{{Macro |Name=Macro Make Circle 3 Points |Icon=Macro_Make_Circle_3_Points.png |Description=This macro creates a circle on 3 selected points. The points can be objects such as cubes, cylinder, then selected coordinates will be the centre of these forms. |Author=Mario52 |Version=01.00 |Date=2013-03-11 |FCVersion=All |Download=[https://www.freecadweb.org/wiki/images/c/c7/Macro_Make_Circle_3_Points.png ToolBar Icon] }}
This macro creates a circle on 3 selected points. The points can be objects such as cubes, cylinder, then selected coordinates will be the centre of these forms.
Select 3 points, or forms in the 3D view and run the macro. If the shape is a line, the coordinate will be the center of the line.
If the selected objects are on different planes, (xy Z10, xy Z2, xy Z5) the circle will be built on the map x,y Z=0. If all of the selected objects have their equal Z coordinates (xy Z5, xy Z5, xy Z5), circle will be built to the plan x,y Z=5.
ToolBar Icon 
Draft_Circle_3_Points.FCMacro
{{MacroCode|code=
import Draft, Part, FreeCAD, math, PartGui, FreeCADGui from math import sqrt, pi, sin, cos from FreeCAD import Base
sel = FreeCADGui.Selection.getSelection() i=0 centreX=0 centreY=0 rayon=0
if len(sel)==3 : i=0 ta=[0,0,0,0,0,0,0,0,0] for obj in sel: x=(obj.Shape.BoundBox.Center) ta[i+0]=(x.x) ta[i+1]=(x.y) ta[i+2]=(x.z) i=i+3
x_point_1=ta[0]
y_point_1=ta[1]
z_point_1=ta[2]x_point_2=ta[3]
y_point_2=ta[4]
z_point_2=ta[5]x_point_3=ta[6]
y_point_3=ta[7]
z_point_3=ta[8]
centreX =((x_point_3**2-x_point_2**2+y_point_3**2-y_point_2**2)/(2*(y_point_3-y_point_2))-(x_point_2**2-x_point_1**2+y_point_2**2-y_point_1**2)/(2*(y_point_2-y_point_1)))/((x_point_3-x_point_2)/(y_point_3-y_point_2)-(x_point_2-x_point_1)/(y_point_2-y_point_1))
centreY =-(x_point_2-x_point_1)/(y_point_2-y_point_1)*centreX+(x_point_2**2-x_point_1**2+y_point_2**2-y_point_1**2)/(2*(y_point_2-y_point_1))
rayon =sqrt((x_point_1-centreX)**2+(y_point_1-centreY)**2)
if z_point_1==z_point_2 and z_point_2==z_point_3:
centreZ=z_point_1
else:
centreZ=0
pl=FreeCAD.Placement()
pl.Rotation.Q=(0.0,-0.0,-0.0,1.0)
pl.Base=FreeCAD.Vector(centreX,centreY,centreZ)
Draft.makeCircle((rayon),placement=pl,face=False,support=None)
FreeCAD.Console.PrintMessage("Coordonnée X : "+str(centreX)+"\r\n")
FreeCAD.Console.PrintMessage("Coordonnée Y : "+str(centreY)+"\r\n")
FreeCAD.Console.PrintMessage("Coordonnée Z : "+str(centreZ)+"\r\n")
FreeCAD.Console.PrintMessage("Rayon : "+str(rayon )+"\r\n")
else:
FreeCAD.Console.PrintError("Sélectionnez 3 points et recommencez\r\n")
}}
In addition to the previous features, this example is used to align an orthogonal circle on each shape in the selection, and the plan "'XY, YZ, XZ ' ' chosen. The circle takes the color of the axis dedicated regardless of current color, and the center point of the circle is drawn (option O/N).
File:Macro Draft Circle 3 Points02.png|Cercle circonscrit sur 3 formes, File:Macro Draft Circle 3 Points03.png|de manière orthogonale sur la forme choisie File:Macro Draft Circle 3 Points04.png| File:Macro Draft Circle 3 Points05.png|
The settings to change.
