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Draft: move functions to draftgeoutils.circle_inversion
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# *************************************************************************** | ||
# * Copyright (c) 2009, 2010 Yorik van Havre <yorik@uncreated.net> * | ||
# * Copyright (c) 2009, 2010 Ken Cline <cline@frii.com> * | ||
# * * | ||
# * This file is part of the FreeCAD CAx development system. * | ||
# * * | ||
# * This program is free software; you can redistribute it and/or modify * | ||
# * it under the terms of the GNU Lesser General Public License (LGPL) * | ||
# * as published by the Free Software Foundation; either version 2 of * | ||
# * the License, or (at your option) any later version. * | ||
# * for detail see the LICENCE text file. * | ||
# * * | ||
# * FreeCAD 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 Library General Public License for more details. * | ||
# * * | ||
# * You should have received a copy of the GNU Library General Public * | ||
# * License along with FreeCAD; if not, write to the Free Software * | ||
# * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 * | ||
# * USA * | ||
# * * | ||
# *************************************************************************** | ||
"""Provides various functions for inversive operations using a circle. | ||
http://en.wikipedia.org/wiki/Inversive_geometry | ||
""" | ||
## @package circle_inversion | ||
# \ingroup DRAFTGEOUTILS | ||
# \brief Provides various functions for inversive geometry operations. | ||
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import lazy_loader.lazy_loader as lz | ||
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import FreeCAD as App | ||
import DraftVecUtils | ||
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from draftgeoutils.general import NORM, geomType | ||
from draftgeoutils.geometry import findDistance | ||
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# Delay import of module until first use because it is heavy | ||
Part = lz.LazyLoader("Part", globals(), "Part") | ||
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def pointInversion(circle, point): | ||
"""Return the circle inversion of a point. | ||
It will return `None` if the given point is equal to the center | ||
of the circle. | ||
""" | ||
if geomType(circle) != "Circle" or isinstance(point, App.Vector): | ||
print("debug: pointInversion bad parameters!") | ||
return None | ||
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cen = circle.Curve.Center | ||
rad = circle.Curve.Radius | ||
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if DraftVecUtils.equals(cen, point): | ||
return None | ||
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# Inverse the distance of the point | ||
# dist(cen -> P) = r^2 / dist(cen -> invP) | ||
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dist = DraftVecUtils.dist(point, cen) | ||
invDist = rad**2 / dist | ||
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invPoint = App.Vector(0, 0, point.z) | ||
invPoint.x = cen.x + (point.x - cen.x) * invDist / dist | ||
invPoint.y = cen.y + (point.y - cen.y) * invDist / dist | ||
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return invPoint | ||
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def polarInversion(circle, edge): | ||
"""Return the inversion pole of a line. The edge is the polar. | ||
The nearest point on the line is inversed. | ||
http://mathworld.wolfram.com/InversionPole.html | ||
""" | ||
if geomType(circle) != "Circle" or geomType(edge) != "Line": | ||
print("debug: circleInversionPole bad parameters! Must be a circle.") | ||
return None | ||
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nearest = circle.Curve.Center.add(findDistance(circle.Curve.Center, | ||
edge, | ||
False)) | ||
if nearest: | ||
inversionPole = pointInversion(circle, nearest) | ||
if inversionPole: | ||
return inversionPole | ||
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return None | ||
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def circleInversion(circle, circle2): | ||
"""Circle inversion of a circle, inverting the center point. | ||
Returns the new circle created from the inverted center of circle2. | ||
""" | ||
if geomType(circle) != "Circle" or geomType(circle2) != "Circle": | ||
print("debug: circleInversion bad parameters! Must be circles.") | ||
return None | ||
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cen1 = circle.Curve.Center | ||
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cen2 = circle2.Curve.Center | ||
rad2 = circle2.Curve.Radius | ||
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if DraftVecUtils.equals(cen1, cen2): | ||
return None | ||
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invCen2 = pointInversion(circle, cen2) | ||
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pointOnCircle2 = App.Vector.add(cen2, App.Vector(rad2, 0, 0)) | ||
invPointOnCircle2 = pointInversion(circle, pointOnCircle2) | ||
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return Part.Circle(invCen2, | ||
NORM, | ||
DraftVecUtils.dist(invCen2, invPointOnCircle2)) |