{{Macro |Name=HilbertCurve |Description=This macro creates an Hilbert curve wire in 2 or 3 dimensions with many iterations. |Author=Simone Bignetti |Download=[https://wiki.freecadweb.org/images/6/69/Hilbert_curve_icon.png toolbar icon] |Date=2021-02-13 |Version=1.2.0 |FCVersion= 0.16 to 0.19 }}
This macro creates a Hilbert curve wire in 2 or 3 dimensions with many iterations.
- Start the macro in a FreeCAD document.
- In the dialog that opens choose the parameters for the Hilbert curve:
- Select if the curve should be 2 dimensional: {{CheckBox|TRUE|2D}}, or 3 dimensional: {{CheckBox|FALSE|3D}}.
- Specify the number of iterations {{SpinBox|1}}. Attention! Increasing the number of iterations will also increase the computation time.
- Specify the length of the wire segment: {{SpinBox|10.00}}.
- Click OK to create the wire or CANCEL to exit the macro.
You can use a Hilbert curve as the path for a Part Sweep, but it's better to apply a radius to the wire first, or the sweep will be badly formed.
Finding the right radius may requires some testing. It depends on the length of the curve segments and the shape of the profile you want to sweep.
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Macro_HilbertCurve.FCMacro
{{MacroCode|code=
You can contact me by mail at simone.bignetti@linux.it
Name = 'HilbertCurve' Comment = 'This macro creates an Hilbert curve wire in 2 or 3 dimensions with many iterations.' Author = 'Simone Bignetti' Version = '1.2.0' Date = '2020-12-29' License = 'GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999' Web = 'https://wiki.freecadweb.org/Macro_HilbertCurve' Wiki = 'https://wiki.freecadweb.org/Macro_HilbertCurve' Icon = 'HilbertCurve.svg' Help = 'Choose the dimensions of the wire, the number of the iterations and the length of the wire segment.' Status = 'Stable' Requires = '' Communication = 'https://forum.freecadweb.org/viewtopic.php?f=22&t=53781' Files = 'HilbertCurve.svg'
import FreeCAD as app import Draft
from PySide import QtGui, QtCore
class HilbertCurve: """The class of the Hilbert curve.By this class it's possible to create a wire of a fractal Hilbert curve with a fixed number of dimensions and iterations. """def init(self, dimensions, iterations): """Initialize the Hilbert curve. Args: iterations (int): iterations to use in constructing the curve dimensions (int): number of dimensions """
self.dimensions = dimensions self.iterations = iterations
self.min_distance = 0
self.max_distance = 2 ** (self.iterations * self.dimensions) - 1
self.min_coordinate = 0
self.max_coordinate = 2 ** self.iterations - 1
self.number_of_points = 2 ** (self.iterations * self.dimensions)
def point_from_distance(self, distance): """Return a point in n-dimensional space given a distance along a the curve. Args: distance (int): integer distance along the curve Returns: point (iterable of ints): an n-dimensional vector of length dimensions where each component value is between 0 and 2**iterations-1. """
bit_string = format(distance, 'b').zfill(self.iterations * self.dimensions) # zero filled binary distance point = [int(bit_string[i::self.dimensions], 2) for i in range(self.dimensions)] # transpose of distance
gray = point[self.dimensions-1] >> 1
for i in range(self.dimensions-1, 0, -1):
point[i] ^= point[i-1]
point[0] ^= gray
q = 2
while q != (2 << (self.iterations-1)):
p = q - 1
for i in range(self.dimensions-1, -1, -1):
if point[i] & q:
# invert
point[0] ^= p
else:
# exchange
gray = (point[0] ^ point[i]) & p
point[0] ^= gray
point[i] ^= gray
q <<= 1
return point
def get_min_distance(self): """Return the minimum distance along the curve.""" return self.min_distance
def get_max_distance(self): """Return the maximum distance along the curve.""" return self.max_distance
def get_min_coordinate(self): """Return the minimum coordinate value in any dimension.""" return self.min_coordinate
def get_max_coordinate(self): """Return the maximum coordinate value in any dimension.""" return self.max_coordinate
