Files
create/src/Mod/Path/PathScripts/PathGeom.py

471 lines
22 KiB
Python

# -*- coding: utf-8 -*-
# ***************************************************************************
# * *
# * Copyright (c) 2016 sliptonic <shopinthewoods@gmail.com> *
# * *
# * 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. *
# * *
# * This program 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 this program; if not, write to the Free Software *
# * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
# * USA *
# * *
# ***************************************************************************
import FreeCAD
import math
import Part
import Path
import PathScripts.PathLog as PathLog
from FreeCAD import Vector
from PySide import QtCore
PathGeomTolerance = 0.000001
PathLog.setLevel(PathLog.Level.INFO, PathLog.thisModule())
# Qt tanslation handling
def translate(context, text, disambig=None):
return QtCore.QCoreApplication.translate(context, text, disambig)
class Side:
"""Class to determine and define the side a Path is on, or Vectors are in relation to each other."""
Left = +1
Right = -1
Straight = 0
On = 0
@classmethod
def toString(cls, side):
"""(side)
Returns a string representation of the enum value."""
if side == cls.Left:
return 'Left'
if side == cls.Right:
return 'Right'
return 'On'
@classmethod
def of(cls, ptRef, pt):
"""(ptRef, pt)
Determine the side of pt in relation to ptRef.
If both Points are viewed as vectors with their origin in (0,0,0)
then the two vectors are either form a straigt line (On) or pt
lies in the left or right hemishpere in regards to ptRef."""
d = -ptRef.x*pt.y + ptRef.y*pt.x
if d < 0:
return cls.Left
if d > 0:
return cls.Right
return cls.Straight
class PathGeom:
"""Class to transform Path Commands into Edges and Wire and back again.
The interface might eventuallly become part of Path itself."""
CmdMoveRapid = ['G0', 'G00']
CmdMoveStraight = ['G1', 'G01']
CmdMoveCW = ['G2', 'G02']
CmdMoveCCW = ['G3', 'G03']
CmdMoveArc = CmdMoveCW + CmdMoveCCW
CmdMove = CmdMoveStraight + CmdMoveArc
Tolerance = PathGeomTolerance
@classmethod
def isRoughly(cls, float1, float2, error=PathGeomTolerance):
"""(float1, float2, [error=%s])
Returns true if the two values are the same within a given error.""" % PathGeomTolerance
return math.fabs(float1 - float2) <= error
@classmethod
def pointsCoincide(cls, p1, p2, error=PathGeomTolerance):
"""(p1, p2, [error=%s])
Return True if two points are roughly identical (see also isRoughly).""" % PathGeomTolerance
return cls.isRoughly(p1.x, p2.x, error) and cls.isRoughly(p1.y, p2.y, error) and cls.isRoughly(p1.z, p2.z, error)
@classmethod
def edgesMatch(cls, e0, e1, error=PathGeomTolerance):
"""(e0, e1, [error=%s]
Return true if the edges start and end at the same point and have the same type of curve.""" % PathGeomTolerance
if type(e0.Curve) != type(e1.Curve):
return False
return all(cls.pointsCoincide(e0.Vertexes[i].Point, e1.Vertexes[i].Point) for i in range(len(e0.Vertexes)))
@classmethod
def edgeConnectsTo(cls, edge, vector, error=PathGeomTolerance):
"""(edge, vector, error=%f)
Returns True if edge connects to given vector.""" % PathGeomTolerance
return cls.pointsCoincide(edge.valueAt(edge.FirstParameter), vector) or cls.pointsCoincide(edge.valueAt(edge.LastParameter), vector)
@classmethod
def getAngle(cls, vector):
"""(vector)
Returns the angle [-pi,pi] of a vector using the X-axis as the reference.
