#
# Copyright (c) 2002, 2003, 2004, 2005, 2006 Art Haas
#
# This file is part of PythonCAD.
#
# PythonCAD 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.
#
# PythonCAD 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 PythonCAD; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
#
#
# class stuff for circles
#
from __future__ import generators
import math
from PythonCAD.Generic import tolerance
from PythonCAD.Generic import point
from PythonCAD.Generic import graphicobject
from PythonCAD.Generic import style
from PythonCAD.Generic import linetype
from PythonCAD.Generic import color
from PythonCAD.Generic import quadtree
from PythonCAD.Generic import util
class Circle(graphicobject.GraphicObject):
"""A base-class for Circles and Arcs
A Circle has two attributes:
center: A Point object
radius: The Circle's radius
A Circle has the following methods:
{get/set}Center(): Get/Set the center Point of a Circle.
{get/set}Radius(): Get/Set the radius of a Circle.
move(): Move the Circle.
circumference(): Get the Circle's circumference.
area(): Get the Circle's area.
mapCoords(): Find the nearest Point on the Circle to a coordinate pair.
inRegion(): Returns whether or not a Circle can be seen in a bounded area.
clone(): Return an indentical copy of a Circle.
"""
__defstyle = None
__messages = {
'moved' : True,
'center_changed' : True,
'radius_changed' : True,
}
def __init__(self, center, radius, st=None, lt=None, col=None, th=None, **kw):
"""Initialize a Circle.
Circle(center, radius[, st, lt, col, th])
The center should be a Point, or a two-entry tuple of floats,
and the radius should be a float greater than 0.
"""
_cp = center
if not isinstance(_cp, point.Point):
_cp = point.Point(center)
_r = util.get_float(radius)
if not _r > 0.0:
raise ValueError, "Invalid radius: %g" % _r
_st = st
if _st is None:
_st = self.getDefaultStyle()
super(Circle, self).__init__(_st, lt, col, th, **kw)
self.__radius = _r
self.__center = _cp
_cp.connect('moved', self.__movePoint)
_cp.connect('change_pending', self.__pointChangePending)
_cp.connect('change_complete', self.__pointChangeComplete)
_cp.storeUser(self)
def __eq__(self, obj):
"""Compare a Circle to another for equality.
"""
if not isinstance(obj, Circle):
return False
if obj is self:
return True
return (self.__center == obj.getCenter() and
abs(self.__radius - obj.getRadius()) < 1e-10)
def __ne__(self, obj):
"""Compare a Circle to another for inequality.
"""
if not isinstance(obj, Circle):
return True
if obj is self:
return False
return (self.__center != obj.getCenter() or
abs(self.__radius - obj.getRadius()) > 1e-10)
def getDefaultStyle(cls):
if cls.__defstyle is None:
_s = style.Style(u'Default Circle Style',
linetype.Linetype(u'Solid', None),
color.Color(0xffffff),
1.0)
cls.__defstyle = _s
return cls.__defstyle
getDefaultStyle = classmethod(getDefaultStyle)
def setDefaultStyle(cls, s):
if not isinstance(s, style.Style):
raise TypeError, "Invalid style: " + `type(s)`
cls.__defstyle = s
setDefaultStyle = classmethod(setDefaultStyle)
def finish(self):
self.__center.disconnect(self)
self.__center.freeUser(self)
self.__center = self.__radius = None
super(Circle, self).finish()
def setStyle(self, s):
"""Set the Style of the Circle.
setStyle(s)
This method extends GraphicObject::setStyle().
"""
_s = s
if _s is None:
_s = self.getDefaultStyle()
super(Circle, self).setStyle(_s)
def getValues(self):
"""Return values comprising the Circle.
getValues()
This method extends the GraphicObject::getValues() method.
"""
_data = super(Circle, self).getValues()
_data.setValue('type', 'circle')
_data.setValue('center', self.__center.getID())
_data.setValue('radius', self.__radius)
return _data
def getCenter(self):
"""Return the center Point of the Circle.
getCenter()
"""
return self.__center
def setCenter(self, c):
"""Set the center Point of the Circle.
setCenter(c)
The argument must be a Point or a tuple containing
two float values.
"""
if self.isLocked():
raise RuntimeError, "Setting center not allowed - object locked."
_cp = self.__center
if not isinstance(c, point.Point):
raise TypeError, "Invalid center point: " + `type(c)`
if _cp is not c:
_cp.disconnect(self)
_cp.freeUser(self)
self.startChange('center_changed')
self.__center = c
self.endChange('center_changed')
self.sendMessage('center_changed', _cp)
c.connect('moved', self.__movePoint)
c.connect('change_pending', self.__pointChangePending)
c.connect('change_complete', self.__pointChangeComplete)
c.storeUser(self)
if abs(_cp.x - c.x) > 1e-10 or abs(_cp.y - c.y) > 1e-10:
self.sendMessage('moved', _cp.x, _cp.y, self.__radius)
self.modified()
center = property(getCenter, setCenter, None, "Circle center")
def getRadius(self):
"""Return the radius of the the Circle.
getRadius()
"""
return self.__radius
def setRadius(self, radius):
"""Set the radius of the Circle.
setRadius(radius)
The argument must be float value greater than 0.
"""
if self.isLocked():
raise RuntimeError, "Setting radius not allowed - object locked."
_r = util.get_float(radius)
if not _r > 0.0:
raise ValueError, "Invalid radius: %g" % _r
_cr = self.__radius
if abs(_cr - _r) > 1e-10:
self.startChange('radius_changed')
self.__radius = _r
self.endChange('radius_changed')
self.sendMessage('radius_changed', _cr)
_cx, _cy = self.__center.getCoords()
self.sendMessage('moved', _cx, _cy, _cr)
self.modified()
radius = property(getRadius, setRadius, None, "Circle radius")
def move(self, dx, dy):
"""Move a Circle.
move(dx, dy)
The first argument gives the x-coordinate displacement,
and the second gives the y-coordinate displacement. Both
values should be floats.
"""
if self.isLocked():
raise RuntimeError, "Setting radius not allowed - object locked."
