# Makrodefinicja: Utwórz okrąg na podstawie trzech punktów

This page is a translated version of the page Macro Make Circle 3 Points and the translation is 6% complete.
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Description Macro Make Circle 3 Points This macro creates a circle circumscribed on 3 selected points, orthogonal manner or in 3D at the option space. Points can be objects such as cubes, cylinders,... then selected coordinates will be the centre of these forms.Macro version: 1.0Last modified: 2014-08-08FreeCAD version: AllDownload: ToolBar IconIcon View-TopIcon View-LeftIcon View-FrontIcon View-C3PAuthor: Mario52 Mario52 ToolBar IconIcon View-TopIcon View-LeftIcon View-FrontIcon View-C3P Macros recipesHow to install macrosHow to customize toolbars 1.0 2014-08-08 All None None

## Description

This macro creates a circle circumscribed on 3 selected points, orthogonal manner or in 3D at the option space. Points can be objects such as cubes, cylinders,... then selected coordinates will be the centre of these forms.

Circle built on 3 selected points

## 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.

## Options

### Mode :

Defaut :

Mode by default, creates a circle on the three points or shapes in 3d space.
The order of selection of fear forms influencing the angle AXIS and reverse the inclination of the circle. In this case, reverse or change the order of selection of the shapes.
Coordinates X, Y, Z value 0 or alignment does not allow calculation, can return a division by zero error, and translated by The three points are aligned

Vue Face :

Creates the circle in the front views of the form chosen, 1, 2 or 3

Vue Dessus :

Creates the circle in the top on the form chosen view, 1, 2 or 3

Vue Droite :

Creates the circle in the view of right on the form chosen, 1, 2 or 3

### Alignement sur :

Forme 1, 2, 3

Forms, in the order of their selections.

### Afficher le centre :

If this box is checked, a point on the centre of the built circle will be created

### Associer les couleurs

If this box is checked, the circle will take the colour of the relevant view,
View-Top (X,Y) = Blue(axe Z)
View-Front (Z,X) = Green(Axe Y)
View-Left (Z,Y) = Red(Axe X)

## Script

The three icons must be in the same directory as the module.