Positive angles for vertexes in the upper hemishpere (positive y values)
and negative angles for the lower hemishpere."""
a = vector.getAngle(Vector(1,0,0))
if vector.y < 0:
return -a
return a
@classmethod
def diffAngle(cls, a1, a2, direction = 'CW'):
"""(a1, a2, [direction='CW'])
Returns the difference between two angles (a1 -> a2) into a given direction."""
if direction == 'CW':
while a1 < a2:
a1 += 2*math.pi
a = a1 - a2
else:
while a2 < a1:
a2 += 2*math.pi
a = a2 - a1
return a
@classmethod
def isVertical(cls, obj):
'''isVertical(obj) ... answer True if obj points into Z'''
if type(obj) == FreeCAD.Vector:
return PathGeom.isRoughly(obj.x, 0) and PathGeom.isRoughly(obj.y, 0)
if obj.ShapeType == 'Face':
if type(obj.Surface) == Part.Plane:
return cls.isHorizontal(obj.Surface.Axis)
if type(obj.Surface) == Part.Cylinder:
return cls.isVertical(obj.Surface.Axis)
if type(obj.Surface) == Part.Sphere:
return True
if type(obj.Surface) == Part.SurfaceOfExtrusion:
return cls.isVertical(obj.Surface.Direction)
PathLog.error(translate('PathGeom', "face isVertical(%s) not supported") % type(obj.Surface))
return None
if obj.ShapeType == 'Edge':
if type(obj.Curve) == Part.Line or type(obj.Curve) == Part.LineSegment:
return cls.isVertical(obj.Vertexes[1].Point - obj.Vertexes[0].Point)
if type(obj.Curve) == Part.Circle or type(obj.Curve) == Part.Ellipse:
return cls.isHorizontal(obj.Curve.Axis)
if type(obj.Curve) == Part.BezierCurve:
# the current assumption is that a bezier curve is vertical if its end points are vertical
return cls.isVertical(obj.Curve.EndPoint - obj.Curve.StartPoint)
PathLog.error(translate('PathGeom', "edge isVertical(%s) not supported") % type(obj.Curve))
return None
PathLog.error(translate('PathGeom', "isVertical(%s) not supported") % obj)
return None
@classmethod
def isHorizontal(cls, obj):
'''isHorizontal(obj) ... answer True if obj points into X or Y'''
if type(obj) == FreeCAD.Vector:
return PathGeom.isRoughly(obj.z, 0)
if obj.ShapeType == 'Face':
if type(obj.Surface) == Part.Plane:
return cls.isVertical(obj.Surface.Axis)
if type(obj.Surface) == Part.Cylinder:
return cls.isHorizontal(obj.Surface.Axis)
if type(obj.Surface) == Part.Sphere:
return True
if type(obj.Surface) == Part.SurfaceOfExtrusion:
return cls.isHorizontal(obj.Surface.Direction)
PathLog.error(translate('PathGeom', "face isHorizontal(%s) not supported") % type(obj.Surface))
return None
if obj.ShapeType == 'Edge':
if type(obj.Curve) == Part.Line or type(obj.Curve) == Part.LineSegment:
return cls.isHorizontal(obj.Vertexes[1].Point - obj.Vertexes[0].Point)
if type(obj.Curve) == Part.Circle or type(obj.Curve) == Part.Ellipse:
return cls.isVertical(obj.Curve.Axis)
if type(obj.Curve) == Part.BezierCurve:
return cls.isRoughly(obj.BoundBox.ZLength, 0)
PathLog.error(translate('PathGeom', "edge isHorizontal(%s) not supported") % type(obj.Curve))
return None
PathLog.error(translate('PathGeom', "isHorizontal(%s) not supported") % obj)
return None
@classmethod
def commandEndPoint(cls, cmd, defaultPoint = Vector(), X='X', Y='Y', Z='Z'):
"""(cmd, [defaultPoint=Vector()], [X='X'], [Y='Y'], [Z='Z'])
Extracts the end point from a Path Command."""
x = cmd.Parameters.get(X, defaultPoint.x)
y = cmd.Parameters.get(Y, defaultPoint.y)
z = cmd.Parameters.get(Z, defaultPoint.z)
return Vector(x, y, z)
@classmethod
def xy(cls, point):
"""(point)
Convenience function to return the projection of the Vector in the XY-plane."""
return Vector(point.x, point.y, 0)
@classmethod
def cmdsForEdge(cls, edge, flip = False, useHelixForBSpline = True, segm = 50):
"""(edge, flip=False, useHelixForBSpline=True, segm=50) -> List(Path.Command)
Returns a list of Path.Command representing the given edge.
If flip is True the edge is considered to be backwards.