_dx = util.get_float(dx)
_dy = util.get_float(dy)
if abs(_dx) > 1e-10 or abs(_dy) > 1e-10:
_x, _y = self.__center.getCoords()
self.ignore('moved')
try:
self.__center.move(_dx, _dy)
finally:
self.receive('moved')
self.sendMessage('moved', _x, _y, self.__radius)
def circumference(self):
"""Return the circumference of the Circle.
circumference()
"""
return 2.0 * math.pi * self.__radius
def area(self):
"""Return the area enclosed by the Circle.
area()
"""
return math.pi * pow(self.__radius, 2)
def mapCoords(self, x, y, tol=tolerance.TOL):
"""Return the nearest Point on the Circle to a coordinate pair.
mapCoords(x, y[, tol])
The function has two required arguments:
x: A Float value giving the x-coordinate
y: A Float value giving the y-coordinate
There is a single optional argument:
tol: A float value equal or greater than 0.0
This function is used to map a possibly near-by coordinate pair to
an actual Point on the Circle. If the distance between the actual
Point and the coordinates used as an argument is less than the tolerance,
the actual Point is returned. Otherwise, this function returns None.
"""
_x = util.get_float(x)
_y = util.get_float(y)
_t = tolerance.toltest(tol)
_cx, _cy = self.__center.getCoords()
_r = self.__radius
_dist = math.hypot((_x - _cx), (_y - _cy))
if abs(_dist - _r) < _t:
_angle = math.atan2((_y - _cy),(_x - _cx))
_xoff = _r * math.cos(_angle)
_yoff = _r * math.sin(_angle)
return (_cx + _xoff), (_cy + _yoff)
return None
def inRegion(self, xmin, ymin, xmax, ymax, fully=False):
"""Return whether or not an Circle exists within a region.
inRegion(xmin, ymin, xmax, ymax[, fully])
The first four arguments define the boundary. The optional
fifth argument 'fully' indicates whether or not the Circle
must be completely contained within the region or just pass
through it.
"""
_xmin = util.get_float(xmin)
_ymin = util.get_float(ymin)
_xmax = util.get_float(xmax)
if _xmax < _xmin:
raise ValueError, "Illegal values: xmax < xmin"
_ymax = util.get_float(ymax)
if _ymax < _ymin:
raise ValueError, "Illegal values: ymax < ymin"
util.test_boolean(fully)
_xc, _yc = self.__center.getCoords()
_r = self.__radius
#
# cheap test to see if circle cannot be in region
#
if (((_xc - _r) > _xmax) or
((_yc - _r) > _ymax) or
((_xc + _r) < _xmin) or
((_yc + _r) < _ymin)):
return False
_val = False
_bits = 0
#
# calculate distances from center to region boundary
#
if abs(_xc - _xmin) < _r: _bits = _bits | 1 # left edge
if abs(_xc - _xmax) < _r: _bits = _bits | 2 # right edge
if abs(_yc - _ymin) < _r: _bits = _bits | 4 # bottom edge
if abs(_yc - _ymax) < _r: _bits = _bits | 8 # top edge
if _bits == 0:
#
# circle must be visible - the center is in
# the region and is more than the radius from
# each edge
#
_val = True
else:
#
# calculate distance to corners of region
#
if math.hypot((_xc - _xmin), (_yc - _ymax)) < _r:
_bits = _bits | 0x10 # upper left
if math.hypot((_xc - _xmax), (_yc - _ymin)) < _r:
_bits = _bits | 0x20 # lower right
if math.hypot((_xc - _xmin), (_yc - _ymin)) < _r:
_bits = _bits | 0x40 # lower left
if math.hypot((_xc - _xmax), (_yc - _ymax)) < _r:
_bits = _bits | 0x80 # upper right
#
# if all bits are set then distance from circle center
# to region endpoints is less than radius - circle
# entirely outside the region
#
_val = not ((_bits == 0xff) or fully)
return _val
def __pointChangePending(self, p, *args):
_alen = len(args)
if _alen < 1:
raise ValueError, "Invalid argument count: %d" % _alen
if args[0] == 'moved':
self.startChange('moved')
def __pointChangeComplete(self, p, *args):
_alen = len(args)
if _alen < 1:
raise ValueError, "Invalid argument count: %d" % _alen
if args[0] == 'moved':
self.endChange('moved')
def __movePoint(self, p, *args):
_alen = len(args)
if _alen < 2:
raise ValueError, "Invalid argument count: %d" % _alen
_x = util.get_float(args[0])
_y = util.get_float(args[1])
_cp = self.__center
if p is not _cp:
raise ValueError, "Point is not circle center: " + `p`
_x, _y = _cp.getCoords()
self.sendMessage('moved', _x, _y, self.__radius)
def clone(self):
"""Create an identical copy of a Circle
clone()
"""
_cp = self.__center.clone()
_st = self.getStyle()
_lt = self.getLinetype()
_col = self.getColor()
_th = self.getThickness()
return Circle(_cp, self.__radius, _st, _lt, _col, _th)
def sendsMessage(self, m):
if m in Circle.__messages:
return True
return super(Circle, self).sendsMessage(m)
def clipToRegion(self, xmin, ymin, xmax, ymax):
"""Return the portions of a circle visible in a region.
clipToRegion(xmin, ymin, xmax, ymax)
This method returns a list of tuples. Each tuple contains two
float values representing arcs which are seen in the region. Each
tuple has the start angle and end angle.
"""
_xmin = util.get_float(xmin)
_ymin = util.get_float(ymin)
_xmax = util.get_float(xmax)
if _xmax < _xmin:
raise ValueError, "Illegal values: xmax < xmin"
_ymax = util.get_float(ymax)
if _ymax < _ymin:
raise ValueError, "Illegal values: ymax < ymin"
_xc, _yc = self.__center.getCoords()
_r = self.__radius
_bits = 0
_arcs = []
#
# calculate distances from center to region boundaries
#
if abs(_xc - _xmin) < _r: _bits = _bits | 1 # left edge
if abs(_xc - _xmax) < _r: _bits = _bits | 2 # right edge
if abs(_yc - _ymin) < _r: _bits = _bits | 4 # bottom edge
if abs(_yc - _ymax) < _r: _bits = _bits | 8 # top edge
#
# test if the circle is entirely contained or entirely
# outside the region
#
# print "bits: %#02x" % _bits
if _bits == 0:
#
# if the circle center is in region then the entire
# circle is visible since the distance from the center
# to any edge is greater than the radius. If the center
# is not in the region then the circle is not visible in
# the region because the distance to any edge is greater
# than the radius, and so one of the bits should have been
# set
#
if ((_xmin < _xc <_xmax) and (_ymin < _yc < _ymax)):
print "circle completely inside region"
_arcs.append((0.0, 360.0)) # fully in region
else:
#
# calculate distance to corners of region
#
if math.hypot((_xc - _xmin), (_yc - _ymax)) < _r:
_bits = _bits | 0x10 # upper left, NW corner
if math.hypot((_xc - _xmax), (_yc - _ymin)) < _r:
_bits = _bits | 0x20 # lower right, SE corner
if math.hypot((_xc - _xmin), (_yc - _ymin)) < _r:
_bits = _bits | 0x40 # lower left, SW corner
if math.hypot((_xc - _xmax), (_yc - _ymax)) < _r:
_bits = _bits | 0x80 # upper right, NE corner
#
# based on the bit pattern the various possible intersections
# can be determined
#
# there is much room for optimization in here - many
# of the distances from the center point to the region
# edges and corners are calculated numerous times, the
# square of these values are also repeatedly calculated ...
#
_rsqr = _r * _r
# _rtd = 180.0/math.pi
print "bits: %#02x" % _bits
if _bits == 0x01: # circle crosses left edge twice
print "circle crosses left edge twice"
_yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
_yt = _yc + _yd
_yb = _yc - _yd
print "yt: %g; yb: %g" % (_yt, _yb)
assert _yt < _ymax, "ytop > ymax"
assert _yb > _ymin, "ybot < ymin"
if (_ymin < _yc < _ymax): # must be true
_at = _calc_angle((_yt - _yc), (_xmin - _xc))
_ab = _calc_angle((_yb - _yc), (_xmin - _xc))
_arcs.append((_ab, ((360.0 - _ab) + _at)))
if _xc > _xmin: # circle inside region
print "circle center inside region"
else:
print "circle center outside"
else:
if _yc < _ymin:
print "yc < ymin (%g < %g)" % (_yc, _ymin)
elif _yc > _ymax:
print "yc > ymax (%g > %g)" % (_yc, _ymax)
else:
print "unexpected y: (%g, %g, %g)" % (_ymin, _yc, _ymax)
elif _bits == 0x02: # circle crosses right edge twice
print "circle crosses right edge twice"
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_yt = _yc + _yd
_yb = _yc - _yd
print "yt: %g; yb: %g" % (_yt, _yb)
assert _yt < _ymax, "ytop > ymax"
assert _yb > _ymin, "ybot < ymin"
if (_ymin < _yc < _ymax): # must be true
_at = _calc_angle((_yt - _yc), (_xmin - _xc))
_ab = _calc_angle((_yb - _yc), (_xmin - _xc))
_arcs.append((_at, (_ab - _at)))
if _xc < _xmax: # circle inside region
print "circle inside"
else:
print "circle outside"
else:
if _yc < _ymin:
print "yc < ymin (%g < %g)" % (_yc, _ymin)
elif _yc > _ymax:
print "yc > ymax (%g > %g)" % (_yc, _ymax)
else:
print "unexpected y: (%g, %g, %g)" % (_ymin, _yc, _ymax)
elif _bits == 0x04: # circle crosses bottom twice
print "circle crosses bottom twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
_xr = _xc + _xd
_xl = _xc - _xd
print "xl: %g; xr: %g" % (_xl, _xr)
assert _xr < _xmax, "xright > xmax"
assert _xl > _xmin, "xeft < xmin"
if (_xmin < _xc < _xmax): # must be true
_al = _calc_angle((_ymin - _yc), (_xl - _xc))
_ar = _calc_angle((_ymin - _yc), (_xr - _xc))
_arcs.append((_ar, (360.0 - _ar + _al)))
if _yc > _ymin: # circle inside region
print "circle inside"
else:
print "circle outside"
else:
if _xc < _xmin:
print "xc < xmin (%g < %g)" % (_xc, _xmin)
elif _yc > _ymax:
print "xc > xmax (%g > %g)" % (_xc, _xmax)
else:
print "unexpected x: (%g, %g, %g)" % (_xmin, _xc, _xmax)
elif _bits == 0x08: # circle crosses top twice
print "circle crosses top twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
_xr = _xc + _xd
_xl = _xc - _xd
print "xl: %g; xr: %g" % (_xl, _xr)
assert _xr < _xmax, "xright > xmax"
assert _xl > _xmin, "xeft < xmin"
if (_xmin < _xc < _xmax): # must be true
_al = _calc_angle((_ymax - _yc), (_xl - _xc))
_ar = _calc_angle((_ymax - _yc), (_xr - _xc))
_arcs.append((_al, (360.0 - _al + _ar)))
if _yc < _ymax: # circle inside region
print "circle inside"
else:
print "circle outside"
else:
if _xc < _xmin:
print "xc < xmin (%g < %g)" % (_xc, _xmin)
elif _yc > _ymax:
print "xc > xmax (%g > %g)" % (_xc, _xmax)
else:
print "unexpected x: (%g, %g, %g)" % (_xmin, _xc, _xmax)
elif _bits == 0x09: # circle crosses left and top twice
print "circle crosses left and top twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
_xr = _xc + _xd
_xl = _xc - _xd
_yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
_yt = _yc + _yd
_yb = _yc - _yd
# top -> left
_a1 = _calc_angle((_ymax - _yc), (_xl - _xc))
_a2 = _calc_angle((_yt - _yc), (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# left -> top
_a1 = _calc_angle((_yb - _yc), (_xmin - _xc))
_a2 = _calc_angle((_ymax - _yc), (_xr - _xc))
_arcs.append((_a1, (360.0 - _a1 + _a2)))
if ((_xmin < _xc < _xmax) and
(_ymin < _yc < _ymax)):
print "circle inside"
else:
print "unexpected center for region: (%g, %g)" % (_xc, _yc)
elif _bits == 0x0a: # circle crosses top and right twice
print "circle crosses top and right twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
_xr = _xc + _xd
_xl = _xc - _xd
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_yt = _yc + _yd
_yb = _yc - _yd
# top -> right
_a1 = _calc_angle((_ymax - _yc), (_xl - _xc))
_a2 = _calc_angle((_yb - _yc), (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# right -> top
_a1 = _calc_angle((_yt - _yc), (_xmax - _xc))
_a2 = _calc_angle((_ymax - _yc), (_xr - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if ((_xmin < _xc < _xmax) and
(_ymin < _yc < _ymax)):
print "circle inside"
else:
print "unexpected center for region: (%g, %g)" % (_xc, _yc)
elif _bits == 0x06: # circle crosses right and bottom twice
print "circle crosses right and bottom twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
_xr = _xc + _xd
_xl = _xc - _xd
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_yt = _yc + _yd
_yb = _yc - _yd
# right -> bottom
_a1 = _calc_angle((_yt - _yc), (_xmax - _xc))
_a2 = _calc_angle((_ymin - _yc), (_xl - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# bottom -> right
_a1 = _calc_angle((_ymin - _yc), (_xr - _xc))
_a2 = _calc_angle((_yb - _yc), (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if ((_xmin < _xc < _xmax) and
(_ymin < _yc < _ymax)):
print "circle inside"
else:
print "unexpected center for region: (%g, %g)" % (_xc, _yc)
elif _bits == 0x05: # circle crosses bottom and left twice
print "circle crosses bottom and left twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
_xr = _xc + _xd
_xl = _xc - _xd
_yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
_yt = _yc + _yd
_yb = _yc - _yd
# left -> bottom
_a1 = _calc_angle((_yb - _yc), (_xmin - _xc))
_a2 = _calc_angle((_ymin - _yc), (_xl - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# bottom -> left
_a1 = _calc_angle((_ymin - _yc), (_xr - _xc))
_a2 = _calc_angle((_yt - _xc), (_xmin - _xc))
_arcs.append((_a1, (360.0 - _a1 + _a2)))
if ((_xmin < _xc < _xmax) and
(_ymin < _yc < _ymax)):
print "circle inside"
else:
print "unexpected center for region: (%g, %g)" % (_xc, _yc)
elif _bits == 0x0c: # circle crosses top and bottom twice
print "circle crosses top and bottom twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
_xtr = _xc + _xd
_xtl = _xc - _xd
_xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
_xbr = _xc + _xd
_xbl = _xc - _xd
# top -> bottom
_a1 = _calc_angle((_ymax - _yc), (_xtl - _xc))
_a2 = _calc_angle((_ymin - _yc), (_xbl - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# bottom -> top
_a1 = _calc_angle((_ymin - _yc), (_xbr - _xc))
_a2 = _calc_angle((_ymax - _yc), (_xtr - _xc))
_arcs.append((_a1, (360.0 - _a1 + _a2)))
if (_ymin < _yc < _ymax): # needed?
