def circlefrom1Line2Points(edge, p1, p2):
"""circlefrom1Line2Points(edge, Vector, Vector)"""
p1_p2 = edg(p1, p2)
s = findIntersection(edge, p1_p2, True, True)
if not s: return None
s = s[0]
v1 = p1.sub(s)
v2 = p2.sub(s)
projectedDist = math.sqrt(abs(v1.dot(v2)))
edgeDir = vec(edge)
edgeDir.normalize()
projectedCen1 = Vector.add(s, Vector(edgeDir).multiply(projectedDist))
projectedCen2 = Vector.add(s, Vector(edgeDir).multiply(-projectedDist))
perpEdgeDir = edgeDir.cross(Vector(0, 0, 1))
perpCen1 = Vector.add(projectedCen1, perpEdgeDir)
perpCen2 = Vector.add(projectedCen2, perpEdgeDir)
mid = findMidpoint(p1_p2)
x = DraftVecUtils.crossproduct(vec(p1_p2))
x.normalize()
perp_mid = Vector.add(mid, x)
cen1 = findIntersection(edg(projectedCen1, perpCen1), edg(mid, perp_mid),
True, True)
cen2 = findIntersection(edg(projectedCen2, perpCen2), edg(mid, perp_mid),
True, True)
circles = []
if cen1:
radius = DraftVecUtils.dist(projectedCen1, cen1[0])
circles.append(Part.Circle(cen1[0], NORM, radius))
if cen2:
radius = DraftVecUtils.dist(projectedCen2, cen2[0])
circles.append(Part.Circle(cen2[0], NORM, radius))
if circles: return circles
else: return None
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
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
def getCircleFromSpline(edge):
"""Return a circle-based edge from a bspline-based edge."""
if geomType(edge) != "BSplineCurve":
return None
if len(edge.Vertexes) != 1:
return None
# get 2 points
p1 = edge.Curve.value(0)
p2 = edge.Curve.value(math.pi / 2)
# get 2 tangents
t1 = edge.Curve.tangent(0)[0]
t2 = edge.Curve.tangent(math.pi / 2)[0]
# get normal
n = p1.cross(p2)
if DraftVecUtils.isNull(n):
return None
# get rays
r1 = DraftVecUtils.rotate(t1, math.pi / 2, n)
r2 = DraftVecUtils.rotate(t2, math.pi / 2, n)
# get center (intersection of rays)
i = findIntersection(p1, p1.add(r1), p2, p2.add(r2), True, True)
if not i:
return None
c = i[0]
r = (p1.sub(c)).Length
circle = Part.makeCircle(r, c, n)
#print(circle.Curve)
return circle
def findRadicalCenter(circle1, circle2, circle3):
"""
findRadicalCenter(circle1, circle2, circle3):
Calculates the radical center (also called the power center) of three circles.
It is the intersection point of the three radical axes of the pairs of circles.
http://en.wikipedia.org/wiki/Power_center_(geometry)
http://mathworld.wolfram.com/RadicalCenter.html
@sa findRadicalAxis
"""
if (geomType(circle1) == "Circle") and (geomType(circle2) == "Circle"):
radicalAxis12 = findRadicalAxis(circle1, circle2)
radicalAxis23 = findRadicalAxis(circle1, circle2)
if not radicalAxis12 or not radicalAxis23:
# No radical center could be calculated.
return None
int = findIntersection(radicalAxis12, radicalAxis23, True, True)
if int:
return int
else:
# No radical center could be calculated.
return None
else:
FreeCAD.Console.PrintMessage(
"debug: findRadicalCenter bad parameters!\n")
return None
def findRadicalCenter(circle1, circle2, circle3):
"""Calculate the radical center of three circles.
It is also called the power center.