If useHelixForBSpline is True an Edge based on a BSplineCurve is considered
to represent a helix and results in G2 or G3 command. Otherwise edge has
no direct Path.Command mapping and will be approximated by straight segments.
segm is a factor for the segmentation of arbitrary curves not mapped to G1/2/3
commands. The higher the value the more segments will be used."""
pt = edge.valueAt(edge.LastParameter) if not flip else edge.valueAt(edge.FirstParameter)
params = {'X': pt.x, 'Y': pt.y, 'Z': pt.z}
if type(edge.Curve) == Part.Line or type(edge.Curve) == Part.LineSegment:
commands = [Path.Command('G1', params)]
else:
p1 = edge.valueAt(edge.FirstParameter) if not flip else edge.valueAt(edge.LastParameter)
p2 = edge.valueAt((edge.FirstParameter + edge.LastParameter)/2)
p3 = pt
if (type(edge.Curve) == Part.Circle and cls.isRoughly(edge.Curve.Axis.x, 0) and cls.isRoughly(edge.Curve.Axis.y, 0)) or (useHelixForBSpline and type(edge.Curve) == Part.BSplineCurve):
# This is an arc or a helix and it should be represented by a simple G2/G3 command
if edge.Curve.Axis.z < 0:
cmd = 'G2' if not flip else 'G3'
else:
cmd = 'G3' if not flip else 'G2'
pd = Part.Circle(PathGeom.xy(p1), PathGeom.xy(p2), PathGeom.xy(p3)).Center
PathLog.info("**** %s.%d: (%.2f, %.2f, %.2f) - (%.2f, %.2f, %.2f) - (%.2f, %.2f, %.2f) -> center=(%.2f, %.2f)" % (cmd, flip, p1.x, p1.y, p1.z, p2.x, p2.y, p2.z, p3.x, p3.y, p3.z, pd.x, pd.y))
# Have to calculate the center in the XY plane, using pd leads to an error if this is a helix
pa = PathGeom.xy(p1)
pb = PathGeom.xy(p2)
pc = PathGeom.xy(p3)
offset = Part.Circle(pa, pb, pc).Center - pa
PathLog.debug("**** (%.2f, %.2f, %.2f) - (%.2f, %.2f, %.2f)" % (pa.x, pa.y, pa.z, pc.x, pc.y, pc.z))
PathLog.debug("**** (%.2f, %.2f, %.2f) - (%.2f, %.2f, %.2f)" % (pb.x, pb.y, pb.z, pd.x, pd.y, pd.z))
PathLog.debug("**** (%.2f, %.2f, %.2f)" % (offset.x, offset.y, offset.z))
params.update({'I': offset.x, 'J': offset.y, 'K': (p3.z - p1.z)/2})
commands = [ Path.Command(cmd, params) ]
else:
# We're dealing with a helix or a more complex shape and it has to get approximated
# by a number of straight segments
eStraight = Part.Edge(Part.LineSegment(p1, p3))
esP2 = eStraight.valueAt((eStraight.FirstParameter + eStraight.LastParameter)/2)
deviation = (p2 - esP2).Length
if cls.isRoughly(deviation, 0):
return [ Path.Command('G1', {'X': p3.x, 'Y': p3.y, 'Z': p3.z}) ]
# at this point pixellation is all we can do
commands = []
segments = int(math.ceil((deviation / eStraight.Length) * segm))
#print("**** pixellation with %d segments" % segments)
dParameter = (edge.LastParameter - edge.FirstParameter) / segments
for i in range(0, segments):
if flip:
p = edge.valueAt(edge.LastParameter - (i + 1) * dParameter)
else:
p = edge.valueAt(edge.FirstParameter + (i + 1) * dParameter)
cmd = Path.Command('G1', {'X': p.x, 'Y': p.y, 'Z': p.z})
#print("***** %s" % cmd)
commands.append(cmd)
#print commands
return commands
@classmethod
def edgeForCmd(cls, cmd, startPoint):
"""(cmd, startPoint).