print "circle inside region"
elif _yc < _ymin:
print "circle below region"
else:
print "circle above region"
elif _bits == 0x03: # circle crosses left and right twice
print "circle crosses left and right twice"
_yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
_ylt = _yc + _yd
_ylb = _yc - _yd
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_yrt = _yc + _yd
_yrb = _yc - _yd
# left -> right
_a1 = _calc_angle((_ylb - _yc), (_xmin - _xc))
_a2 = _calc_angle((_yrb - _yc), (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# right -> left
_a1 = _calc_angle((_yrt - _yc), (_xmax - _xc))
_a2 = _calc_angle((_ylt - _yc), (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if (_xmin < _xc < _xmax):
print "circle inside region"
elif _xc < _xmin:
print "circle left of region"
else:
print "circle right of region"
elif _bits == 0x0b: # circle through left, top, right twice
print "circle through left & top & right twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
_xtr = _xc + _xd
_xtl = _xc - _xd
_yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
_ylt = _yc + _yd
_ylb = _yc - _yd
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_yrt = _yc + _yd
_yrb = _yc - _yd
# top -> left
_a1 = _calc_angle((_ymax - _yc), (_xtl - _xc))
_a2 = _calc_angle((_ylt - _yc), (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# left -> right
_a1 = _calc_angle((_ylb - _yc), (_xmin - _xc))
_a2 = _calc_angle((_yrb - _yc), (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# right > top
_a1 = _calc_angle((_yrt - _yc), (_xmax - _xc))
_a2 = _calc_angle((_ymax - _yc), (_xtr - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if (_xmin < _xc < _xmax):
print "circle inside region"
elif _xc < _xmin:
print "xc < xmin (%g, %g)" % (_xc, _xmin)
else:
print "xc > xmax (%g, %g)" % (_xc, _xmax)
if _yc < _ymin:
print "yc < ymin (%g, %g)" % (_yc, _ymin)
else:
if _yc > _ymax:
print "yc > ymax (%g, %g)" % (_yc, _ymax)
elif _bits == 0x0e: # circle through top, right, bottom twice
print "circle through top & right & bottom twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
_xtr = _xc + _xd
_xtl = _xc - _xd
_xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
_xbr = _xc + _xd
_xbl = _xc - _xd
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_yrt = _yc + _yd
_yrb = _yc - _yd
# top -> bottom
_a1 = _calc_angle((_ymax - _yc), (_xtl - _xc))
_a2 = _calc_angle((_ymin - _yc), (_xbl - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# bottom -> right
_a1 = _calc_angle((_ymin - _yc), (_xbr - _xc))
_a2 = _calc_angle((_yrb - _yc), (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# right -> top
_a1 = _calc_angle((_yrt - _yc), (_xmax - _xc))
_a2 = _calc_angle((_ymax - _yc), (_xtr - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if (_ymin < _yc < _ymax):
print "circle inside region"
elif _yc < _ymin:
print "yc < ymin (%g, %g)" % (_yc, _ymin)
else:
print "yc > ymax (%g, %g)" % (_yc, _ymax)
if _xc < _xmin:
print "xc < xmin (%g, %g)" % (_xc, _xmin)
else:
if _xc > _xmax:
print "xc > xmax (%g, %g)" % (_xc, _xmax)
elif _bits == 0x07: # circle though right, bottom, left twice
print "circle through right & bottom & left twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
_xbr = _xc + _xd
_xbl = _xc - _xd
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_yrt = _yc + _yd
_yrb = _yc - _yd
_yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
_ylt = _yc + _yd
_ylb = _yc - _yd
# right -> left
_a1 = _calc_angle((_yrt - _yc), (_xmax - _xc))
_a2 = _calc_angle((_ylt - _yc), (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# left -> bottom
_a1 = _calc_angle((_ylb - _yc), (_xmin - _xc))
_a2 = _calc_angle((_ymin - _yc), (_xbl - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# bottom -> right
_a1 = _calc_angle((_ymin - _yc), (_xbr - _xc))
_a2 = _calc_angle((_yrb - _yc), (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if (_xmin < _xc < _xmax):
print "circle inside region"
elif _xc < _xmin:
print "xc < xmin (%g, %g)" % (_xc, _xmin)
else:
print "xc > xmax (%g, %g)" % (_xc, _xmax)
if _yc < _ymin:
print "yc < ymin (%g, %g)" % (_yc, _ymin)
else:
if _yc > _ymax:
print "yc > ymax (%g, %g)" % (_yc, _ymax)
elif _bits == 0x0d: # circle through bottom, left, top twice
print "circle through bottom & left & top twice"
_xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
_xbr = _xc + _xd
_xbl = _xc - _xd
_xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
_xtr = _xc + _xd
_xtl = _xc - _xd
_yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
_ylt = _yc + _yd
_ylb = _yc - _yd
# bottom -> top
_a1 = _calc_angle((_ymin - _yc), (_xbr - _xc))
_a2 = _calc_angle((_ymax - _yc), (_xtr - _xc))
_arcs.append((_a1, (360.0 - _a1 + _a2)))
# top -> left
_a1 = _calc_angle((_ymax - _yc), (_xtl - _xc))
_a2 = _calc_angle((_ylt - _yc), (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# left -> bottom
_a1 = _calc_angle((_ylb - _yc), (_xmin - _xc))
_a2 = _calc_angle((_ymin - _yc), (_xbl - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if (_ymin < _yc < _ymax):
print "circle inside region"
elif _yc < _ymin:
print "yc < ymin (%g, %g)" % (_yc, _ymin)
else:
print "yc > ymax (%g, %g)" % (_yc, _ymax)
if _xc < _xmin:
print "xc < xmin (%g, %g)" % (_xc, _xmin)
else:
if _xc > _xmax:
print "xc > xmax (%g, %g)" % (_xc, _xmax)
elif _bits == 0x19: # circle through left, top, and NW corner
print "circle through left and top with NW corner"
_xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
_yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_a2 = _calc_angle((_ymax - _yc), _xd)
if _xc > _xmax:
_arcs.append((_a1, (_a2 - _a1)))
else:
_arcs.append((_a1, (360.0 - _a1 + _a2)))
if ((_xmin < _xc < _xmax) and
(_ymin < _yc < _ymax)):