It is the intersection point of the three radical axes of the pairs
of circles.
http://en.wikipedia.org/wiki/Power_center_(geometry)
http://mathworld.wolfram.com/RadicalCenter.html
See Also
--------
findRadicalAxis
"""
if (geomType(circle1) != "Circle"
or geomType(circle2) != "Circle"
or geomType(circle3) != "Circle"):
print("debug: findRadicalCenter bad parameters! Must be circles.")
return None
radicalAxis12 = findRadicalAxis(circle1, circle2)
radicalAxis23 = findRadicalAxis(circle2, circle3)
if not radicalAxis12 or not radicalAxis23:
# No radical center could be calculated.
return None
intersect = findIntersection(radicalAxis12, radicalAxis23, True, True)
if intersect:
return intersect
else:
# No radical center could be calculated.
return None
def circleFrom2LinesRadius(edge1, edge2, radius):
"""Retun a list of circles from two edges and one radius.
It calculates 4 centers.
"""
intsec = findIntersection(edge1, edge2, True, True)
if not intsec:
return None
intsec = intsec[0]
bis12 = angleBisection(edge1, edge2)
bis21 = Part.LineSegment(bis12.Vertexes[0].Point,
DraftVecUtils.rotate(vec(bis12), math.pi/2.0))
ang12 = abs(DraftVecUtils.angle(vec(edge1), vec(edge2)))
ang21 = math.pi - ang12
dist12 = radius / math.sin(ang12 * 0.5)
dist21 = radius / math.sin(ang21 * 0.5)
circles = []
cen = App.Vector.add(intsec, vec(bis12).multiply(dist12))
circles.append(Part.Circle(cen, NORM, radius))
cen = App.Vector.add(intsec, vec(bis12).multiply(-dist12))
circles.append(Part.Circle(cen, NORM, radius))
cen = App.Vector.add(intsec, vec(bis21).multiply(dist21))
circles.append(Part.Circle(cen, NORM, radius))
cen = App.Vector.add(intsec, vec(bis21).multiply(-dist21))
circles.append(Part.Circle(cen, NORM, radius))
return circles
def circleFrom3LineTangents(edge1, edge2, edge3):
"""Return a list of circles from three edges.
It calculates up to 6 possible centers.
"""
def rot(ed):
geo = Part.LineSegment(v1(ed),
v1(ed).add(DraftVecUtils.rotate(vec(ed),
math.pi/2)))
return geo.toShape()
bis12 = angleBisection(edge1, edge2)
bis23 = angleBisection(edge2, edge3)
bis31 = angleBisection(edge3, edge1)
intersections = []
intsec = findIntersection(bis12, bis23, True, True)
if intsec:
radius = findDistance(intsec[0], edge1).Length
intersections.append(Part.Circle(intsec[0], NORM, radius))
intsec = findIntersection(bis23, bis31, True, True)
if intsec:
radius = findDistance(intsec[0], edge1).Length
intersections.append(Part.Circle(intsec[0], NORM, radius))
intsec = findIntersection(bis31, bis12, True, True)
if intsec:
radius = findDistance(intsec[0], edge1).Length
intersections.append(Part.Circle(intsec[0], NORM, radius))
intsec = findIntersection(rot(bis12), rot(bis23), True, True)
if intsec:
radius = findDistance(intsec[0], edge1).Length
intersections.append(Part.Circle(intsec[0], NORM, radius))
intsec = findIntersection(rot(bis23), rot(bis31), True, True)
if intsec:
radius = findDistance(intsec[0], edge1).Length
intersections.append(Part.Circle(intsec[0], NORM, radius))
intsec = findIntersection(rot(bis31), rot(bis12), True, True)
if intsec:
radius = findDistance(intsec[0], edge1).Length
intersections.append(Part.Circle(intsec[0], NORM, radius))
circles = []
for intsec in intersections:
exists = False
for cir in circles:
if DraftVecUtils.equals(cir.Center, intsec.Center):