Returns an Edge representing the given command, assuming a given startPoint."""
endPoint = cls.commandEndPoint(cmd, startPoint)
if (cmd.Name in cls.CmdMoveStraight) or (cmd.Name in cls.CmdMoveRapid):
if cls.pointsCoincide(startPoint, endPoint):
return None
return Part.Edge(Part.LineSegment(startPoint, endPoint))
if cmd.Name in cls.CmdMoveArc:
center = startPoint + cls.commandEndPoint(cmd, Vector(0,0,0), 'I', 'J', 'K')
A = cls.xy(startPoint - center)
B = cls.xy(endPoint - center)
d = -B.x * A.y + B.y * A.x
if cls.isRoughly(d, 0, 0.005):
PathLog.info("Half circle arc at: (%.2f, %.2f, %.2f)" % (center.x, center.y, center.z))
# we're dealing with half a circle here
angle = cls.getAngle(A) + math.pi/2
if cmd.Name in cls.CmdMoveCW:
angle -= math.pi
else:
C = A + B
angle = cls.getAngle(C)
PathLog.info("Arc (%8f) at: (%.2f, %.2f, %.2f) -> angle=%f" % (d, center.x, center.y, center.z, angle / math.pi))
R = A.Length
PathLog.debug("arc: p1=(%.2f, %.2f) p2=(%.2f, %.2f) -> center=(%.2f, %.2f)" % (startPoint.x, startPoint.y, endPoint.x, endPoint.y, center.x, center.y))
PathLog.debug("arc: A=(%.2f, %.2f) B=(%.2f, %.2f) -> d=%.2f" % (A.x, A.y, B.x, B.y, d))
PathLog.debug("arc: R=%.2f angle=%.2f" % (R, angle/math.pi))
if cls.isRoughly(startPoint.z, endPoint.z):
midPoint = center + Vector(math.cos(angle), math.sin(angle), 0) * R
PathLog.debug("arc: (%.2f, %.2f) -> (%.2f, %.2f) -> (%.2f, %.2f)" % (startPoint.x, startPoint.y, midPoint.x, midPoint.y, endPoint.x, endPoint.y))
return Part.Edge(Part.Arc(startPoint, midPoint, endPoint))
# It's a Helix
#print('angle: A=%.2f B=%.2f' % (cls.getAngle(A)/math.pi, cls.getAngle(B)/math.pi))
if cmd.Name in cls.CmdMoveCW:
cw = True
else:
cw = False
angle = cls.diffAngle(cls.getAngle(A), cls.getAngle(B), 'CW' if cw else 'CCW')
height = endPoint.z - startPoint.z
pitch = height * math.fabs(2 * math.pi / angle)
if angle > 0:
cw = not cw
#print("Helix: R=%.2f h=%.2f angle=%.2f pitch=%.2f" % (R, height, angle/math.pi, pitch))
helix = Part.makeHelix(pitch, height, R, 0, not cw)
helix.rotate(Vector(), Vector(0,0,1), 180 * cls.getAngle(A) / math.pi)
e = helix.Edges[0]
helix.translate(startPoint - e.valueAt(e.FirstParameter))
return helix.Edges[0]
return None
@classmethod
def wireForPath(cls, path, startPoint = Vector(0, 0, 0)):
"""(path, [startPoint=Vector(0,0,0)])
Returns a wire representing all move commands found in the given path."""
edges = []
rapid = []
if hasattr(path, "Commands"):
for cmd in path.Commands:
edge = cls.edgeForCmd(cmd, startPoint)
if edge:
if cmd.Name in cls.CmdMoveRapid:
rapid.append(edge)
edges.append(edge)
startPoint = cls.commandEndPoint(cmd, startPoint)
return (Part.Wire(edges), rapid)
@classmethod
def wiresForPath(cls, path, startPoint = Vector(0, 0, 0)):
"""(path, [startPoint=Vector(0,0,0)])
Returns a collection of wires, each representing a continuous cutting Path in path."""
wires = []
if hasattr(path, "Commands"):
edges = []
for cmd in path.Commands:
if cmd.Name in cls.CmdMove:
edges.append(cls.edgeForCmd(cmd, startPoint))
startPoint = cls.commandEndPoint(cmd, startPoint)
elif cmd.Name in cls.CmdMoveRapid:
wires.append(Part.Wire(edges))
edges = []
startPoint = cls.commandEndPoint(cmd, startPoint)
if edges:
wires.append(Part.Wire(edges))
return wires
@classmethod
def arcToHelix(cls, edge, z0, z1):
"""(edge, z0, z1)
Assuming edge is an arc it'll return a helix matching the arc starting at z0 and rising/falling to z1."""