ToolBar Icon

Make_Circle_3_Points.FCMacro

```# -*- coding: utf-8 -*-
# Cercle sur 3 points.py
# create a circle from 3 points selected
# combination of the two programs 'create a circle from 3 points selected'
# with as options (orthogonal) circle can be built on a choice plans
# to coordinate one of the three selected choice shapes
# mode by default, creates the circle in 3D space
# the options create the circle of orthogonal way on the map and view the choice
# with the creation of a central color related to the axes Y/N Y/N
# 04/03/2013 # 24/03/2013 # 08/08/2014 by mario52
# the formula adapted (with permission of its author) by "mario52" for orthogonal circles comes from
# http://www-obs.univ-lyon1.fr/labo/fc/Ateliers_archives/ateliers_2005-06/cercle_3pts.pdf
# read the note in pdf, on the order of selection points,
# If the formula returns an error (example the 3 points in the same alignment)
# the formula adapted by "galou_breizh" for the cecle in 3D space comes from
# http://en.wikipedia.org/wiki/Circumscribed_circle
# the window is always visible and allows you to work on other programs
# as for example to select other items in FreeCAD

#08/08/2014 PyQt4 and PySide

#OS: Windows Vista
#Word size: 32-bit
#Version: 0.14.3700 (Git)
#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 sqrt, pi, sin, cos, asin

# vueChoix = 0 et alignerSur = 0 , mode par défaut
global vueChoix		# choix de la vue Dessus=1 XY, vue Face=2 ZX, vue Droite=3 ZY (Orthogonal)
global alignerSur   # aligne le cercle sur une forme au choix (1,2 ou 3) ou sur Z=0 (Orthogonal)
global afficherPoint# affiche le point central du cercle
global colorer     	# colorer suivant l'axe 1=Ok 0=Couleur courante uniquement Orthogonal !
vueChoix = 0
alignerSur = 0
afficherPoint = 1
colorer = 1

try:
_fromUtf8 = QtCore.QString.fromUtf8
except AttributeError:
def _fromUtf8(s):
return s

try:
_encoding = QtGui.QApplication.UnicodeUTF8
def _translate(context, text, disambig):
return QtGui.QApplication.translate(context, text, disambig, _encoding)
except AttributeError:
def _translate(context, text, disambig):
return QtGui.QApplication.translate(context, text, disambig)

class Ui_MainWindow(object):

def __init__(self, MainWindow):
self.window = MainWindow

MainWindow.setObjectName(_fromUtf8("MainWindow"))
MainWindow.resize(490, 302)
MainWindow.setWindowIcon(QtGui.QIcon(path+'View-C3P.png'))
self.centralWidget = QtGui.QWidget(MainWindow)
self.centralWidget.setObjectName(_fromUtf8("centralWidget"))

self.groupBox = QtGui.QGroupBox(self.centralWidget)
self.groupBox.setGeometry(QtCore.QRect(20, 10, 130, 161))
self.groupBox.setObjectName(_fromUtf8("groupBox_1"))

self.radioButton_1.setToolTip(_translate("MainWindow", "Cercle sur 3 points dans l'espace", None))

self.radioButton_2.setToolTip(_translate("MainWindow", "Cercle orthogonal sur la vue de face", None))
self.image_01 = path+"View-Front.png"
icon01 = QtGui.QIcon()

self.radioButton_3.setToolTip(_translate("MainWindow", "Cercle orthogonal sur la vue de dessus", None))
self.image_02 = path+"View-Top.png"
icon02 = QtGui.QIcon()

self.radioButton_4.setToolTip(_translate("MainWindow", "Cercle orthogonal sur la vue de droite", None))
self.image_03 = path+"View-Left.png"
icon03 = QtGui.QIcon()

self.groupBox_2 = QtGui.QGroupBox(self.centralWidget)
self.groupBox_2.setGeometry(QtCore.QRect(170, 10, 120, 161))
self.groupBox_2.setObjectName(_fromUtf8("groupBox_2"))

self.radioButton_5.setToolTip(_translate("MainWindow", "Cercle sur 3 points dans l'espace", None))

self.radioButton_6.setToolTip(_translate("MainWindow", "Cercle orthogonal sur la forme 1", None))

self.radioButton_7.setToolTip(_translate("MainWindow", "Cercle orthogonal sur la forme 2", None))

self.radioButton_8.setToolTip(_translate("MainWindow", "Cercle orthogonal sur la forme 3", None))

self.checkBox_1 = QtGui.QCheckBox(self.centralWidget)
self.checkBox_1.setGeometry(QtCore.QRect(20, 190, 140, 20))
self.checkBox_1.setChecked(True)
self.checkBox_1.setObjectName(_fromUtf8("checkBox_1"))
self.checkBox_1.setToolTip(_translate("MainWindow", "Affiche un point sur le centre du cercle", None))
#        self.checkBox_1.clicked.connect(self.on_checkBox_1_clicked) #connection checkBox_1

self.checkBox_2 = QtGui.QCheckBox(self.centralWidget)
self.checkBox_2.setGeometry(QtCore.QRect(170, 190, 150, 20))
self.checkBox_2.setChecked(True)
self.checkBox_2.setObjectName(_fromUtf8("checkBox_2"))
self.checkBox_2.setToolTip(_translate("MainWindow", "Associe la couleur du cercle à la couleur des axes X,Y,Z (Orthogonal)", None))
#        self.checkBox_2.clicked.connect(self.on_checkBox_2_clicked) #connection checkBox_1

self.lineEdit_1 = QtGui.QLineEdit(self.centralWidget)
