# Macro Draft Circle 3 Points 3D

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Description
This macro creates a circle on 3 selected points in the space. The points can be objects such as cubes, cylinder, then selected coordinates will be the centre of these forms.

Macro version: 01.00
Last modified: 2013-03-16
FreeCAD version: All
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Author
galou_breizh
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Links
Macro Version
01.00
Date last modified
2013-03-16
FreeCAD Version(s)
All
Default shortcut
None
See also
None

## Description

This macro creates a circle on 3 selected points in the space. The points can be objects such as cubes, cylinder, then selected coordinates will be the centre of these forms.

## Usage

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.

## Limits

The order of selection of fear forms influencing the AXIS angle and reverse the inclination of the circle. In this case, reverse or change the order of selection of the shapes.
The coordinates X, Y, Z of value 0 or alignment not allowing not calculating, can return a division by zero error, and translated as "The three points are aligned"

## Script

Macro_Draft_Circle_3_Points_3D.FCMacro

```# -*- coding: utf-8 -*-
# Create a circle from 3 points selected on the X, Y, Z map
# 04/03/2013
# From https://en.wikipedia.org/wiki/Circumscribed_circle#Cartesian_coordinates_from_cross-_and_dot-products
# Also see : https://math.stackexchange.com/questions/2658318/how-to-find-the-circumcenter-of-a-triangle-and-the-length-of-the-corresponding-r
# O=R/2S*(acosα⋅A+bcosβ⋅B+ccosγ⋅C)  ; R is circumradius, S is area of triangle
# 08/08/2014 PyQt4 and PySide

#OS: Windows Vista
#Word size: 32-bit
#Version: 0.14.3700 (Git)
#Branch: releases/FreeCAD-0-14
#Hash: 32f5aae0a64333ec8d5d160dbc46e690510c8fe1
#Python version: 2.6.2
#Qt version: 4.5.2
#Coin version: 3.1.0
#SoQt version: 1.4.1
#OCC version: 6.5.1

try:
import PyQt4
from PyQt4 import QtCore, QtGui
except Exception:
import PySide
from PySide import QtCore, QtGui
from math import pi, asin
import Draft, FreeCAD, FreeCADGui
from FreeCAD import Base

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,r,angle):
diag = QtGui.QMessageBox(QtGui.QMessageBox.Information,u"Coordinates",u"Coordinate X : "+str(x)+"\r\n"+u"Coordinate Y : "+str(y)+"\n"+u"Coordinate Z : "+str(z)+"\nRadius\t   : "+str(r)+"\nAngle\t   : "+str(angle))
diag.setWindowModality(QtCore.Qt.ApplicationModal)
diag.setWindowModality(QtCore.Qt.NonModal)
diag.exec_()

# objects selected
sel = FreeCADGui.Selection.getSelection()
# If there are 3 selected points so...
if len(sel)==3 :
# Assignment of variables
P1 = sel.Shape.BoundBox.Center
P2 = sel.Shape.BoundBox.Center
P3 = sel.Shape.BoundBox.Center

P1P2 = (P2 - P1).Length
P2P3 = (P3 - P2).Length
P3P1 = (P1 - P3).Length

# Circle radius.
l = ((P1 - P2).cross(P2 - P3)).Length
try:
#if l < 1e-8:
#    errorDialog("The three points are aligned")
r = P1P2 * P2P3 * P3P1 / 2 / l
except:
errorDialog("The three points are aligned")
else:
# Sphere center.
a = P2P3**2 * (P1 - P2).dot(P1 - P3) / 2 / l**2
b = P3P1**2 * (P2 - P1).dot(P2 - P3) / 2 / l**2
c = P1P2**2 * (P3 - P1).dot(P3 - P2) / 2 / l**2
P1.multiply(a)
P2.multiply(b)
P3.multiply(c)
PC = P1 + P2 + P3

# Creation of a circle
pl = Base.Placement()
v = (P1 - P2).cross(P3 - P2)
v.normalize()
axis = Base.Vector(0, 0, 1).cross(v)
angle = asin(axis.Length) * 180 / pi
axis.normalize()
pl = Base.Placement(PC, axis, angle)
Draft.makeCircle(r, placement=pl, face=False, support=None)
# Displays the result in the windows
affiche((PC.x),(PC.y),(PC.z),r,angle)
# Displays the result in the FreeCAD report view
#FreeCAD.Console.PrintMessage("Coordinate X : "+str(PC.x)+"\n")
#FreeCAD.Console.PrintMessage("Coordinate Y : "+str(PC.y)+"\n")
#FreeCAD.Console.PrintMessage("Coordinate Z : "+str(PC.z)+"\n")
#FreeCAD.Console.PrintMessage("Radius       : "+str(r)+"\n")
#FreeCAD.Console.PrintMessage("Angle        : "+str(angle)+"\n")
else:
# If the condition is not met, repeat
#FreeCAD.Console.PrintError("Select 3 points and repeat\n")
errorDialog("Select 3 points and repeat\n")```