print "circle inside region"
else:
print "circle outside region"
elif _bits == 0x8a: # circle through right, top, and NE corner
print "circle through right and top with NE corner"
_xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_a1 = _calc_angle((_ymax - _yc), -_xd)
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if ((_xmin < _xc < _xmax) and
(_ymin < _yc < _ymax)):
print "circle inside region"
else:
print "circle outside region"
elif _bits == 0x26: # circle through right, bottom, and SE corner
print "circle through right and bottom with SE corner"
_xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_a1 = _calc_angle(_yd, (_xmax - _xc))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
if ((_xmin < _xc < _xmax) and
(_ymin < _yc < _ymax)):
print "circle inside region"
else:
print "circle outside region"
elif _bits == 0x45: # circle through left, bottom, and SW corner
print "circle through left and bottom with SW corner"
_xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_a1 = _calc_angle((_ymin - _yc), _xd)
_a2 = _calc_angle(_yd, (_xmin - _xc))
if _xc < _xmin:
_arcs.append((_a1, (_a2 - _a1)))
else:
_arcs.append((_a1, (360.0 - _a1 + _a2)))
if ((_xmin < _xc < _xmax) and
(_ymin < _yc < _ymax)):
print "circle inside region"
else:
print "circle outside region"
elif _bits == 0x9b: # circle through left, right, NE and NW corner
print "circle through left and right with NE, NW corners"
_yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if _xc < _xmin:
print "x < xmin (%g < %g)" % (_xc, _xmin)
elif _xc > _xmax:
print "x > xmax (%g > %g)" % (_xc, _xmax)
else:
if _yc < _ymax:
print "circle center in region"
else:
print "circle center outside region"
elif _bits == 0xae: # circle through top, botton, NE and SE corner
print "circle through top and bottom with NE, SE corners"
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a1 = _calc_angle((_ymax - _yc), -_xd)
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
if _yc < _ymin:
print "y < ymin (%g < %g)" % (_yc, _ymin)
elif _yc > _ymax:
print "y > ymax (%g > %g)" % (_yc, _ymax)
else:
if _xc < _xmax:
print "circle center in region"
else:
print "circle center outside region"
elif _bits == 0x67: # circle through left, right, SE and SW corner
print "circle through left and right with SE, SW corners"
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a1 = _calc_angle(_yd, (_xmax - _xc))
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if _xc < _xmin:
print "x < xmin (%g < %g)" % (_xc, _xmin)
elif _xc > _xmax:
print "x > xmax (%g > %g)" % (_xc, _xmax)
else:
if _yc > _ymin:
print "circle center inside region"
else:
print "circle center outside region"
elif _bits == 0x5d: # circle through top, bottom, SW and NW corner
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a1 = _calc_angle((_ymin - _yc), _xd)
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
if _xc > _xmin:
_arcs.append((_a1, (_a2 - _a1)))
else:
_arcs.append((_a1, (360.0 - _a1 + _a2)))
print "circle through top and bottom with SW, NW corners"
if _yc < _ymin:
print "y < ymin (%g < %g)" % (_yc, _ymin)
elif _yc > _ymax:
print "y > ymax (%g > %g)" % (_yc, _ymax)
else:
if _xc > _xmin:
print "circle center inside region"
else:
print "circle center outside region"
elif _bits == 0xbf: # circle center NE, crosses left and bottom
print "circle center NE of region, crosses left and bottom"
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
elif _bits == 0xef: # circle center SE, crosses left and top
print "circle center SE of region, crosses left and top"
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a1 = _calc_angle((_ymax - _yc), -_xd)
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
elif _bits == 0x7f: # circle center SW, crosses top and right
print "circle center SW of region, crosses top and right"
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a1 = _calc_angle(_yd, (_xmax - _xc))
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
_arcs.append((_a1, (_a2 - _a1)))
elif _bits == 0xdf: # circle center NW, crosses right and bottom
print "circle center NW of region, crosses right and bottom"
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a1 = _calc_angle((_ymin - _yc), _xd)
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
elif _bits == 0x9f: # circle center N, crosses left, right, bottom
print "circle center N, crosses left, right, and twice bottom"
# left -> bottom
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a1 = _calc_angle(-_yd, (xmin - _xc))
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
# bottom -> right; _xd now positive
_a1 = _calc_angle((_ymin - _yc), _xd)
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if _yc < _ymax:
print "yc < ymax (%g < %g)" % (_yc, _ymax)
if ((_xc < _xmin) or (_xc > _xmax)):
print "xc: %g; xmin: %g; xmax: %g" % (_xc, _xmin, _xmax)
elif _bits == 0xaf: # circle center W, crosses bottom, left, top
print "circle center W, crosses bottom, top, and twice left"
# top -> left
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a1 = _calc_angle((_ymax - _yc), -_xd)
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# left -> bottom; _yd now negative
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
if _xc < _xmax:
print "xc < xmax (%g < %g)" % (_xc, _xmax)
if ((_yc < _ymin) or (_yc > _ymax)):
print "yc: %g; ymin: %g; ymax: %g" % (_yc, _ymin, _ymax)
elif _bits == 0x6f: # circle center S, crosses left, top, right
print "circle center S, crosses left, right, and twice top"
# right -> top
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a1 = _calc_angle(_yd, (_xmax - _xc))
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
_arcs.append((_a1, (_a2 - _a1)))