self.lineEdit_1.setGeometry(QtCore.QRect(320, 30, 151, 22))
self.lineEdit_1.setObjectName(_fromUtf8("lineEdit_1"))

self.lineEdit_2 = QtGui.QLineEdit(self.centralWidget)
self.lineEdit_2.setGeometry(QtCore.QRect(320, 80, 151, 22))
self.lineEdit_2.setObjectName(_fromUtf8("lineEdit_2"))

self.lineEdit_3 = QtGui.QLineEdit(self.centralWidget)
self.lineEdit_3.setGeometry(QtCore.QRect(320, 130, 151, 22))
self.lineEdit_3.setObjectName(_fromUtf8("lineEdit_3"))

self.lineEdit_4 = QtGui.QLineEdit(self.centralWidget)
self.lineEdit_4.setGeometry(QtCore.QRect(320, 180, 151, 22))
self.lineEdit_4.setObjectName(_fromUtf8("lineEdit_4"))

self.lineEdit_5 = QtGui.QLineEdit(self.centralWidget)
self.lineEdit_5.setGeometry(QtCore.QRect(320, 230, 151, 22))
self.lineEdit_5.setObjectName(_fromUtf8("lineEdit_5"))

self.label_1 = QtGui.QLabel(self.centralWidget)
self.label_1.setGeometry(QtCore.QRect(320, 10, 91, 16))
self.label_1.setObjectName(_fromUtf8("label_1"))

self.label_2 = QtGui.QLabel(self.centralWidget)
self.label_2.setGeometry(QtCore.QRect(320, 60, 91, 16))
self.label_2.setObjectName(_fromUtf8("label_2"))

self.label_3 = QtGui.QLabel(self.centralWidget)
self.label_3.setGeometry(QtCore.QRect(320, 110, 91, 16))
self.label_3.setObjectName(_fromUtf8("label_3"))

self.label_4 = QtGui.QLabel(self.centralWidget)
self.label_4.setGeometry(QtCore.QRect(320, 160, 53, 16))
self.label_4.setObjectName(_fromUtf8("label_4"))

self.label_5 = QtGui.QLabel(self.centralWidget)
self.label_5.setGeometry(QtCore.QRect(320, 210, 81, 16))
self.label_5.setObjectName(_fromUtf8("label_5"))

self.pushButton_1 = QtGui.QPushButton(self.centralWidget)
self.pushButton_1.setGeometry(QtCore.QRect(20, 230, 90, 28))
self.pushButton_1.setObjectName(_fromUtf8("pushButton_1"))
self.pushButton_1.clicked.connect(self.on_pushButton_1_clicked) #connection pushButton_1
self.pushButton_1.setToolTip(_translate("MainWindow", "Quitte la fonction", None))

self.pushButton_2 = QtGui.QPushButton(self.centralWidget)
self.pushButton_2.setGeometry(QtCore.QRect(110, 230, 90, 28))
self.pushButton_2.setObjectName(_fromUtf8("pushButton_2"))
self.pushButton_2.clicked.connect(self.on_pushButton_2_clicked) #connection pushButton_2
self.pushButton_2.setToolTip(_translate("MainWindow", "Applique la fonction sans quitter", None))
#self.pushButton_2.setStyleSheet("background-color: red") #cette fonction donne une couleur au bouton
#self.pushButton_2.setStyleSheet("color : #ff0000") #cette fonction donne une couleur au texte du bouton
#self.pushButton_2.setStyleSheet("color : #ff0000; background-color : #0000ff;" ) #combinaison des deux

self.pushButton_3 = QtGui.QPushButton(self.centralWidget)
self.pushButton_3.setGeometry(QtCore.QRect(200, 230, 90, 28))
self.pushButton_3.setObjectName(_fromUtf8("pushButton_3"))
self.pushButton_3.clicked.connect(self.on_pushButton_3_clicked) #connection pushButton_3
self.pushButton_3.setToolTip(_translate("MainWindow", "Définit le mode par défaut (Cercle sur 3 points dans l'espace)", None))

MainWindow.setCentralWidget(self.centralWidget)
self.statusBar = QtGui.QStatusBar(MainWindow)
self.statusBar.setObjectName(_fromUtf8("statusBar"))
MainWindow.setStatusBar(self.statusBar)

self.retranslateUi(MainWindow)
QtCore.QMetaObject.connectSlotsByName(MainWindow)

def retranslateUi(self, MainWindow):
try:
MainWindow.setWindowFlags(PyQt4.QtCore.Qt.WindowStaysOnTopHint) # PyQt4 cette fonction met la fenêtre en avant
except Exception:
MainWindow.setWindowFlags(PySide.QtCore.Qt.WindowStaysOnTopHint) # PySide cette fonction met la fenêtre en avant
#MainWindow.setStyleSheet("background-color: red") #cette fonction donne une couleur à la fenêtre
#MainWindow.setWindowOpacity(0.5)    #cette fonction donne une transparence à la fenêtre
MainWindow.setWindowTitle(_translate("MainWindow", "Cercle sur 3 points", None))
self.groupBox.setTitle(_translate("MainWindow", "Mode", None))
self.groupBox_2.setTitle(_translate("MainWindow", "Alignement sur", None))
self.checkBox_1.setText(_translate("MainWindow", "Afficher le centre", None))
self.checkBox_2.setText(_translate("MainWindow", "Associer les couleurs", None))
self.label_1.setText(_translate("MainWindow", "Coordonnée X", None))
self.label_2.setText(_translate("MainWindow", "Coordonnée Y", None))
self.label_3.setText(_translate("MainWindow", "Coordonnée Z", None))
self.label_4.setText(_translate("MainWindow", "Rayon", None))
self.label_5.setText(_translate("MainWindow", "Angle", None))
self.pushButton_1.setText(_translate("MainWindow", "Quitter", None))
self.pushButton_2.setText(_translate("MainWindow", "Appliquer", None))
