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985c397 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 | # SPDX-License-Identifier: LGPL-2.1-or-later
# ***************************************************************************
# * 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.
import lazy_loader.lazy_loader as lz
import FreeCAD as App
import DraftVecUtils
from draftgeoutils.general import NORM, geomType
from draftgeoutils.geometry import findDistance
# Delay import of module until first use because it is heavy
Part = lz.LazyLoader("Part", globals(), "Part")
## \addtogroup draftgeoutils
# @{
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
cen = circle.Curve.Center
rad = circle.Curve.Radius
if DraftVecUtils.equals(cen, point):
return None
# Inverse the distance of the point
# dist(cen -> P) = r^2 / dist(cen -> invP)
dist = DraftVecUtils.dist(point, cen)
invDist = rad**2 / dist
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
return invPoint
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
nearest = circle.Curve.Center.add(findDistance(circle.Curve.Center, edge, False))
if nearest:
inversionPole = pointInversion(circle, nearest)
if inversionPole:
return inversionPole
return None
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
cen1 = circle.Curve.Center
cen2 = circle2.Curve.Center
rad2 = circle2.Curve.Radius
if DraftVecUtils.equals(cen1, cen2):
return None
invCen2 = pointInversion(circle, cen2)
pointOnCircle2 = App.Vector.add(cen2, App.Vector(rad2, 0, 0))
invPointOnCircle2 = pointInversion(circle, pointOnCircle2)
return Part.Circle(invCen2, NORM, DraftVecUtils.dist(invCen2, invPointOnCircle2))
## @}
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