# top -> left; _xd now negative
_a1 = _calc_angle((_ymax - _yc), -_xd)
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if _yc > _ymin:
print "yc > ymin (%g > %g)" % (_yc, _ymin)
if ((_xc < _xmin) or (_xc > _xmax)):
print "xc: %g; xmin: %g; xmax: %g" % (_xc, _xmin, _xmax)
elif _bits == 0x5f: # circle center E, crosses top, right, bottom
print "circle center E, crosses top, bottom, and twice right"
# bottom -> right
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a1 = _calc_angle((_ymin - _yc), _xd)
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# right -> top, _yd now positive
_a1 = _calc_angle(_yd, (_xmax - _xc))
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
_arcs.append((_a1, (_a2 - _a1)))
if _xc > _xmin:
print "xc > xmin (%g > %g)" % (_xc, _xmin)
if ((_yc < _ymin) or (_yc > _ymax)):
print "yc: %g; ymin: %g; ymax: %g" % (_yc, _ymin, _ymax)
elif _bits == 0x1d:
print "circle center N near NW, crosses T&L once, B twice"
# left -> bottom
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
# top -> bottom; _xd now positive
_a1 = _calc_angle((_ymin - _yc), _xd)
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
if _yc > _ymax:
_arcs.append((_a1, (_a2 - _a1)))
else:
_arcs.append((_a1, (360.0 - _a1 + _a2)))
if _xc < _xmin:
print "x < xmin (%g < %g)" % (_xc, _xmin)
if _yc < _ymax:
print "y < ymax (%g < %g)" % (_yc, _ymax)
elif _bits == 0x4d:
print "circle center S near SW, crosses B&L once, T twice"
# bottom -> top
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a1 = _calc_angle((_ymin - _yc), _xd)
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
_arcs.append((_a1, (_a2 - _a1)))
# top -> left, _xd now negative
_a1 = _calc_angle((_ymax - _yc), -_xd)
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if _xc < _xmin:
print "x < xmin (%g < %g)" % (_xc, _xmin)
if _yc > _ymin:
print "y > ymin (%g > %g)" % (_yc, _ymin)
elif _bits == 0x2e:
print "circle center S near SE, crosses B&R once, T twice"
# right -> top
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a1 = _calc_angle(_yd, (_xmax - _xc))
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
_arcs.append((_a1, (_a2 - _a1)))
# top -> bottom; _xd now negative
_a1 = _calc_angle((_ymax - _yc), -_xd)
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
if _xc > _xmax:
print "x > xmax (%g > %g)" % (_xc, _xmax)
if _yc > _ymin:
print "y > ymin (%g > %g)" % (_yc, _ymin)
elif _bits == 0x8e:
print "circle center N near NE, crosses T&R once, B twice"
# top -> bottom
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a1 = _calc_angle((_ymax - _yc), -_xd)
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
# bottom -> right, _xd now positive
_a1 = _calc_angle((_ymin - _yc), _xd)
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if _xc > _xmax:
print "x > xmax (%g > %g)" % (_xc, _xmax)
if _yc < _ymax:
print "y < ymax (%g < %g)" % (_yc, _ymax)
elif _bits == 0x1b:
print "circle center E near NW, crosses T&L once, R twice"
# left -> right
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# right -> top; _yd now positive
_a1 = _calc_angle(_yd, (_xmax - _xc))
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
_arcs.append((_a1, (_a2 - _a1)))
if _yc > _ymax:
print "y > ymax (%g > %g)" % (_yc, _ymax)
if _xc > _xmin:
print "x > xmin (%g > %g)" % (_xc, _xmin)
elif _bits == 0x8b:
print "circle center W near NE, crosses T&R once, L twice"
# top -> left
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a1 = _calc_angle((_ymax - _yc), -_xd)
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# left -> right; _yd now negative
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if _yc > _ymax:
print "y > ymax (%g > %g)" % (_yc, _ymax)
if _xc < _xmax:
print "x < xmax (%g < %g)" % (_xc, _xmax)
elif _bits == 0x27:
print "circle center W near SE, crosses B&R once, L twice"
# right -> left
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a1 = _calc_angle(_yd, (_xmax - _xc))
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
print "a1: %g; a2: %g" % (_a1, _a2)
_arcs.append((_a1, (_a2 - _a1)))
# left -> bottom; now _yd is negative
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
print "a1: %g; a2: %g" % (_a1, _a2)
_arcs.append((_a1, (_a2 - _a1)))
if _yc < _ymin:
print "y < ymin (%g < %g)" % (_yc, _ymin)
if _xc < _xmax:
print "x < xmax (%g < %g)" % (_xc, _xmax)
elif _bits == 0x47:
print "circle center E near SW, crosses B&L once, R twice"
# bottom -> right
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a1 = _calc_angle((_ymin - _yc), _xd)
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# right -> left; now _yd is positive
_a1 = _calc_angle(_yd, (_xmax - _xc))
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if _yc < ymin:
print "y < ymin (%g < %g)" % (_yc, _ymin)
if _xc > _xmin:
print "x > xmin (%g > %g)" % (_xc, _xmin)
elif _bits == 0x1f:
print "circle center NW, crosses L&T once, R&B twice"
# right -> top
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a1 = _calc_angle(_yd, (_xmax - _xc))
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
_arcs.append((_a1, (_a2 - _a1)))
# left -> bottom
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
# bottom -> right; _xd now positive
_a1 = _calc_angle((_ymin - _yc), _xd)
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if ((_xmin < _xc < _xmax) and (_ymin < _yc < _ymax)):
print "circle center in region"
else:
print "circle center out of region"
elif _bits == 0x8f:
print "circle center NE, crosses T&R once, B&L twice"
# top -> left
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a1 = _calc_angle((_ymax - _yc), -_xd)
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# left -> bottom; _yd now negative
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