self.pushButton_3.setText(_translate("MainWindow", "Défaut", None))
# Boutons
def on_pushButton_1_clicked(self):    # Bouton Quitte la fonction
App.Console.PrintMessage("Terminé\r\n")
self.window.hide()

def on_pushButton_2_clicked(self):    # Bouton Appliquer
vueChoix=0
vueChoix=1
vueChoix=2
vueChoix=3

alignerSur=0
alignerSur=1
alignerSur=2
alignerSur=3

if self.checkBox_1.checkState()==0:
afficherPoint=0
else:
afficherPoint=1
if self.checkBox_2.checkState()==0:
colorer=0
else:
colorer=1

# App.Console.PrintMessage("Appliquer\r\n")
# App.Console.PrintMessage(str(vueChoix)+" \t")
# App.Console.PrintMessage(str(alignerSur)+" \t")
# App.Console.PrintMessage(str(afficherPoint)+" \t")
# App.Console.PrintMessage(str(colorer)+" \r\n")

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)
try:
diag.setWindowFlags(PyQt4.QtCore.Qt.WindowStaysOnTopHint) # PyQt4 cette fonction met la fenêtre en avant
except Exception:
diag.setWindowFlags(PySide.QtCore.Qt.WindowStaysOnTopHint) # PySide cette fonction met la fenêtre en avant
#diag.setWindowModality(QtCore.Qt.ApplicationModal) # la fonction a été désactivée pour favoriser "WindowStaysOnTopHint"
diag.exec_()

def affiche(x,y,z,rayon,r,v,b,afficherPoint,angle):
Draft.makeCircle((rayon),placement=pl,face=False,support=None)
if colorer==1:
if afficherPoint==1:
Draft.makePoint(x,y,z)
if colorer==1:
str(self.lineEdit_1.setText(str(x)))
str(self.lineEdit_2.setText(str(y)))
str(self.lineEdit_3.setText(str(z)))
str(self.lineEdit_4.setText(str(rayon)))
str(self.lineEdit_5.setText(str(angle)))

# prendre les objets selectionnes
i=0
centreX=0;centreY=0;rayon=0

# S'il y a 3 points sélectionnés alors..
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

if vueChoix==3:        # Vue de droite ZY (Rouge)
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:    # Vue de face ZX (Vert)
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:                # Vue de dessus XY (Bleu)
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]

# Calcul des coordonnées du centre du cercle
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"Calcul impossible trop d'élements alignés")
else:
#finally: # si finally est présent, il sera TOUJOURS exécuté
# Définition de la coordonnée Z
centreZ=0
# Création du cercle
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,0)
elif alignerSur==2:
affiche(centreX,centreY,z_point_2,rayon,0.0,0.0,1.0,afficherPoint,0)
elif alignerSur==3:
affiche(centreX,centreY,z_point_3,rayon,0.0,0.0,1.0,afficherPoint,0)
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,0)
elif alignerSur==2:
affiche(centreY,z_point_2,centreX,rayon,0.0,1.0,0.0,afficherPoint,0)
elif alignerSur==3:
affiche(centreY,z_point_3,centreX,rayon,0.0,1.0,0.0,afficherPoint,0)
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,0)
elif alignerSur==2:
affiche(z_point_2,centreX,centreY,rayon,1.0,0.0,0.0,afficherPoint,0)
elif alignerSur==3:
affiche(z_point_3,centreX,centreY,rayon,1.0,0.0,0.0,afficherPoint,0)
else:    # 3D XYZ
P1 = sel[0].Shape.BoundBox.Center
P2 = sel[1].Shape.BoundBox.Center
P3 = sel[2].Shape.BoundBox.Center

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

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)
affiche((PC.x),(PC.y),(PC.z),r,0.0,0.0,0.0,afficherPoint,angle)

else:
# Si la condition n'est pas remplie, recommencer
errorDialog(u"Sélectionnez 3 points et recommencez")
#________________________________________________________________________________
def on_pushButton_3_clicked(self):    # Valeurs d'origine
App.Console.PrintMessage("Défaut\r\n")
vueChoix=0		# choix de la vue Dessus=1 XY, vue Face=2 ZX, vue Droite=3 ZY
alignerSur=0	# aligne le cercle sur une forme au choix (1,2 ou 3) ou sur Z=0
afficherPoint=1	# affiche le point central du cercle
self.checkBox_1.setChecked(True)
colorer=1		# colorer suivant l'axe 1=Ok 0=Couleur courante uniquement Orthogonal !
self.checkBox_2.setChecked(True)

#______________________________________________________________________________________

MainWindow = QtGui.QMainWindow()
ui = Ui_MainWindow(MainWindow)
MainWindow.show()```

## Path

The file should be copied to " C:/Program Files/FreeCAD0.13/ " If you want to put it in another directory, modify the path to line 53

```path = FreeCAD.ConfigGet("AppHomePath") # chemin
```

## Anaglyphe

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.

## Crédits

The genesis of the macro Draft_Circle_3_Points sur le 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.
The formula adapted by " galou_breizh " circle in 3D space comes from Circumscribed_circle
Separate programs are located here,
Macro Draft Circle 3 Points
Macro Draft Circle 3 Points 3D