# -*- coding: ISO-8859-1 -*-
#
#
# Copyright (C) 2002-2004 Jrg Lehmann <joergl@users.sourceforge.net>
# Copyright (C) 2003-2004 Michael Schindler <m-schindler@users.sourceforge.net>
# Copyright (C) 2002-2004 Andr Wobst <wobsta@users.sourceforge.net>
#
# This file is part of PyX (http://pyx.sourceforge.net/).
#
# PyX is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# PyX is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with PyX; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
import types, math
import bbox, path, unit, trafo
class _marker: pass
class BoxCrossError(Exception): pass
class polygon_pt:
def __init__(self, corners=None, center=None):
self.corners = corners
self.center = center
if self.center is None:
self._ensurecenter()
def _ensurecenter(self):
if self.center is None:
self.center = 0, 0
for corn in self.corners:
self.center = self.center[0] + corn[0], self.center[1] + corn[1]
self.center = self.center[0]/len(self.corners), self.center[1]/len(self.corners)
def path(self, centerradius=None, bezierradius=None, beziersoftness=None):
pathitems = []
if centerradius is not None and self.center is not None:
r = unit.topt(centerradius)
pathitems.append(path.arc_pt(self.center[0], self.center[1], r, 0, 360))
pathitems.append(path.closepath())
if bezierradius is not None or beziersoftness is not None:
raise ValueError("smooth functionality removed; apply smooth deformer on path")
pathitems.append(path.moveto_pt(self.corners[0][0], self.corners[0][1]))
for x, y in self.corners[1:]:
pathitems.append(path.lineto_pt(x, y))
pathitems.append(path.closepath())
return path.path(*pathitems)
def transform(self, *trafos):
for trafo in trafos:
if self.center is not None:
self.center = trafo.apply_pt(*self.center)
self.corners = [trafo.apply_pt(*point) for point in self.corners]
def reltransform(self, *trafos):
if self.center is not None:
trafos = ([trafo.translate_pt(-self.center[0], -self.center[1])] +
list(trafos) +
[trafo.translate_pt(self.center[0], self.center[1])])
self.transform(*trafos)
def successivepointnumbers(self):
return [i and (i - 1, i) or (len(self.corners) - 1, 0) for i in range(len(self.corners))]
def successivepoints(self):
return [(self.corners[i], self.corners[j]) for i, j in self.successivepointnumbers()]
def circlealignlinevector_pt(self, a, dx, dy, ex, ey, fx, fy, epsilon=1e-10):
cx, cy = self.center
gx, gy = ex - fx, ey - fy # direction vector
if gx*gx + gy*gy < epsilon: # zero line length
return None # no solution -> return None
rsplit = (dx*gx + dy*gy) * 1.0 / (gx*gx + gy*gy)
bx, by = dx - gx * rsplit, dy - gy * rsplit
if bx*bx + by*by < epsilon: # zero projection
return None # no solution -> return None
if bx*gy - by*gx < 0: # half space
return None # no solution -> return None
sfactor = math.sqrt((dx*dx + dy*dy) / (bx*bx + by*by))
bx, by = a * bx * sfactor, a * by * sfactor
alpha = ((bx+cx-ex)*dy - (by+cy-ey)*dx) * 1.0 / (gy*dx - gx*dy)
if alpha > 0 - epsilon and alpha < 1 + epsilon:
beta = ((ex-bx-cx)*gy - (ey-by-cy)*gx) * 1.0 / (gx*dy - gy*dx)
return beta*dx, beta*dy # valid solution -> return align tuple
# crossing point at the line, but outside a valid range
if alpha < 0:
return 0 # crossing point outside e
return 1 # crossing point outside f
def linealignlinevector_pt(self, a, dx, dy, ex, ey, fx, fy, epsilon=1e-10):
cx, cy = self.center
gx, gy = ex - fx, ey - fy # direction vector
if gx*gx + gy*gy < epsilon: # zero line length