def get_number_of_points(self): """Return the number of points in the curve.""" return self.number_of_points
def get_points(self): """Return the list of points in the curve.""" points = [] for point_number in range(self.number_of_points): points.append(self.point_from_distance(point_number)) return points
def str(self): return f"HilbertCurve(dimensions={self.dimensions}, iterations={self.iterations})"
def repr(self): return self.str()
class Hilbert_Dialog(QtGui.QDialog): """The dialog for the Hilbert curveThis class opens in FreeCAD a dialog to input the number of dimensions and the number of iterations to create the Hilbert curve. OK creates the curve. CANCEL quit the macro. """
def init(self): super(Hilbert_Dialog, self).init() self.setupUi()
def setupUi(self): self.dimensions = 2 self.iterations = 3
self.setGeometry(250, 250, 400, 300) # Window definition self.setWindowTitle("Hilbert curve Macro")
titleLabel = QtGui.QLabel("Create an Hilbert curve in two or three dimensions") # Title and subtitle titleFont = QtGui.QFont() titleFont.setBold(True) titleFont.setWeight(75) titleLabel.setFont(titleFont) subtitleLabel = QtGui.QLabel("This macro creates a wire in the draft workbench\nwith the shape of an Hilbert curve in two or three dimensions.\nFor example, you can use this wire as a sweep path.\nIt's recommended to apply a radius at the wire,\nin order to obtain a correct sweep generation.") titleBox = QtGui.QVBoxLayout() titleBox.addWidget(titleLabel) titleBox.addWidget(subtitleLabel) titleBox.insertStretch(-1)
dimensionsLabel = QtGui.QLabel("Number of dimensions: ") # Number of dimensions self.twoDradioButton = QtGui.QRadioButton() self.twoDradioButton.setText("2D") self.twoDradioButton.setChecked(True) self.threeDradioButton = QtGui.QRadioButton() self.threeDradioButton.setText("3D") dimensionsBox=QtGui.QHBoxLayout() dimensionsBox.addWidget(dimensionsLabel) dimensionsBox.addWidget(self.twoDradioButton) dimensionsBox.addWidget(self.threeDradioButton)
iterationsLabel = QtGui.QLabel("Iterations:") # Iterations and length spins in a grid self.iterationsSpin = QtGui.QSpinBox() self.iterationsSpin.setMinimum(1) self.iterationsSpin.setMaximum(10) lengthLabel = QtGui.QLabel("Length:") self.lengthSpin = QtGui.QDoubleSpinBox() self.lengthSpin.setMinimum(1.0) self.lengthSpin.setMaximum(999999.000000000000000) self.lengthSpin.setValue(10.000000000000000) grid = QtGui.QGridLayout() grid.setSpacing(10) grid.addWidget(iterationsLabel, 1, 0) grid.addWidget(self.iterationsSpin, 1, 1) grid.addWidget(lengthLabel, 2, 0) grid.addWidget(self.lengthSpin, 2, 1)
okButton = QtGui.QPushButton("OK") # Ok and Cancel Buttons at right bottom okButton.clicked.connect(self.onOkButton) cancelButton = QtGui.QPushButton("Cancel") cancelButton.clicked.connect(self.onCancelButton) buttonBox = QtGui.QHBoxLayout() buttonBox.addStretch() buttonBox.addWidget(okButton) buttonBox.addWidget(cancelButton)
vbox = QtGui.QVBoxLayout() vbox.addLayout(titleBox) vbox.addLayout(dimensionsBox) vbox.addLayout(grid) vbox.addLayout(buttonBox) vbox.setSpacing(30) vbox.insertStretch(1) self.setLayout(vbox)
self.show()
def onOkButton(self): if self.twoDradioButton.isChecked(): dimensions = 2 else: dimensions = 3 iterations = self.iterationsSpin.value() length = self.lengthSpin.value() HC=HilbertCurve(dimensions, iterations) points = HC.get_points() pl = app.Placement() pl.Rotation.Q = (0.0, 0.0, 0.0, 1.0) pl.Base = app.Vector(0.0, 0.0, 0.0) vectors = [] if dimensions == 2: for point in points: vectors.append(app.Vector(point[0]*length, point[1]*length, 0.0)) else: for point in points: vectors.append(app.Vector(point[0]*length, point[1]*length, point[2]*length)) wire = Draft.makeWire(vectors, placement=pl, closed=False, face=False, support=None) wire.Label = "Hilbert" Draft.autogroup(wire) self.close()
def onCancelButton(self): self.close()
hilbert_dialog = Hilbert_Dialog() hilbert_dialog.exec() }}
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