# bottom -> right; _xd now positive
_a1 = _calc_angle((_ymin - _yc), _xd)
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if ((_xmin < _xc < _xmax) and (_ymin < _yc < _ymax)):
print "circle center in region"
else:
print "circle center out of region"
elif _bits == 0x2f:
print "circle center SE, crosses L&T twice, R&B once"
# top -> left
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a1 = _calc_angle((_ymax - _yc), -_xd)
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# left -> bottom; _yd now negative
_a1 = _calc_angle(-_yd, (_xmin - _xc))
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a2 = _calc_angle((_ymin - _yc), -_xd)
_arcs.append((_a1, (_a2 - _a1)))
# right -> top
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a1 = _calc_angle(_yd, (_xmax - _xc))
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
_arcs.append((_a1, (_a2 - _a1)))
if ((_xmin < _xc < _xmax) and (_ymin < _yc < _ymax)):
print "circle center in region"
else:
print "circle center out of region"
elif _bits == 0x4f:
print "circle center SW, crosses T&R twice, B&L once"
# bottom -> right
_xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
_a1 = _calc_angle((_ymin - _yc), _xd)
_yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
_a2 = _calc_angle(-_yd, (_xmax - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# right -> top; _yd now positive
_a1 = _calc_angle(_yd, (_xmax - _xc))
_xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
_a2 = _calc_angle((_ymax - _yc), _xd)
_arcs.append((_a1, (_a2 - _a1)))
# top -> left; _xd now negative
_a1 = _calc_angle((_ymax - _yc), -_xd)
_yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
_a2 = _calc_angle(_yd, (_xmin - _xc))
_arcs.append((_a1, (_a2 - _a1)))
if ((_xmin < _xc < _xmax) and (_ymin < _yc < _ymax)):
print "circle center in region"
else:
print "circle center out of region"
elif _bits == 0x0f:
print "circle crosses all edges twice"
_yld = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
_yrd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
_xtd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
_xbd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
# right -> top
_x1 = _xmax
_y1 = _yc + _yrd
_x2 = _xc + _xtd
_y2 = _ymax
_a1 = _calc_angle((_y1 - _yc), (_x1 - _xc))
_a2 = _calc_angle((_y2 - _yc), (_x2 - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# top -> left
_x1 = _xc - _xtd
_y1 = _ymax
_x2 = _xmin
_y2 = _yc + _yld
_a1 = _calc_angle((_y1 - _yc), (_x1 - _xc))
_a2 = _calc_angle((_y2 - _yc), (_x2 - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# left -> bottom
_x1 = _xmin
_y1 = _yc - _yld
_x2 = _xc - _xbd
_y2 = _ymin
_a1 = _calc_angle((_y1 - _yc), (_x1 - _xc))
_a2 = _calc_angle((_y2 - _yc), (_x2 - _xc))
_arcs.append((_a1, (_a2 - _a1)))
# bottom -> right
_x1 = _xc + _xbd
_y1 = _ymin
_x2 = _xmax
_y2 = _yc - _yrd
_a1 = _calc_angle((_y1 - _yc), (_x1 - _xc))
_a2 = _calc_angle((_y2 - _yc), (_x2 - _xc))
_arcs.append((_a1, (_a2 - _a1)))
elif _bits == 0xff:
print "circle outside region"
else:
print "Unexpected bit pattern: %#02x" % _bits
return _arcs
def _calc_angle(dy, dx):
_angle = math.atan2(dy, dx) * (180.0/math.pi)
if _angle < 0.0:
_angle = _angle + 360.0
return _angle
#
# Quadtree Circle storage
#
class CircleQuadtree(quadtree.Quadtree):
def __init__(self):
super(CircleQuadtree, self).__init__()
def getNodes(self, *args):
_alen = len(args)
if _alen != 3:
raise ValueError, "Expected 3 arguments, got %d" % _alen
_x = util.get_float(args[0])
_y = util.get_float(args[1])
_r = util.get_float(args[2])
_cxmin = _x - _r
_cxmax = _x + _r
_cymin = _y - _r
_cymax = _y + _r
_nodes = [self.getTreeRoot()]
while len(_nodes):
_node = _nodes.pop()
_xmin, _ymin, _xmax, _ymax = _node.getBoundary()
if ((_cxmin > _xmax) or
(_cxmax < _xmin) or
(_cymin > _ymax) or
(_cymax < _ymin)):
continue
if _node.hasSubnodes():
_xmid = (_xmin + _xmax)/2.0
_ymid = (_ymin + _ymax)/2.0
_ne = _nw = _sw = _se = True
if _cxmax < _xmid: # circle on left side
_ne = _se = False
if _cxmin > _xmid: # circle on right side
_nw = _sw = False
if _cymax < _ymid: # circle below
_nw = _ne = False
if _cymin > _ymid: # circle above
_sw = _se = False
if _ne:
_nodes.append(_node.getSubnode(quadtree.QTreeNode.NENODE))
if _nw:
_nodes.append(_node.getSubnode(quadtree.QTreeNode.NWNODE))
if _sw:
_nodes.append(_node.getSubnode(quadtree.QTreeNode.SWNODE))
if _se:
_nodes.append(_node.getSubnode(quadtree.QTreeNode.SENODE))
else:
yield _node
def addObject(self, obj):
if not isinstance(obj, Circle):
raise TypeError, "Invalid Circle object: " + `type(obj)`
if obj in self:
return
_x, _y = obj.getCenter().getCoords()
_r = obj.getRadius()
_bounds = self.getTreeRoot().getBoundary()
_xmin = _ymin = _xmax = _ymax = None
_cxmin = _x - _r
_cxmax = _x + _r
_cymin = _y - _r
_cymax = _y + _r
_resize = False
if _bounds is None: # first node in tree
_resize = True
_xmin = _cxmin - 1.0
_ymin = _cymin - 1.0
_xmax = _cxmax + 1.0
_ymax = _cymax + 1.0
else:
_xmin, _ymin, _xmax, _ymax = _bounds
if _cxmin < _xmin:
_xmin = _cxmin - 1.0
_resize = True
if _cxmax > _xmax:
_xmax = _cxmax + 1.0
_resize = True
if _cymin < _ymin:
_ymin = _cymin - 1.0
_resize = True
if _cymax > _ymax:
_ymax = _cymax + 1.0
_resize = True
if _resize:
self.resize(_xmin, _ymin, _xmax, _ymax)
for _node in self.getNodes(_x, _y, _r):
_xmin, _ymin, _xmax, _ymax = _node.getBoundary()
if obj.inRegion(_xmin, _ymin, _xmax, _ymax):
_node.addObject(obj)
super(CircleQuadtree, self).addObject(obj)
obj.connect('moved', self._moveCircle)
def delObject(self, obj):
if obj not in self:
return
_x, _y = obj.getCenter().getCoords()
_r = obj.getRadius()
_pdict = {}
for _node in self.getNodes(_x, _y, _r):
_node.delObject(obj) # circle may not be in the node ...
