Fixed helix construction.
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Markus Lampert
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0fabe5c079
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@ -128,6 +128,33 @@ class PathGeom:
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Convenience function to return the projection of the Vector in the XY-plane."""
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return Vector(point.x, point.y, 0)
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@classmethod
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def cmdForEdge(cls, edge):
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pt = edge.valueAt(edge.LastParameter)
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params = {'X': pt.x, 'Y': pt.y, 'Z': pt.z}
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if type(edge.Curve) == Part.Line or type(edge.Curve) == Part.LineSegment:
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command = Path.Command('G1', params)
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else:
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p1 = edge.valueAt(edge.FirstParameter)
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p2 = edge.valueAt((edge.FirstParameter + edge.LastParameter)/2)
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p3 = pt
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if Side.Left == Side.of(p2 - p1, p3 - p2):
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cmd = 'G3'
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else:
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cmd = 'G2'
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pa = PathGeom.xy(p1)
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pb = PathGeom.xy(p2)
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pc = PathGeom.xy(p3)
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pd = Part.Circle(PathGeom.xy(p1), PathGeom.xy(p2), PathGeom.xy(p3)).Center
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#print("**** (%.2f, %.2f, %.2f) - (%.2f, %.2f, %.2f)" % (pa.x, pa.y, pa.z, pc.x, pc.y, pc.z))
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#print("**** (%.2f, %.2f, %.2f) - (%.2f, %.2f, %.2f)" % (pb.x, pb.y, pb.z, pd.x, pd.y, pd.z))
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offset = Part.Circle(PathGeom.xy(p1), PathGeom.xy(p2), PathGeom.xy(p3)).Center - p1
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#print("**** (%.2f, %.2f, %.2f)" % (offset.x, offset.y, offset.z))
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params.update({'I': offset.x, 'J': offset.y, 'K': (p3.z - p1.z)/2})
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command = Path.Command(cmd, params)
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#print command
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return command
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@classmethod
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def edgeForCmd(cls, cmd, startPoint):
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"""(cmd, startPoint).
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@ -215,26 +242,76 @@ class PathGeom:
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@classmethod
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def arcToHelix(cls, edge, z0, z1):
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m = FreeCAD.Matrix()
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m.unity()
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"""(edge, z0, z1)
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Assuming edge is an arc it'll return a helix matching the arc starting at z0 and rising/falling to z1."""
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p1 = edge.valueAt(edge.FirstParameter)
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p2 = edge.valueAt(edge.LastParameter)
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z = p1.z
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pd = p2 - p1
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dz = z1 - z0
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cmd = cls.cmdForEdge(edge)
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params = cmd.Parameters
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params.update({'Z': z1, 'K': (z1 - z0)/2})
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command = Path.Command(cmd.Name, params)
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#print("arcToHelix(%.2f, %.2f): dz=%.2f, dy=%.2f, z=%.2f" % (z0 ,z1, dz, pd.y, z))
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return cls.edgeForCmd(command, FreeCAD.Vector(p1.x, p1.y, z0))
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m.A32 = dz / pd.y
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m.A34 = - m.A32
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if dz < 0:
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m.A34 *= p2.y
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m.A34 += z1 - z
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@classmethod
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def helixToArc(cls, edge, z = 0):
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"""(edge, z=0)
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Returns the projection of the helix onto the XY-plane with a given offset."""
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p1 = edge.valueAt(edge.FirstParameter)
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p2 = edge.valueAt((edge.FirstParameter + edge.LastParameter)/2)
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p3 = edge.valueAt(edge.LastParameter)
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p01 = FreeCAD.Vector(p1.x, p1.y, z)
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p02 = FreeCAD.Vector(p2.x, p2.y, z)
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p03 = FreeCAD.Vector(p3.x, p3.y, z)
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return Part.Edge(Part.Arc(p01, p02, p03))
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@classmethod
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def splitArcAt(cls, edge, pt):
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"""(edge, pt)
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Returns a list of 2 edges which together form the original arc split at the given point.
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The Vector pt has to represnt a point on the given arc."""
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p1 = edge.valueAt(edge.FirstParameter)
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p2 = pt
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p3 = edge.valueAt(edge.LastParameter)
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edges = []
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p = edge.Curve.parameter(p2)
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#print("splitArcAt(%.2f, %.2f, %.2f): %.2f - %.2f - %.2f" % (pt.x, pt.y, pt.z, edge.FirstParameter, p, edge.LastParameter))
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p12 = edge.Curve.value((edge.FirstParameter + p)/2)
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p23 = edge.Curve.value((p + edge.LastParameter)/2)
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#print("splitArcAt: p12=(%.2f, %.2f, %.2f) p23=(%.2f, %.2f, %.2f)" % (p12.x, p12.y, p12.z, p23.x, p23.y, p23.z))
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edges.append(Part.Edge(Part.Arc(p1, p12, p2)))
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edges.append(Part.Edge(Part.Arc(p2, p23, p3)))
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return edges
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@classmethod
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def splitEdgeAt(cls, edge, pt):
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"""(edge, pt)
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Returns a list of 2 edges, forming the original edge split at the given point.
