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Draft: move functions to draftgeoutils.circles_apollonius

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This commit is contained in:
vocx-fc
2020-06-01 03:34:39 -05:00
committed by Yorik van Havre
parent 627e665c5d
commit 0ba43a993e
3 changed files with 226 additions and 157 deletions
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1
src/Mod/Draft/CMakeLists.txt
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@@ -43,6 +43,7 @@ SET (Draft_geoutils
draftgeoutils/linear_algebra.py
draftgeoutils/cuboids.py
draftgeoutils/circles.py
draftgeoutils/circles_apollonius.py
)
SET(Draft_tests

160
src/Mod/Draft/DraftGeomUtils.py
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@@ -385,167 +385,13 @@ from draftgeoutils.arcs import arcFrom2Pts
#############################33 to include
from draftgeoutils.circles_apollonius import outerSoddyCircle
from draftgeoutils.circles_apollonius import innerSoddyCircle
def outerSoddyCircle(circle1, circle2, circle3):
"""Compute the outer soddy circle for three tightly packed circles."""
if (geomType(circle1) == "Circle") and (geomType(circle2) == "Circle") \
and (geomType(circle3) == "Circle"):
# Original Java code Copyright (rc) 2008 Werner Randelshofer
# Converted to python by Martin Buerbaum 2009
# http://www.randelshofer.ch/treeviz/
# Either Creative Commons Attribution 3.0, the MIT license, or the GNU Lesser General License LGPL.
A = circle1.Curve.Center
B = circle2.Curve.Center
C = circle3.Curve.Center
ra = circle1.Curve.Radius
rb = circle2.Curve.Radius
rc = circle3.Curve.Radius
# Solution using Descartes' theorem, as described here:
# http://en.wikipedia.org/wiki/Descartes%27_theorem
k1 = 1 / ra
k2 = 1 / rb
k3 = 1 / rc
k4 = abs(k1 + k2 + k3 - 2 * math.sqrt(k1 * k2 + k2 * k3 + k3 * k1))
q1 = (k1 + 0j) * (A.x + A.y * 1j)
q2 = (k2 + 0j) * (B.x + B.y * 1j)
q3 = (k3 + 0j) * (C.x + C.y * 1j)
temp = ((q1 * q2) + (q2 * q3) + (q3 * q1))
q4 = q1 + q2 + q3 - ((2 + 0j) * cmath.sqrt(temp) )
z = q4 / (k4 + 0j)
# If the formula is not solvable, we return no circle.
if (not z or not (1 / k4)):
return None
X = -z.real
Y = -z.imag
print("Outer Soddy circle: " + str(X) + " " + str(Y) + "\n") # Debug
# The Radius of the outer soddy circle can also be calculated with the following formula:
# radiusOuter = abs(r1*r2*r3 / (r1*r2 + r1*r3 + r2*r3 - 2 * math.sqrt(r1*r2*r3 * (r1+r2+r3))))
circ = Part.Circle(Vector(X, Y, A.z), norm, 1 / k4)
return circ
else:
print("debug: outerSoddyCircle bad parameters!\n")
# FreeCAD.Console.PrintMessage("debug: outerSoddyCircle bad parameters!\n")
return None
def innerSoddyCircle(circle1, circle2, circle3):
"""Compute the inner soddy circle for three tightly packed circles."""
if (geomType(circle1) == "Circle") and (geomType(circle2) == "Circle") \
and (geomType(circle3) == "Circle"):
# Original Java code Copyright (rc) 2008 Werner Randelshofer
# Converted to python by Martin Buerbaum 2009
# http://www.randelshofer.ch/treeviz/
A = circle1.Curve.Center
B = circle2.Curve.Center
C = circle3.Curve.Center
ra = circle1.Curve.Radius
rb = circle2.Curve.Radius
rc = circle3.Curve.Radius
# Solution using Descartes' theorem, as described here:
# http://en.wikipedia.org/wiki/Descartes%27_theorem
k1 = 1 / ra
k2 = 1 / rb
k3 = 1 / rc
k4 = abs(k1 + k2 + k3 + 2 * math.sqrt(k1 * k2 + k2 * k3 + k3 * k1))
q1 = (k1 + 0j) * (A.x + A.y * 1j)
q2 = (k2 + 0j) * (B.x + B.y * 1j)
q3 = (k3 + 0j) * (C.x + C.y * 1j)
temp = ((q1 * q2) + (q2 * q3) + (q3 * q1))
q4 = q1 + q2 + q3 + ((2 + 0j) * cmath.sqrt(temp) )
z = q4 / (k4 + 0j)