exists = True
break
if not exists:
circles.append(intsec)
if circles:
return circles
else:
return None
def circleFrom3LineTangents(edge1, edge2, edge3):
"""circleFrom3LineTangents(edge,edge,edge)"""
def rot(ed):
return Part.LineSegment(
v1(ed),
v1(ed).add(DraftVecUtils.rotate(vec(ed), math.pi / 2))).toShape()
bis12 = angleBisection(edge1, edge2)
bis23 = angleBisection(edge2, edge3)
bis31 = angleBisection(edge3, edge1)
intersections = []
int = findIntersection(bis12, bis23, True, True)
if int:
radius = findDistance(int[0], edge1).Length
intersections.append(Part.Circle(int[0], NORM, radius))
int = findIntersection(bis23, bis31, True, True)
if int:
radius = findDistance(int[0], edge1).Length
intersections.append(Part.Circle(int[0], NORM, radius))
int = findIntersection(bis31, bis12, True, True)
if int:
radius = findDistance(int[0], edge1).Length
intersections.append(Part.Circle(int[0], NORM, radius))
int = findIntersection(rot(bis12), rot(bis23), True, True)
if int:
radius = findDistance(int[0], edge1).Length
intersections.append(Part.Circle(int[0], NORM, radius))
int = findIntersection(rot(bis23), rot(bis31), True, True)
if int:
radius = findDistance(int[0], edge1).Length
intersections.append(Part.Circle(int[0], NORM, radius))
int = findIntersection(rot(bis31), rot(bis12), True, True)
if int:
radius = findDistance(int[0], edge1).Length
intersections.append(Part.Circle(int[0], NORM, radius))
circles = []
for int in intersections:
exists = False
for cir in circles:
if DraftVecUtils.equals(cir.Center, int.Center):
exists = True
break
if not exists:
circles.append(int)
if circles:
return circles
else:
return None
def circleFrom2LinesRadius(edge1, edge2, radius):
"""circleFrom2LinesRadius(edge,edge,radius)"""
int = findIntersection(edge1, edge2, True, True)
if not int: return None
int = int[0]
bis12 = angleBisection(edge1, edge2)
bis21 = Part.LineSegment(bis12.Vertexes[0].Point,
DraftVecUtils.rotate(vec(bis12), math.pi / 2.0))
ang12 = abs(DraftVecUtils.angle(vec(edge1), vec(edge2)))
ang21 = math.pi - ang12
dist12 = radius / math.sin(ang12 * 0.5)
dist21 = radius / math.sin(ang21 * 0.5)
circles = []
cen = Vector.add(int, vec(bis12).multiply(dist12))
circles.append(Part.Circle(cen, NORM, radius))
cen = Vector.add(int, vec(bis12).multiply(-dist12))
circles.append(Part.Circle(cen, NORM, radius))
cen = Vector.add(int, vec(bis21).multiply(dist21))
circles.append(Part.Circle(cen, NORM, radius))
cen = Vector.add(int, vec(bis21).multiply(-dist21))
circles.append(Part.Circle(cen, NORM, radius))
return circles
def angleBisection(edge1, edge2):
"""angleBisection(edge,edge) - Returns an edge that bisects the angle between the 2 edges."""
if (geomType(edge1) == "Line") and (geomType(edge2) == "Line"):
p1 = edge1.Vertexes[0].Point
p2 = edge1.Vertexes[-1].Point
p3 = edge2.Vertexes[0].Point
p4 = edge2.Vertexes[-1].Point
int = findIntersection(edge1, edge2, True, True)
if int:
line1Dir = p2.sub(p1)
angleDiff = DraftVecUtils.angle(line1Dir, p4.sub(p3))
ang = angleDiff * 0.5
origin = int[0]
line1Dir.normalize()
dir = DraftVecUtils.rotate(line1Dir, ang)
return Part.LineSegment(origin, origin.add(dir)).toShape()
else:
diff = p3.sub(p1)
origin = p1.add(diff.multiply(0.5))
dir = p2.sub(p1)
dir.normalize()
return Part.LineSegment(origin, origin.add(dir)).toShape()
else:
return None