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The results are undefined if the Vector representing the point is not part of the edge."""
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# I could not get the OCC parameterAt and split to work ...
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# pt HAS to be on the edge, otherwise the results are undefined
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p1 = edge.valueAt(edge.FirstParameter)
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p2 = pt
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p3 = edge.valueAt(edge.LastParameter)
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edges = []
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if type(edge.Curve) == Part.Line or type(edge.Curve) == Part.LineSegment:
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# it's a line
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return [Part.Edge(Part.LineSegment(p1, p2)), Part.Edge(Part.LineSegment(p2, p3))]
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elif type(edge.Curve) == Part.Circle:
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# it's an arc
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return cls.splitArcAt(edge, pt)
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else:
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m.A34 *= p1.y
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m.A34 += z0 - z
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# it's a helix
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arc = cls.helixToArc(edge, 0)
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aes = cls.splitArcAt(arc, FreeCAD.Vector(pt.x, pt.y, 0))
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return [cls.arcToHelix(aes[0], p1.z, p2.z), cls.arcToHelix(aes[1], p2.z, p3.z)]
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e = edge.transformGeometry(m).Edges[0]
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return e
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@ -172,3 +172,69 @@ class TestPathGeom(PathTestBase):
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e = PathGeom.arcToHelix(Part.Edge(Part.Arc(p11, p12, p13)), 2, -2)
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self.assertCurve(e, p1 + Vector(0,0,2), p2, p3 + Vector(0,0,-2))
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o = 10*math.sin(math.pi/4)
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p1 = Vector(10, -10, 1)
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p2 = Vector(10 - 10*math.sin(math.pi/4), -10*math.cos(math.pi/4), 1)
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p3 = Vector(0, 0, 1)
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e = PathGeom.arcToHelix(Part.Edge(Part.Arc(p1, p2, p3)), 0, 5)
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self.assertCurve(e, Vector(10,-10,0), Vector(p2.x,p2.y,2.5), Vector(0, 0, 5))
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def test62(self):
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"""Verify splitArcAt returns proper subarcs."""
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p1 = Vector(10,-10,0)
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p2 = Vector(0,0,0)
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p3 = Vector(10,10,0)
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arc = Part.Edge(Part.Arc(p1, p2, p3))
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o = 10*math.sin(math.pi/4)
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p12 = Vector(10 - o, -o, 0)
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p23 = Vector(10 - o, +o, 0)
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e = PathGeom.splitArcAt(arc, p2)
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self.assertCurve(e[0], p1, p12, p2)
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self.assertCurve(e[1], p2, p23, p3)
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p34 = Vector(10 - 10*math.sin(1*math.pi/8), -10*math.cos(1*math.pi/8), 0)
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p45 = Vector(10 - 10*math.sin(5*math.pi/8), -10*math.cos(5*math.pi/8), 0)
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e = PathGeom.splitArcAt(arc, p12)
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self.assertCurve(e[0], p1, p34, p12)
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self.assertCurve(e[1], p12, p45, p3)
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def test65(self):
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"""Verify splitEdgeAt."""
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e = PathGeom.splitEdgeAt(Part.Edge(Part.LineSegment(Vector(), Vector(2, 4, 6))), Vector(1, 2, 3))
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self.assertLine(e[0], Vector(), Vector(1,2,3))
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self.assertLine(e[1], Vector(1,2,3), Vector(2,4,6))
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# split an arc
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p1 = Vector(10,-10,1)
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p2 = Vector(0,0,1)
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p3 = Vector(10,10,1)
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arc = Part.Edge(Part.Arc(p1, p2, p3))
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e = PathGeom.splitEdgeAt(arc, p2)
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o = 10*math.sin(math.pi/4)
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p12 = Vector(10 - o, -o, 1)
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p23 = Vector(10 - o, +o, 1)
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self.assertCurve(e[0], p1, p12, p2)
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self.assertCurve(e[1], p2, p23, p3)
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# split a helix
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p1 = Vector(10,-10,0)
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p2 = Vector(0,0,5)
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p3 = Vector(10,10,10)
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h = PathGeom.arcToHelix(arc, 0, 10)
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self.assertCurve(h, p1, p2, p3)
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e = PathGeom.splitEdgeAt(h, p2)
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o = 10*math.sin(math.pi/4)
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p12 = Vector(10 - o, -o, 2.5)
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p23 = Vector(10 - o, +o, 7.5)
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pf = e[0].valueAt((e[0].FirstParameter + e[0].LastParameter)/2)
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pl = e[1].valueAt((e[1].FirstParameter + e[1].LastParameter)/2)
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self.assertCurve(e[0], p1, p12, p2)
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self.assertCurve(e[1], p2, p23, p3)
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