# If the formula is not solvable, we return no circle.
if (not z or not (1 / k4)):
return None
X = z.real
Y = z.imag
print("Outer Soddy circle: " + str(X) + " " + str(Y) + "\n") # Debug
# The Radius of the inner soddy circle can also be calculated with the following formula:
# radiusInner = abs(r1*r2*r3 / (r1*r2 + r1*r3 + r2*r3 + 2 * math.sqrt(r1*r2*r3 * (r1+r2+r3))))
circ = Part.Circle(Vector(X, Y, A.z), norm, 1 / k4)
return circ
else:
print("debug: innerSoddyCircle bad parameters!\n")
# FreeCAD.Console.PrintMessage("debug: innerSoddyCircle bad parameters!\n")
return None
def circleFrom3CircleTangents(circle1, circle2, circle3):
"""
http://en.wikipedia.org/wiki/Problem_of_Apollonius#Inversive_methods
http://mathworld.wolfram.com/ApolloniusCircle.html
http://mathworld.wolfram.com/ApolloniusProblem.html
"""
if (geomType(circle1) == "Circle") and (geomType(circle2) == "Circle") \
and (geomType(circle3) == "Circle"):
int12 = findIntersection(circle1, circle2, True, True)
int23 = findIntersection(circle2, circle3, True, True)
int31 = findIntersection(circle3, circle1, True, True)
if int12 and int23 and int31:
if len(int12) == 1 and len(int23) == 1 and len(int31) == 1:
# Only one intersection with each circle.
# => "Soddy Circle" - 2 solutions.
# http://en.wikipedia.org/wiki/Problem_of_Apollonius#Mutually_tangent_given_circles:_Soddy.27s_circles_and_Descartes.27_theorem
# http://mathworld.wolfram.com/SoddyCircles.html
# http://mathworld.wolfram.com/InnerSoddyCenter.html
# http://mathworld.wolfram.com/OuterSoddyCenter.html
r1 = circle1.Curve.Radius
r2 = circle2.Curve.Radius
r3 = circle3.Curve.Radius
outerSoddy = outerSoddyCircle(circle1, circle2, circle3)
# print(str(outerSoddy) + "\n") # Debug
innerSoddy = innerSoddyCircle(circle1, circle2, circle3)
# print(str(innerSoddy) + "\n") # Debug
circles = []
if outerSoddy:
circles.append(outerSoddy)
if innerSoddy:
circles.append(innerSoddy)
return circles
# @todo Calc all 6 homothetic centers.
# @todo Create 3 lines from the inner and 4 from the outer h. center.
# @todo Calc. the 4 inversion poles of these lines for each circle.
# @todo Calc. the radical center of the 3 circles.
# @todo Calc. the intersection points (max. 8) of 4 lines (through each inversion pole and the radical center) with the circle.
# This gives us all the tangent points.
else:
# Some circles are inside each other or an error has occurred.
return None
else:
print("debug: circleFrom3CircleTangents bad parameters!\n")
# FreeCAD.Console.PrintMessage("debug: circleFrom3CircleTangents bad parameters!\n")
return None
from draftgeoutils.circles_apollonius import circleFrom3CircleTangents
from draftgeoutils.linear_algebra import linearFromPoints

222
src/Mod/Draft/draftgeoutils/circles_apollonius.py Normal file
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@@ -0,0 +1,222 @@
# ***************************************************************************
# * 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 Appollonius and Soddy circle operations.
The 'problem of Appollonius' consists of finding a circle that is
simultaneously tangent to three circles on a plane.
- http://en.wikipedia.org/wiki/Problem_of_Apollonius#Inversive_methods
- http://mathworld.wolfram.com/ApolloniusCircle.html
- http://mathworld.wolfram.com/ApolloniusProblem.html
If each circle only has one intersection with each other, the problem is that
of finding a 'Soddy circle', which has two solutions, and inner circle
and an outer circle.
- http://en.wikipedia.org/wiki/Problem_of_Apollonius#Mutually_tangent_given_circles:_Soddy.27s_circles_and_Descartes.27_theorem
- http://mathworld.wolfram.com/SoddyCircles.html
- http://mathworld.wolfram.com/InnerSoddyCenter.html
- http://mathworld.wolfram.com/OuterSoddyCenter.html
"""
## @package circles_apollonius
# \ingroup DRAFTGEOUTILS
# \brief Provides various functions for Appollonius and Soddy circles.
import cmath
import math
import lazy_loader.lazy_loader as lz
import FreeCAD as App
import DraftVecUtils
from draftgeoutils.general import geomType, vec, NORM
from draftgeoutils.intersections import findIntersection
# Delay import of module until first use because it is heavy
Part = lz.LazyLoader("Part", globals(), "Part")
def outerSoddyCircle(circle1, circle2, circle3):
"""Compute the outer soddy circle for three tightly packed circles.
Original Java code Copyright (rc) 2008 Werner Randelshofer
Converted to python by Martin Buerbaum 2009
http://www.randelshofer.ch/treeviz/
Either Creative Commons Attribution 3.0, the MIT license,
or the GNU Lesser General License LGPL.
