         if self.center is None:
  42             self.center = 0, 0
  43             for corn in self.corners:
  44                 self.center = self.center[0] + corn[0], self.center[1] + corn[1]
  45             self.center = self.center[0]/len(self.corners), self.center[1]/len(self.corners)
  46
  47     def path(self, centerradius=None, bezierradius=None, beziersoftness=None):
  48         pathitems = []
  49         if centerradius is not None and self.center is not None:
  50             r = unit.topt(centerradius)
  51             pathitems.append(path.arc_pt(self.center[0], self.center[1], r, 0, 360))
  52             pathitems.append(path.closepath())
  53         if bezierradius is not None or beziersoftness is not None:
  54             raise ValueError("smooth functionality removed; apply smooth deformer on path")
  55         pathitems.append(path.moveto_pt(self.corners[0][0], self.corners[0][1]))
  56         for x, y in self.corners[1:]:
  57             pathitems.append(path.lineto_pt(x, y))
  58         pathitems.append(path.closepath())
  59         return path.path(*pathitems)
  60
  61     def transform(self, *trafos):
  62         for trafo in trafos:
  63             if self.center is not None:
  64                 self.center = trafo.apply_pt(*self.center)
  65             self.corners = [trafo.apply_pt(*point) for point in self.corners]
  66
  67     def reltransform(self, *trafos):
  68         if self.center is not None:
  69             trafos = ([trafo.translate_pt(-self.center[0], -self.center[1])] +
  70                       list(trafos) +
  71                       [trafo.translate_pt(self.center[0], self.center[1])])
  72         self.transform(*trafos)
  73
  74     def successivepointnumbers(self):
  75         return [i and (i - 1, i) or (len(self.corners) - 1, 0) for i in range(len(self.corners))]
  76
  77     def successivepoints(self):
  78         return [(self.corners[i], self.corners[j]) for i, j in self.successivepointnumbers()]
  79
  80     def circlealignlinevector_pt(self, a, dx, dy, ex, ey, fx, fy, epsilon=1e-10):
  81         cx, cy = self.center
  82         gx, gy = ex - fx, ey - fy # direction vector
  83         if gx*gx + gy*gy < epsilon: # zero line length
  84             return None             # no solution -> return None
  85         rsplit = (dx*gx + dy*gy) * 1.0 / (gx*gx + gy*gy)
  86         bx, by = dx - gx * rsplit, dy - gy * rsplit
  87         if bx*bx + by*by < epsilon: # zero projection
  88             return None             # no solution -> return None
  89         if bx*gy - by*gx < 0: # half space
  90             return None       # no solution -> return None
  91         sfactor = math.sqrt((dx*dx + dy*dy) / (bx*bx + by*by))
  92         bx, by = a * bx * sfactor, a * by * sfactor
  93         alpha = ((bx+cx-ex)*dy - (by+cy-ey)*dx) * 1.0 / (gy*dx - gx*dy)
  94         if alpha > 0 - epsilon and alpha < 1 + epsilon:
  95                 beta = ((ex-bx-cx)*gy - (ey-by-cy)*gx) * 1.0 / (gx*dy - gy*dx)
  96                 return beta*dx, beta*dy # valid solution -> return align tuple
  97         # crossing point at the line, but outside a valid range
  98         if alpha < 0:
  99             return 0 # crossing point outside e
 100         return 1 # crossing point outside f
 101
 102     def linealignlinevector_pt(self, a, dx, dy, ex, ey, fx, fy, epsilon=1e-10):
 103         cx, cy = self.center
 104         gx, gy = ex - fx, ey - fy # direction vector
 105         if gx*gx + gy*gy < epsilon: # zero line length
 106             return None             # no solution -> return None
 107         if gy*dx - gx*dy < -epsilon: # half space
 108             return None              # no solution -> return None
 109         if dx*gx + dy*gy > epsilon or dx*gx + dy*gy < -epsilon:
 110             if dx*gx + dy*gy < 0: # angle bigger 90 degree
 111                 return 0 # use point e
 112             return 1 # use point f
 113         # a and g are othorgonal
 114         alpha = ((a*dx+cx-ex)*dy - (a*dy+cy-ey)*dx) * 1.0 / (gy*dx - gx*dy)
 115         if alpha > 0 - epsilon and alpha < 1 + epsilon:
 116             beta = ((ex-a*dx-cx)*gy - (ey-a*dy-cy)*gx) * 1.0 / (gx*dy - gy*dx)
 117             return beta*dx, beta*dy # valid solution -> return align tuple
 118         # crossing point at the line, but outside a valid range
 119         if alpha < 0:
 120             return 0 # crossing point outside e