_parent = _node.getParent()
if _parent is not None:
_pid = id(_parent)
if _pid not in _pdict:
_pdict[_pid] = _parent
super(CircleQuadtree, self).delObject(obj)
obj.disconnect(self)
for _parent in _pdict.values():
self.purgeSubnodes(_parent)
def find(self, *args):
_alen = len(args)
if _alen < 3:
raise ValueError, "Invalid argument count: %d" % _alen
_x = util.get_float(args[0])
_y = util.get_float(args[1])
_r = util.get_float(args[2])
_t = tolerance.TOL
if _alen > 3:
_t = tolerance.toltest(args[4])
_xmin = _x - _r - _t
_xmax = _x + _r + _t
_ymin = _y - _r - _t
_ymax = _y + _r + _t
_circs = []
for _circ in self.getInRegion(_xmin, _ymin, _xmax, _ymax):
_cx, _cy = _circ.getCenter().getCoords()
if ((abs(_cx - _x) < _t) and
(abs(_cy - _y) < _t) and
(abs(_circ.getRadius() - _r) < _t)):
_circs.append(_circ)
return _circs
def _moveCircle(self, obj, *args):
if obj not in self:
raise ValueError, "Circle not stored in Quadtree: " + `obj`
_alen = len(args)
if _alen < 3:
raise ValueError, "Invalid argument count: %d" % _alen
_x = util.get_float(args[0])
_y = util.get_float(args[1])
_r = util.get_float(args[2])
for _node in self.getNodes(_x, _y, _r):
_node.delObject(obj) # circle may not be in node ...
super(CircleQuadtree, self).delObject(obj)
obj.disconnect(self)
self.addObject(obj)
def getClosest(self, x, y, tol=tolerance.TOL):
_x = util.get_float(x)
_y = util.get_float(y)
_t = tolerance.toltest(tol)
_circ = _tsep = None
_bailout = False
_cdict = {}
_nodes = [self.getTreeRoot()]
while len(_nodes):
_node = _nodes.pop()
_xmin, _ymin, _xmax, _ymax = _node.getBoundary()
if ((_x < (_xmin - _t)) or
(_x > (_xmax + _t)) or
(_y < (_ymin - _t)) or
(_y > (_ymax + _t))):
continue
if _node.hasSubnodes():
_nodes.extend(_node.getSubnodes())
else:
for _c in _node.getObjects():
_cid = id(_c)
if _cid not in _cdict:
_cp = _c.mapCoords(_x, _y, _t)
if _cp is not None:
_cx, _cy = _cp
_sep = math.hypot((_cx - _x), (_cy - _y))
if _tsep is None:
_tsep = _sep
_circ = _c
else:
if _sep < _tsep:
_tsep = _sep
_circ = _c
if _sep < 1e-10 and _circ is not None:
_bailout = True
break
if _bailout:
break
return _circ
def getInRegion(self, xmin, ymin, xmax, ymax):
_xmin = util.get_float(xmin)
_ymin = util.get_float(ymin)
_xmax = util.get_float(xmax)
if _xmax < _xmin:
raise ValueError, "Illegal values: xmax < xmin"
_ymax = util.get_float(ymax)
if _ymax < _ymin:
raise ValueError, "Illegal values: ymax < ymin"
_circs = []
if not len(self):
return _circs
_nodes = [self.getTreeRoot()]
_cdict = {}
while len(_nodes):
_node = _nodes.pop()
if _node.hasSubnodes():
for _subnode in _node.getSubnodes():
_sxmin, _symin, _sxmax, _symax = _subnode.getBoundary()
if ((_sxmin > _xmax) or
(_symin > _ymax) or
(_sxmax < _xmin) or
(_symax < _ymin)):
continue
_nodes.append(_subnode)
else:
for _circ in _node.getObjects():
_cid = id(_circ)
if _cid not in _cdict:
if _circ.inRegion(_xmin, _ymin, _xmax, _ymax):
_circs.append(_circ)
_cdict[_cid] = True
return _circs
#
# Circle history class
#
class CircleLog(graphicobject.GraphicObjectLog):
def __init__(self, c):
if not isinstance(c, Circle):
raise TypeError, "Invalid circle: " + `type(c)`
super(CircleLog, self).__init__(c)
c.connect('center_changed', self.__centerChanged)
c.connect('radius_changed', self.__radiusChanged)
def __radiusChanged(self, c, *args):
_alen = len(args)
if _alen < 1:
raise ValueError, "Invalid argument count: %d" % _alen
_r = args[0]
if not isinstance(_r, float):
raise TypeError, "Unxpected type for radius: " + `type(_r)`
self.saveUndoData('radius_changed', _r)
def __centerChanged(self, c, *args):
_alen = len(args)
if _alen < 1:
raise ValueError, "Invalid argument count: %d" % _alen
_old = args[0]
if not isinstance(_old, point.Point):
raise TypeError, "Invalid old center point: " + `type(_old)`
self.saveUndoData('center_changed', _old.getID())
def execute(self, undo, *args):
util.test_boolean(undo)
_alen = len(args)
if _alen == 0:
raise ValueError, "No arguments to execute()"
_c = self.getObject()
_cp = _c.getCenter()
_op = args[0]
if _op == 'radius_changed':
if len(args) < 2:
raise ValueError, "Invalid argument count: %d" % _alen
_r = args[1]
if not isinstance(_r, float):
raise TypeError, "Unexpected type for radius: " + `type(_r)`
_sdata = _c.getRadius()
self.ignore(_op)
try:
if undo:
_c.startUndo()
try:
_c.setRadius(_r)
finally:
_c.endUndo()
else:
_c.startRedo()
try:
_c.setRadius(_r)
finally:
_c.endRedo()
finally:
self.receive(_op)
self.saveData(undo, _op, _sdata)
elif _op == 'center_changed':
if _alen < 2:
raise ValueError, "Invalid argument count: %d" % _alen
_oid = args[1]
_parent = _c.getParent()
if _parent is None:
raise ValueError, "Circle has no parent - cannot undo"
_pt = _parent.getObject(_oid)
if _pt is None or not isinstance(_pt, point.Point):
raise ValueError, "Center point missing: id=%d" % _oid
_sdata = _cp.getID()
self.ignore(_op)
try:
if undo:
_c.startUndo()
try:
_c.setCenter(_pt)
finally:
_c.endUndo()
else:
_c.startRedo()
try:
_c.setCenter(_pt)
finally:
_c.endRedo()
finally:
self.receive(_op)
self.saveData(undo, _op, _sdata)
else:
super(CircleLog, self).execute(undo, *args)
