121 lines
2.8 KiB
Python
121 lines
2.8 KiB
Python
#! python
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# -*- coding: utf-8 -*-
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# (c) 2010 Werner Mayer LGPL
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__author__ = "Werner Mayer <wmayer[at]users.sourceforge.net>"
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# Formulas:
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# M2 = P + b*r2 + t*u
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# S1 = (r2*M1 + r1*M2)/(r1+r2)
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# S2 = M2-b*r2
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import math
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# 3d vector class
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class Vector:
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def __init__(self,x,y,z):
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self.x=x
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self.y=y
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self.z=z
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def add(self,vec):
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return Vector(self.x+vec.x,self.y+vec.y,self.z+vec.z)
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def sub(self,vec):
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return Vector(self.x-vec.x,self.y-vec.y,self.z-vec.z)
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def dot(self,vec):
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return self.x*vec.x+self.y*vec.y+self.z*vec.z
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def mult(self,s):
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return Vector(self.x*s,self.y*s,self.z*s)
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def cross(self,vec):
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return Vector(
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self.y * vec.z - self.z * vec.y,
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self.z * vec.x - self.x * vec.z,
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self.x * vec.y - self.y * vec.x)
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def length(self):
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return math.sqrt(self.x*self.x+self.y*self.y+self.z*self.z)
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def norm(self):
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l = self.length()
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if l > 0:
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self.x /= l
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self.y /= l
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self.z /= l
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def __repr__(self):
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return "(%f,%f,%f)" % (self.x,self.y,self.z)
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# A signum function
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def sgn(val):
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if val > 0:
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return 1
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elif val < 0:
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return -1
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else:
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return 0
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# M1 ... is the center of the arc
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# P ... is the end point of the arc and start point of the line
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# Q .. is a second point on the line
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# N ... is the normal of the plane where the arc and the line lie on, usually N=(0,0,1)
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# r2 ... the fillet radius
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# ccw ... counter-clockwise means which part of the arc is given. ccw must be either True or False
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def makeFilletArc(M1,P,Q,N,r2,ccw):
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u = Q.sub(P)
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v = P.sub(M1)
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if ccw:
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b = u.cross(N)
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else:
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b = N.cross(u)
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b.norm()
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uu = u.dot(u)
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uv = u.dot(v)
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r1 = v.length()
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# distinguish between internal and external fillets
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r2 *= sgn(uv);
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cc = 2.0 * r2 * (b.dot(v)-r1)
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dd = uv * uv - uu * cc
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if dd < 0:
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raise RuntimeError("Unable to calculate intersection points")
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t1 = (-uv + math.sqrt(dd)) / uu
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t2 = (-uv - math.sqrt(dd)) / uu
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if (abs(t1) < abs(t2)):
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t = t1
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else:
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t = t2
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br2 = b.mult(r2)
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print(br2)
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ut = u.mult(t)
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print(ut)
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M2 = P.add(ut).add(br2)
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S1 = M1.mult(r2/(r1+r2)).add(M2.mult(r1/(r1+r2)))
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S2 = M2.sub(br2)
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return (S1,S2,M2)
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def test():
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from FreeCAD import Base
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import Part
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P1=Base.Vector(1,-5,0)
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P2=Base.Vector(-5,2,0)
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P3=Base.Vector(1,5,0)
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#Q=Base.Vector(5,10,0)
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#Q=Base.Vector(5,11,0)
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Q=Base.Vector(5,0,0)
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r2=3.0
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axis=Base.Vector(0,0,1)
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ccw=False
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arc=Part.ArcOfCircle(P1,P2,P3)
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C=arc.Center
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Part.show(Part.makeLine(P3,Q))
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Part.show(arc.toShape())
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(S1,S2,M2) = makeArc(Vector(C.x,C.y,C.z),Vector(P3.x,P3.y,P3.z),Vector(Q.x,Q.y,Q.z),Vector(axis.x,axis.y,axis.z),r2,ccw)
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circle=Part.Circle(Base.Vector(M2.x,M2.y,M2.z), Base.Vector(0,0,1), math.fabs(r2))
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Part.show(circle.toShape())
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