 121         return 1 # crossing point outside f
 122
 123     def circlealignpointvector_pt(self, a, dx, dy, px, py, epsilon=1e-10):
 124         if a*a < epsilon:
 125             return None
 126         cx, cy = self.center
 127         p = 2 * ((px-cx)*dx + (py-cy)*dy)
 128         q = ((px-cx)*(px-cx) + (py-cy)*(py-cy) - a*a)
 129         if p*p/4 - q < 0:
 130             return None
 131         if a > 0:
 132             alpha = - p / 2 + math.sqrt(p*p/4 - q)
 133         else:
 134             alpha = - p / 2 - math.sqrt(p*p/4 - q)
 135         return alpha*dx, alpha*dy
 136
 137     def linealignpointvector_pt(self, a, dx, dy, px, py):
 138         cx, cy = self.center
 139         beta = (a*dx+cx-px)*dy - (a*dy+cy-py)*dx
 140         return a*dx - beta*dy - px + cx, a*dy + beta*dx - py + cy
 141
 142     def alignvector_pt(self, a, dx, dy, alignlinevector, alignpointvector):
 143         n = math.hypot(dx, dy)
 144         dx, dy = dx / n, dy / n
 145         linevectors = map(lambda (p1, p2), self=self, a=a, dx=dx, dy=dy, alignlinevector=alignlinevector:
 146                                 alignlinevector(a, dx, dy, *(p1 + p2)), self.successivepoints())
 147         for linevector in linevectors:
 148             if type(linevector) is types.TupleType:
 149                 return linevector
 150         for i, j in self.successivepointnumbers():
 151             l1, l2 = linevectors[i], linevectors[j]
 152             if (l1 is not None or l2 is not None) and (l1 == 1 or l1 is None) and (l2 == 0 or l2 is None):
 153                 return alignpointvector(a, dx, dy, *self.successivepoints()[j][0])
 154         return a*dx, a*dy
 155
 156     def circlealignvector_pt(self, a, dx, dy):
 157         return self.alignvector_pt(a, dx, dy, self.circlealignlinevector_pt, self.circlealignpointvector_pt)
 158
 159     def linealignvector_pt(self, a, dx, dy):
 160         return self.alignvector_pt(a, dx, dy, self.linealignlinevector_pt, self.linealignpointvector_pt)
 161
 162     def circlealignvector(self, a, dx, dy):
 163         ndx, ndy = self.circlealignvector_pt(unit.topt(a), dx, dy)
 164         return ndx * unit.t_pt, ndy * unit.t_pt
 165
 166     def linealignvector(self, a, dx, dy):
 167         ndx, ndy = self.linealignvector_pt(unit.topt(a), dx, dy)
 168         return ndx * unit.t_pt, ndy * unit.t_pt
 169
 170     def circlealign_pt(self, *args):
 171         self.transform(trafo.translate_pt(*self.circlealignvector_pt(*args)))
 172         return self
 173
 174     def linealign_pt(self, *args):
 175         self.transform(trafo.translate_pt(*self.linealignvector_pt(*args)))
 176         return self
 177
 178     def circlealign(self, *args):
 179         self.transform(trafo.translate(*self.circlealignvector(*args)))
 180         return self
 181
 182     def linealign(self, *args):
 183         self.transform(trafo.translate(*self.linealignvector(*args)))
 184         return self
 185
 186     def extent_pt(self, dx, dy):
 187         n = math.hypot(dx, dy)
 188         dx, dy = dx / n, dy / n
 189         oldcenter = self.center
 190         if self.center is None:
 191             self.center = 0, 0
 192         x1, y1 = self.linealignvector_pt(0, dx, dy)
 193         x2, y2 = self.linealignvector_pt(0, -dx, -dy)
 194         self.center = oldcenter
 195         return (x1-x2)*dx + (y1-y2)*dy
 196
 197     def extent(self, dx, dy):
 198         return self.extent_pt(dx, dy) * unit.t_pt
 199
 200     def pointdistance_pt(self, x, y):
 201         result = None
 202         for p1, p2 in self.successivepoints():
 203             gx, gy = p2[0] - p1[0], p2[1] - p1[1]
 204             if gx * gx + gy * gy < 1e-10:
 205                 dx, dy = p1[0] - x, p1[1] - y
 206             else:
 207                 a = (gx * (x - p1[0]) + gy * (y - p1[1])) / (gx * gx + gy * gy)
 208                 if a < 0:
 209                     dx, dy = p1[0] - x, p1[1] - y
 210                 elif a > 1:
 211                     dx, dy = p2[0] - x, p2[1] - y
 212                 else:
 213                     dx, dy = x - p1[0] - a * gx, y - p1[1] - a * gy
 214             new = math.hypot(dx, dy)
 215             if result is None or new < result:
 216                 result = new
 217         return result
 218
 219     def pointdistance(self, x, y):
 220         return self.pointdistance_pt(unit.topt(x), unit.topt(y)) * unit.t_pt
 221