"""
if (geomType(circle1) != "Circle"
or geomType(circle2) != "Circle"
or geomType(circle3) != "Circle"):
print("debug: outerSoddyCircle bad parameters! Must be circles.")
return None
A = circle1.Curve.Center
B = circle2.Curve.Center
C = circle3.Curve.Center
ra = circle1.Curve.Radius
rb = circle2.Curve.Radius
rc = circle3.Curve.Radius
# Solution using Descartes' theorem, as described here:
# http://en.wikipedia.org/wiki/Descartes%27_theorem
k1 = 1 / ra
k2 = 1 / rb
k3 = 1 / rc
k4 = abs(k1 + k2 + k3 - 2 * math.sqrt(k1 * k2 + k2 * k3 + k3 * k1))
q1 = (k1 + 0j) * (A.x + A.y * 1j)
q2 = (k2 + 0j) * (B.x + B.y * 1j)
q3 = (k3 + 0j) * (C.x + C.y * 1j)
temp = ((q1 * q2) + (q2 * q3) + (q3 * q1))
q4 = q1 + q2 + q3 - ((2 + 0j) * cmath.sqrt(temp))
z = q4 / (k4 + 0j)
# If the formula is not solvable, we return no circle.
if not z or not (1 / k4):
return None
X = -z.real
Y = -z.imag
print("Outer Soddy circle: " + str(X) + " " + str(Y) + "\n") # Debug
# The Radius of the outer soddy circle can also be calculated
# with the following formula:
# radiusOuter = abs(r1*r2*r3 / (r1*r2 + r1*r3 + r2*r3 - 2 * math.sqrt(r1*r2*r3 * (r1+r2+r3))))
circ = Part.Circle(App.Vector(X, Y, A.z), NORM, 1 / k4)
return circ
def innerSoddyCircle(circle1, circle2, circle3):
"""Compute the inner soddy circle for three tightly packed circles.
Original Java code Copyright (rc) 2008 Werner Randelshofer
Converted to python by Martin Buerbaum 2009
http://www.randelshofer.ch/treeviz/
"""
if (geomType(circle1) != "Circle"
and geomType(circle2) != "Circle"
and geomType(circle3) != "Circle"):
print("debug: innerSoddyCircle bad parameters! Must be circles.")
return None
A = circle1.Curve.Center
B = circle2.Curve.Center
C = circle3.Curve.Center
ra = circle1.Curve.Radius
rb = circle2.Curve.Radius
rc = circle3.Curve.Radius
# Solution using Descartes' theorem, as described here:
# http://en.wikipedia.org/wiki/Descartes%27_theorem
k1 = 1 / ra
k2 = 1 / rb
k3 = 1 / rc
k4 = abs(k1 + k2 + k3 + 2 * math.sqrt(k1 * k2 + k2 * k3 + k3 * k1))
q1 = (k1 + 0j) * (A.x + A.y * 1j)
q2 = (k2 + 0j) * (B.x + B.y * 1j)
q3 = (k3 + 0j) * (C.x + C.y * 1j)
temp = ((q1 * q2) + (q2 * q3) + (q3 * q1))
q4 = q1 + q2 + q3 + ((2 + 0j) * cmath.sqrt(temp))
z = q4 / (k4 + 0j)
# If the formula is not solvable, we return no circle.
if (not z or not (1 / k4)):
return None
X = z.real
Y = z.imag
print("Outer Soddy circle: " + str(X) + " " + str(Y) + "\n") # Debug
# The Radius of the inner soddy circle can also be calculated
# with the following formula:
# radiusInner = abs(r1*r2*r3 / (r1*r2 + r1*r3 + r2*r3 + 2 * math.sqrt(r1*r2*r3 * (r1+r2+r3))))
circ = Part.Circle(App.Vector(X, Y, A.z), NORM, 1 / k4)
return circ
def circleFrom3CircleTangents(circle1, circle2, circle3):
"""Return the circle that is tangent to three other circles.
This problem is called the 'Problem of Appollonius'.
A special case is that of 'Soddy circles'.
To Do
-----
Currently not all possible solutions are found, only the Soddy circles.
* Calc all 6 homothetic centers.
* Create 3 lines from the inner and 4 from the outer h. center.
* Calc. the 4 inversion poles of these lines for each circle.
* Calc. the radical center of the 3 circles.
* Calc. the intersection points (max. 8) of 4 lines (through each
inversion pole and the radical center) with the circle.
* This gives us all the tangent points.
"""
if (geomType(circle1) != "Circle"
and geomType(circle2) != "Circle"
and geomType(circle3) == "Circle"):
print("debug: circleFrom3CircleTangents bad input! Must be circles")
return None
int12 = findIntersection(circle1, circle2, True, True)
int23 = findIntersection(circle2, circle3, True, True)
int31 = findIntersection(circle3, circle1, True, True)
if int12 and int23 and int31:
if len(int12) == 1 and len(int23) == 1 and len(int31) == 1:
# If only one intersection with each circle, Soddy circle
# r1 = circle1.Curve.Radius
# r2 = circle2.Curve.Radius
# r3 = circle3.Curve.Radius
outerSoddy = outerSoddyCircle(circle1, circle2, circle3)
# print(str(outerSoddy)) # Debug
innerSoddy = innerSoddyCircle(circle1, circle2, circle3)
# print(str(innerSoddy)) # Debug
circles = []
if outerSoddy:
circles.append(outerSoddy)
if innerSoddy:
circles.append(innerSoddy)
return circles
# Here the rest of the circles should be calculated
# ...
else:
# Some circles are inside each other or an error has occurred.
return None