{{MacroCode|code=
# mode by default vueChoix = 0 and alignerSur = 0
vueChoix=0 # choice of the top view = 1 XY, view Front = 2 ZX, Right view = 3 ZY
alignerSur=0 # Aligns the circle shaped the choice (1,2 or 3) or Z = 0
afficherPoint=1 # Displays the center point of the circle
}}
{{MacroCode|code=
import Draft, Part, FreeCAD, math, PartGui, FreeCADGui from math import sqrt, pi, sin, cos from FreeCAD import Base from PySide import QtCore, QtGui
def errorDialog(msg): # Create a simple dialog QMessageBox # The first argument indicates the icon used: one of QtGui.QMessageBox.{NoIcon, Information, Warning, Critical, Question} diag = QtGui.QMessageBox(QtGui.QMessageBox.Critical,u"Error Message",msg) diag.setWindowModality(QtCore.Qt.ApplicationModal) diag.exec_()
def affiche(x,y,z,rayon,r,v,b,afficherPoint): pl.Base=FreeCAD.Vector(x,y,z) Draft.makeCircle((rayon),placement=pl,face=False,support=None) FreeCADGui.activeDocument().activeObject().LineColor = (r,v,b) if afficherPoint==1: Draft.makePoint(x,y,z) diag = QtGui.QMessageBox(QtGui.QMessageBox.Information,u"Coordinates",u"Coordinates X : "+str(x)+"\r\n"+u"Coordinates Y : "+str(y)+"\n"+u"Coordinates Z : "+str(z)+"\nRayon\t : "+str(rayon)) diag.setWindowModality(QtCore.Qt.ApplicationModal) diag.exec_()
sel = FreeCADGui.Selection.getSelection() i=0 centreX=0;centreY=0;rayon=0
if len(sel)==3 : i=0 ta=[0,0,0,0,0,0,0,0,0] for obj in sel: x=(obj.Shape.BoundBox.Center) ta[i+0]=(x.x) ta[i+1]=(x.y) ta[i+2]=(x.z) i=i+3
# mode by default vueChoix = 0 and alignerSur = 0
vueChoix=0 # choice of the top view = 1 XY, view Front = 2 ZX, Right view = 3 ZY
alignerSur=0 # Aligns the circle shaped the choice (1,2 or 3) or Z = 0
afficherPoint=1 # Displays the center point of the circle
# Affectation des variables
if vueChoix==3: # View of right ZY (Red)
z_point_1=ta[0]
x_point_1=ta[1]
y_point_1=ta[2] z_point_2=ta[3]
x_point_2=ta[4]
y_point_2=ta[5] z_point_3=ta[6]
x_point_3=ta[7]
y_point_3=ta[8]
elif vueChoix==2: # Front view ZX (Green)
y_point_1=ta[0]
z_point_1=ta[1]
x_point_1=ta[2] y_point_2=ta[3]
z_point_2=ta[4]
x_point_2=ta[5] y_point_3=ta[6]
z_point_3=ta[7]
x_point_3=ta[8]
else: # Top view XY (blue)
x_point_1=ta[0]
y_point_1=ta[1]
z_point_1=ta[2] x_point_2=ta[3]
y_point_2=ta[4]
z_point_2=ta[5] x_point_3=ta[6]
y_point_3=ta[7]
z_point_3=ta[8]
# Calculation of coordinates of the center of the circle
try:
centreX =((x_point_3**2-x_point_2**2+y_point_3**2-y_point_2**2)/(2*(y_point_3-y_point_2))-(x_point_2**2-x_point_1**2+y_point_2**2-y_point_1**2)/(2*(y_point_2-y_point_1)))/((x_point_3-x_point_2)/(y_point_3-y_point_2)-(x_point_2-x_point_1)/(y_point_2-y_point_1))
centreY =-(x_point_2-x_point_1)/(y_point_2-y_point_1)*centreX+(x_point_2**2-x_point_1**2+y_point_2**2-y_point_1**2)/(2*(y_point_2-y_point_1))
rayon =sqrt((x_point_1-centreX)**2+(y_point_1-centreY)**2)
except:
errorDialog(u"Impossible calculation too aligned elements")
else:
#finally: sera TOUJOURS exécuté
# Definition of the coordinate Z
centreZ=0
# Création du cercle
pl=FreeCAD.Placement()
if vueChoix==1: # Plan XY Dessus
pl.Rotation.Q=(0,0,0,1.0)
if alignerSur==1:
affiche(centreX,centreY,z_point_1,rayon,0.0,0.0,1.0,afficherPoint)
elif alignerSur==2:
affiche(centreX,centreY,z_point_2,rayon,0.0,0.0,1.0,afficherPoint)
elif alignerSur==3:
affiche(centreX,centreY,z_point_3,rayon,0.0,0.0,1.0,afficherPoint)
elif vueChoix==2: # Plan XZ Face
pl.Rotation.Q=(1,0,0,1.0)
if alignerSur==1:
affiche(centreY,z_point_1,centreX,rayon,0.0,1.0,0.0,afficherPoint)
elif alignerSur==2:
affiche(centreY,z_point_2,centreX,rayon,0.0,1.0,0.0,afficherPoint)
elif alignerSur==3:
affiche(centreY,z_point_3,centreX,rayon,0.0,1.0,0.0,afficherPoint)
elif vueChoix==3: # Plan YZ Droite
pl.Rotation.Q=(0,1,0,1.0)
if alignerSur==1:
affiche(z_point_1,centreX,centreY,rayon,1.0,0.0,0.0,afficherPoint)
elif alignerSur==2:
affiche(z_point_2,centreX,centreY,rayon,1.0,0.0,0.0,afficherPoint)
elif alignerSur==3:
affiche(z_point_3,centreX,centreY,rayon,1.0,0.0,0.0,afficherPoint)
else: # modifier pour avoir XYZ
# si les coordonnées Z sont égales alors le cercle s'aligne à Z
if z_point_1==z_point_2 and z_point_2==z_point_3:
centreZ=z_point_1
affiche(centreX,centreY,z_point_1,rayon,0.0,0.0,0.0,afficherPoint)
else:
# Si une coordonnée est différente alors Z=0
affiche(centreX,centreY,0,rayon,0.0,0.0,0.0,afficherPoint)
else: # Si la condition n'est pas remplie, recommencer errorDialog(u"Select 3 points and repeat") #FreeCAD.Console.PrintError("Select 3 points and repeatr\n")
}}
Here an Anaglyph view that allows you to see two different positions of the view by using glasses with filters red and Cyan 
.
Watch alternately with the left eye and the right eye to see the views separately.
The genesis of the macro Draft Circle 3 Points on the forum (PYTHON) coordonnées d'un point helped flachyjoe thanks. The formula comes from cercle_3pts.pdf and used with the kind permission of its author.
documentation index > Macro Draft Circle 3 Points