 222     def boxdistance_pt(self, other, epsilon=1e-10):
 223         # XXX: boxes crossing and distance calculation is O(N^2)
 224         for p1, p2 in self.successivepoints():
 225             for p3, p4 in other.successivepoints():
 226                 a = (p4[1] - p3[1]) * (p3[0] - p1[0]) - (p4[0] - p3[0]) * (p3[1] - p1[1])
 227                 b = (p2[1] - p1[1]) * (p3[0] - p1[0]) - (p2[0] - p1[0]) * (p3[1] - p1[1])
 228                 c = (p2[0] - p1[0]) * (p4[1] - p3[1]) - (p2[1] - p1[1]) * (p4[0] - p3[0])
 229                 if (abs(c) > 1e-10 and
 230                     a / c > -epsilon and a / c < 1 + epsilon and
 231                     b / c > -epsilon and b / c < 1 + epsilon):
 232                     raise BoxCrossError
 233         result = None
 234         for x, y in other.corners:
 235             new = self.pointdistance_pt(x, y)
 236             if result is None or new < result:
 237                 result = new
 238         for x, y in self.corners:
 239             new = other.pointdistance_pt(x, y)
 240             if result is None or new < result:
 241                 result = new
 242         return result
 243
 244     def boxdistance(self, other):
 245         return self.boxdistance_pt(other) * unit.t_pt
 246
 247     def bbox(self):
 248         return bbox.bbox_pt(min([x[0] for x in self.corners]),
 249                           min([x[1] for x in self.corners]),
 250                           max([x[0] for x in self.corners]),
 251                           max([x[1] for x in self.corners]))
 252
 253
 254 def genericalignequal_pt(method, polygons, a, dx, dy):
 255     vec = None
 256     for p in polygons:
 257         v = method(p, a, dx, dy)
 258         if vec is None or vec[0] * dx + vec[1] * dy < v[0] * dx + v[1] * dy:
 259             vec = v
 260     for p in polygons:
 261         p.transform(trafo.translate_pt(*vec))
 262
 263
 264 def circlealignequal_pt(polygons, *args):
 265     genericalignequal_pt(polygon_pt.circlealignvector_pt, polygons, *args)
 266
 267 def linealignequal_pt(polygons, *args):
 268     genericalignequal_pt(polygon_pt.linealignvector_pt, polygons, *args)
 269
 270 def circlealignequal(polygons, a, *args):
 271     circlealignequal_pt(polygons, unit.topt(a), *args)
 272
 273 def linealignequal(polygons, a, *args):
 274     linealignequal_pt(polygons, unit.topt(a), *args)
 275
 276
 277 def tile_pt(polygons, a, dx, dy):
 278     maxextent = polygons[0].extent_pt(dx, dy)
 279     for p in polygons[1:]:
 280         extent = p.extent_pt(dx, dy)
 281         if extent > maxextent:
 282             maxextent = extent
 283     delta = maxextent + a
 284     d = 0
 285     for p in polygons:
 286         p.transform(trafo.translate_pt(d*dx, d*dy))
 287         d += delta
 288     return delta
 289
 290
 291 def tile(polygons, a, dx, dy):
 292     return tile_pt(polygons, unit.topt(a), dx, dy) * unit.t_pt
 293
 294
 295 class polygon(polygon_pt):
 296
 297     def __init__(self, corners=None, center=None, **args):
 298         corners = [[unit.topt(x) for x in corner] for corner in corners]
 299         if center is not None:
 300             center = unit.topt(center[0]), unit.topt(center[1])
 301         polygon_pt.__init__(self, corners=corners, center=center, **args)
 302
 303
 304 class rect_pt(polygon_pt):
 305
 306     def __init__(self, x, y, width, height, relcenter=(0, 0), abscenter=(0, 0),
 307                        corners=_marker, center=_marker, **args):
 308         if corners != _marker or center != _marker:
 309             raise ValueError
 310         polygon_pt.__init__(self, corners=((x, y),
 311                                          (x + width, y),
 312                                          (x + width, y + height),
 313                                          (x, y + height)),
 314                                 center=(x + relcenter[0] * width + abscenter[0],
 315                                         y + relcenter[1] * height + abscenter[1]),
 316                                 **args)
 317
 318
 319 class rect(rect_pt):
 320
 321     def __init__(self, x, y, width, height, relcenter=(0, 0), abscenter=(0, 0), **args):
 322         rect_pt.__init__(self, unit.topt(x), unit.topt(y), unit.topt(width), unit.topt(height),
 323                                relcenter=relcenter,
 324                                abscenter=(unit.topt(abscenter[0]), unit.topt(abscenter[1])), **args)
 325