p1 = edge.valueAt(edge.FirstParameter)
p2 = edge.valueAt(edge.LastParameter)
cmd = cls.cmdsForEdge(edge)[0]
params = cmd.Parameters
params.update({'Z': z1, 'K': (z1 - z0)/2})
command = Path.Command(cmd.Name, params)
#print("- (%.2f, %.2f, %.2f) - (%.2f, %.2f, %.2f): %.2f:%.2f" % (edge.Vertexes[0].X, edge.Vertexes[0].Y, edge.Vertexes[0].Z, edge.Vertexes[1].X, edge.Vertexes[1].Y, edge.Vertexes[1].Z, z0, z1))
#print("- %s -> %s" % (cmd, command))
return cls.edgeForCmd(command, Vector(p1.x, p1.y, z0))
@classmethod
def helixToArc(cls, edge, z = 0):
"""(edge, z=0)
Returns the projection of the helix onto the XY-plane with a given offset."""
p1 = edge.valueAt(edge.FirstParameter)
p2 = edge.valueAt((edge.FirstParameter + edge.LastParameter)/2)
p3 = edge.valueAt(edge.LastParameter)
p01 = Vector(p1.x, p1.y, z)
p02 = Vector(p2.x, p2.y, z)
p03 = Vector(p3.x, p3.y, z)
return Part.Edge(Part.Arc(p01, p02, p03))
@classmethod
def splitArcAt(cls, edge, pt):
"""(edge, pt)
Returns a list of 2 edges which together form the original arc split at the given point.
The Vector pt has to represnt a point on the given arc."""
p1 = edge.valueAt(edge.FirstParameter)
p2 = pt
p3 = edge.valueAt(edge.LastParameter)
edges = []
p = edge.Curve.parameter(p2)
#print("splitArcAt(%.2f, %.2f, %.2f): %.2f - %.2f - %.2f" % (pt.x, pt.y, pt.z, edge.FirstParameter, p, edge.LastParameter))
p12 = edge.Curve.value((edge.FirstParameter + p)/2)
p23 = edge.Curve.value((p + edge.LastParameter)/2)
#print("splitArcAt: p12=(%.2f, %.2f, %.2f) p23=(%.2f, %.2f, %.2f)" % (p12.x, p12.y, p12.z, p23.x, p23.y, p23.z))
edges.append(Part.Edge(Part.Arc(p1, p12, p2)))
edges.append(Part.Edge(Part.Arc(p2, p23, p3)))
return edges
@classmethod
def splitEdgeAt(cls, edge, pt):
"""(edge, pt)
Returns a list of 2 edges, forming the original edge split at the given point.
The results are undefined if the Vector representing the point is not part of the edge."""
# I could not get the OCC parameterAt and split to work ...
# pt HAS to be on the edge, otherwise the results are undefined
p1 = edge.valueAt(edge.FirstParameter)
p2 = pt
p3 = edge.valueAt(edge.LastParameter)
edges = []
if type(edge.Curve) == Part.Line or type(edge.Curve) == Part.LineSegment:
# it's a line
return [Part.Edge(Part.LineSegment(p1, p2)), Part.Edge(Part.LineSegment(p2, p3))]
elif type(edge.Curve) == Part.Circle:
# it's an arc
return cls.splitArcAt(edge, pt)
else:
# it's a helix
arc = cls.helixToArc(edge, 0)
aes = cls.splitArcAt(arc, Vector(pt.x, pt.y, 0))
return [cls.arcToHelix(aes[0], p1.z, p2.z), cls.arcToHelix(aes[1], p2.z, p3.z)]
@classmethod
def combineConnectedShapes(cls, shapes):
done = False
while not done:
done = True
combined = []
PathLog.debug("shapes: {}".format(shapes))
for shape in shapes:
connected = [f for f in combined if cls.isRoughly(shape.distToShape(f)[0], 0.0)]
PathLog.debug(" {}: connected: {} dist: {}".format(len(combined), connected, [shape.distToShape(f)[0] for f in combined]))
if connected:
combined = [f for f in combined if f not in connected]
connected.append(shape)
combined.append(Part.makeCompound(connected))
done = False
else:
combined.append(shape)
shapes = combined
return shapes
@classmethod
def removeDuplicateEdges(cls, wire):
unique = []
for e in wire.Edges:
if not any(cls.edgesMatch(e, u) for u in unique):
unique.append(e)
return Part.Wire(unique)