return None # no solution -> return None
if gy*dx - gx*dy < -epsilon: # half space
return None # no solution -> return None
if dx*gx + dy*gy > epsilon or dx*gx + dy*gy < -epsilon:
if dx*gx + dy*gy < 0: # angle bigger 90 degree
return 0 # use point e
return 1 # use point f
# a and g are othorgonal
alpha = ((a*dx+cx-ex)*dy - (a*dy+cy-ey)*dx) * 1.0 / (gy*dx - gx*dy)
if alpha > 0 - epsilon and alpha < 1 + epsilon:
beta = ((ex-a*dx-cx)*gy - (ey-a*dy-cy)*gx) * 1.0 / (gx*dy - gy*dx)
return beta*dx, beta*dy # valid solution -> return align tuple
# crossing point at the line, but outside a valid range
if alpha < 0:
return 0 # crossing point outside e
return 1 # crossing point outside f
def circlealignpointvector_pt(self, a, dx, dy, px, py, epsilon=1e-10):
if a*a < epsilon:
return None
cx, cy = self.center
p = 2 * ((px-cx)*dx + (py-cy)*dy)
q = ((px-cx)*(px-cx) + (py-cy)*(py-cy) - a*a)
if p*p/4 - q < 0:
return None
if a > 0:
alpha = - p / 2 + math.sqrt(p*p/4 - q)
else:
alpha = - p / 2 - math.sqrt(p*p/4 - q)
return alpha*dx, alpha*dy
def linealignpointvector_pt(self, a, dx, dy, px, py):
cx, cy = self.center
beta = (a*dx+cx-px)*dy - (a*dy+cy-py)*dx
return a*dx - beta*dy - px + cx, a*dy + beta*dx - py + cy
def alignvector_pt(self, a, dx, dy, alignlinevector, alignpointvector):
n = math.hypot(dx, dy)
dx, dy = dx / n, dy / n
linevectors = map(lambda (p1, p2), self=self, a=a, dx=dx, dy=dy, alignlinevector=alignlinevector:
alignlinevector(a, dx, dy, *(p1 + p2)), self.successivepoints())
for linevector in linevectors:
if type(linevector) is types.TupleType:
return linevector
for i, j in self.successivepointnumbers():
l1, l2 = linevectors[i], linevectors[j]
if (l1 is not None or l2 is not None) and (l1 == 1 or l1 is None) and (l2 == 0 or l2 is None):
return alignpointvector(a, dx, dy, *self.successivepoints()[j][0])
return a*dx, a*dy
def circlealignvector_pt(self, a, dx, dy):
return self.alignvector_pt(a, dx, dy, self.circlealignlinevector_pt, self.circlealignpointvector_pt)
def linealignvector_pt(self, a, dx, dy):
return self.alignvector_pt(a, dx, dy, self.linealignlinevector_pt, self.linealignpointvector_pt)
def circlealignvector(self, a, dx, dy):
ndx, ndy = self.circlealignvector_pt(unit.topt(a), dx, dy)
return ndx * unit.t_pt, ndy * unit.t_pt
def linealignvector(self, a, dx, dy):
ndx, ndy = self.linealignvector_pt(unit.topt(a), dx, dy)
return ndx * unit.t_pt, ndy * unit.t_pt
def circlealign_pt(self, *args):
self.transform(trafo.translate_pt(*self.circlealignvector_pt(*args)))
return self
def linealign_pt(self, *args):
self.transform(trafo.translate_pt(*self.linealignvector_pt(*args)))
return self
def circlealign(self, *args):
self.transform(trafo.translate(*self.circlealignvector(*args)))
return self
def linealign(self, *args):
self.transform(trafo.translate(*self.linealignvector(*args)))
return self
def extent_pt(self, dx, dy):
n = math.hypot(dx, dy)
dx, dy = dx / n, dy / n
oldcenter = self.center
if self.center is None:
self.center = 0, 0
x1, y1 = self.linealignvector_pt(0, dx, dy)
x2, y2 = self.linealignvector_pt(0, -dx, -dy)
self.center = oldcenter
return (x1-x2)*dx + (y1-y2)*dy
def extent(self, dx, dy):
return self.extent_pt(dx, dy) * unit.t_pt
def pointdistance_pt(self, x, y):
result = None
for p1, p2 in self.successivepoints():
gx, gy = p2[0] - p1[0], p2[1] - p1[1]
if gx * gx + gy * gy < 1e-10:
dx, dy = p1[0] - x, p1[1] - y
else:
a = (gx * (x - p1[0]) + gy * (y - p1[1])) / (gx * gx + gy * gy)
