def circleFromPointLineRadius(point, edge, radius):
"""Return a list of circles from one point, one edge, and one radius.
It calculates up to 2 possible centers.
"""
dist = findDistance(point, edge, False)
center1 = None
center2 = None
if dist.Length == 0:
segment = vec(edge)
perpVec = DraftVecUtils.crossproduct(segment)
perpVec.normalize()
normPoint_c1 = App.Vector(perpVec).multiply(radius)
normPoint_c2 = App.Vector(perpVec).multiply(-radius)
center1 = point.add(normPoint_c1)
center2 = point.add(normPoint_c2)
elif dist.Length > 2 * radius:
return None
elif dist.Length == 2 * radius:
normPoint = point.add(findDistance(point, edge, False))
dummy = (normPoint.sub(point)).multiply(0.5)
cen = point.add(dummy)
circ = Part.Circle(cen, NORM, radius)
if circ:
return [circ]
else:
return None
else:
normPoint = point.add(findDistance(point, edge, False))
normDist = DraftVecUtils.dist(normPoint, point)
dist = math.sqrt(radius**2 - (radius - normDist)**2)
centerNormVec = DraftVecUtils.scaleTo(point.sub(normPoint), radius)
edgeDir = edge.Vertexes[0].Point.sub(normPoint)
edgeDir.normalize()
center1 = centerNormVec.add(
normPoint.add(App.Vector(edgeDir).multiply(dist)))
center2 = centerNormVec.add(
normPoint.add(App.Vector(edgeDir).multiply(-dist)))
circles = []
if center1:
circ = Part.Circle(center1, NORM, radius)
if circ:
circles.append(circ)
if center2:
circ = Part.Circle(center2, NORM, radius)
if circ:
circles.append(circ)
if circles:
return circles
else:
return None
def mirror(point, edge):
"""Find mirror point relative to an edge."""
normPoint = point.add(findDistance(point, edge, False))
if normPoint:
normPoint_point = Vector.sub(point, normPoint)
normPoint_refl = normPoint_point.negative()
refl = Vector.add(normPoint, normPoint_refl)
return refl
else:
return None
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 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 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 polarInversion(circle, edge):
"""Return the inversion pole of a line.
polarInversion(circle, edge):
edge ... The polar.
i.e. The nearest point on the line is inversed.
http://mathworld.wolfram.com/InversionPole.html
"""
if (geomType(circle) == "Circle") and (geomType(edge) == "Line"):
nearest = circle.Curve.Center.add(
findDistance(circle.Curve.Center, edge, False))
if nearest:
inversionPole = pointInversion(circle, nearest)
if inversionPole:
return inversionPole
else:
FreeCAD.Console.PrintMessage(
"debug: circleInversionPole bad parameters!\n")
return None