if a < 0:
dx, dy = p1[0] - x, p1[1] - y
elif a > 1:
dx, dy = p2[0] - x, p2[1] - y
else:
dx, dy = x - p1[0] - a * gx, y - p1[1] - a * gy
new = math.hypot(dx, dy)
if result is None or new < result:
result = new
return result
def pointdistance(self, x, y):
return self.pointdistance_pt(unit.topt(x), unit.topt(y)) * unit.t_pt
def boxdistance_pt(self, other, epsilon=1e-10):
# XXX: boxes crossing and distance calculation is O(N^2)
for p1, p2 in self.successivepoints():
for p3, p4 in other.successivepoints():
a = (p4[1] - p3[1]) * (p3[0] - p1[0]) - (p4[0] - p3[0]) * (p3[1] - p1[1])
b = (p2[1] - p1[1]) * (p3[0] - p1[0]) - (p2[0] - p1[0]) * (p3[1] - p1[1])
c = (p2[0] - p1[0]) * (p4[1] - p3[1]) - (p2[1] - p1[1]) * (p4[0] - p3[0])
if (abs(c) > 1e-10 and
a / c > -epsilon and a / c < 1 + epsilon and
b / c > -epsilon and b / c < 1 + epsilon):
raise BoxCrossError
result = None
for x, y in other.corners:
new = self.pointdistance_pt(x, y)
if result is None or new < result:
result = new
for x, y in self.corners:
new = other.pointdistance_pt(x, y)
if result is None or new < result:
result = new
return result
def boxdistance(self, other):
return self.boxdistance_pt(other) * unit.t_pt
def bbox(self):
return bbox.bbox_pt(min([x[0] for x in self.corners]),
min([x[1] for x in self.corners]),
max([x[0] for x in self.corners]),
max([x[1] for x in self.corners]))
def genericalignequal_pt(method, polygons, a, dx, dy):
vec = None
for p in polygons:
v = method(p, a, dx, dy)
if vec is None or vec[0] * dx + vec[1] * dy < v[0] * dx + v[1] * dy:
vec = v
for p in polygons:
p.transform(trafo.translate_pt(*vec))
def circlealignequal_pt(polygons, *args):
genericalignequal_pt(polygon_pt.circlealignvector_pt, polygons, *args)
def linealignequal_pt(polygons, *args):
genericalignequal_pt(polygon_pt.linealignvector_pt, polygons, *args)
def circlealignequal(polygons, a, *args):
circlealignequal_pt(polygons, unit.topt(a), *args)
def linealignequal(polygons, a, *args):
linealignequal_pt(polygons, unit.topt(a), *args)
def tile_pt(polygons, a, dx, dy):
maxextent = polygons[0].extent_pt(dx, dy)
for p in polygons[1:]:
extent = p.extent_pt(dx, dy)
if extent > maxextent:
maxextent = extent
delta = maxextent + a
d = 0
for p in polygons:
p.transform(trafo.translate_pt(d*dx, d*dy))
d += delta
return delta
def tile(polygons, a, dx, dy):
return tile_pt(polygons, unit.topt(a), dx, dy) * unit.t_pt
class polygon(polygon_pt):
def __init__(self, corners=None, center=None, **args):
corners = [[unit.topt(x) for x in corner] for corner in corners]
if center is not None:
center = unit.topt(center[0]), unit.topt(center[1])
polygon_pt.__init__(self, corners=corners, center=center, **args)
class rect_pt(polygon_pt):
def __init__(self, x, y, width, height, relcenter=(0, 0), abscenter=(0, 0),
corners=_marker, center=_marker, **args):
if corners != _marker or center != _marker:
raise ValueError
polygon_pt.__init__(self, corners=((x, y),
(x + width, y),
(x + width, y + height),
(x, y + height)),
center=(x + relcenter[0] * width + abscenter[0],
y + relcenter[1] * height + abscenter[1]),
**args)
class rect(rect_pt):
def __init__(self, x, y, width, height, relcenter=(0, 0), abscenter=(0, 0), **args):
rect_pt.__init__(self, unit.topt(x), unit.topt(y), unit.topt(width), unit.topt(height),
relcenter=relcenter,
abscenter=(unit.topt(abscenter[0]), unit.topt(abscenter[1])), **args)
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