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@mrrclb48z

円に内接する四角形(等脚台形)「2022 慶応義塾大学 総合政策学部【5】」をsympyとFreeCADでやってみたい。

Last updated at Posted at 2023-08-19

・いつものベクトルの成分表示?です。
・問題文は2次元ですが、３次元FreeCADのマクロで、XY平面上に作図しました。

オリジナル(youtube)

上と同じです。大学入試数学問題集成 様＞テキスト 【5】
？？？ジャンプの調子が悪いです。？？？

sympyで(MathLABO 様の方法で)

勉強中。

sympyで(ベクトルの成分表示?です。)

・仮ABCの外心を座標原点へ移動しました。
・全点の座標計算後、解答です。

from sympy import *
var('s,t',real=True)
def myTriangle_Move_CircumcenterToOrigin_Point(dumABC):
    dumO=dumABC.circumcircle.args[0]
    myT=Triangle( dumABC.vertices[0]-dumO,
                  dumABC.vertices[1]-dumO,
                  dumABC.vertices[2]-dumO )
    return myT.args[0],myT.args[1],myT.args[2]
def mySolve (a,b,c):
    ans=solve([ Eq(a.x,(s*b+t*c).x),
                Eq(a.y,(s*b+t*c).y) ],[s,t]  ) 
    return ans[s],ans[t] 
(AB     ,BC)     =(2,1)
(Rad_BAD,Rad_CDA)=(60*pi/180,60*pi/180)
dumA=     Point(0,0)
dumB=dumA+Point(AB*cos(Rad_BAD),AB*sin(Rad_BAD) )
dumC=dumB+Point(BC             ,0               )
(A,B,C)=myTriangle_Move_CircumcenterToOrigin_Point( Triangle( dumA,dumB,dumC ) )
(O)=( Point(0,0) )
(D)=( C+Point(AB*cos(Rad_CDA),AB*sin(-Rad_CDA))   )
print("#(1)",B.distance(D)        )
print("#(1)",Circle(A,B,C).radius )
print("#(2)",(B-A).dot(O-A)       )
print("#(2)",(D-A).dot(O-A)       )
print("#(3)",mySolve( O-A,B-A,D-A ))
#(1) sqrt(7)
#(1) sqrt(21)/3
#(2) 2
#(2) 9/2
#(3) (1/6, 4/9)

FreeCADのマクロで作図

・いつものベクトルの成分表示?です。
・問題文は2次元ですが、３次元FreeCADのマクロで、XY平面上に作図しました。

import FreeCAD
import Part
import DraftTools
import Draft
import Mesh
############################################################################
# 計算
from sympy import *
var('s,t',real=True)
def myTriangle_Move_CircumcenterToOrigin_Point(dumABC):
    dumO=dumABC.circumcircle.args[0]
    myT=Triangle( dumABC.vertices[0]-dumO,
                  dumABC.vertices[1]-dumO,
                  dumABC.vertices[2]-dumO )
    return myT.args[0],myT.args[1],myT.args[2]
def mySolve (a,b,c):
    ans=solve([ Eq(a.x,(s*b+t*c).x),
                Eq(a.y,(s*b+t*c).y) ],[s,t]  ) 
    return ans[s],ans[t] 
(AB     ,BC)     =(2,1)
(Rad_BAD,Rad_CDA)=(60*pi/180,60*pi/180)
dumA=     Point(0,0)
dumB=dumA+Point(AB*cos(Rad_BAD),AB*sin(Rad_BAD) )
dumC=dumB+Point(BC             ,0               )
(A,B,C)=myTriangle_Move_CircumcenterToOrigin_Point( Triangle( dumA,dumB,dumC ) )
(O)=( Point(0,0) )
(D)=( C+Point(AB*cos(Rad_CDA),AB*sin(-Rad_CDA))   )
print("#(1)",B.distance(D)        )
print("#(1)",Circle(A,B,C).radius )
print("#(2)",(B-A).dot(O-A)       )
print("#(2)",(D-A).dot(O-A)       )
print("#(3)",mySolve( O-A,B-A,D-A ))
#(1) sqrt(7)
#(1) sqrt(21)/3
#(2) 2
#(2) 9/2
#(3) (1/6, 4/9)
############################################################################
# 作図用
myCi=Circle( O,O.distance(A))
B2=A+mySolve( O-A,B-A,D-A )[0]*(B-A)
D2=A+mySolve( O-A,B-A,D-A )[1]*(D-A)
############################################################################
# 3D作図 z=0 XY平面に作図しました。
############################################################################
############################################################################
# 円の作図　FrecCADのdocより
# https://wiki.freecad.org/Macro_Circle
def Freecad3D_circle(x=0.0,y=0.0,z=0.0,radius=0.0,diameter=0.0,circumference=0.0,area=0.0,startangle=0.0,endangle=0.0,arc=0.0,anglecenter=0.0,cord=0.0,arrow=0.0,center=0,placemObject=""):
    from math import sqrt, pi
    if placemObject == "":
        pl = FreeCAD.Placement()
        pl.Rotation = FreeCADGui.ActiveDocument.ActiveView.getCameraOrientation()   
        pl.Base = FreeCAD.Vector(x,y,z)
    else:
        pl = FreeCAD.Placement()
        pl = placemObject                                  # placement imposted
    if diameter != 0:                                      # with diameter
        radius = diameter / 2.0
    elif circumference != 0:                               # with circumference
        radius = (circumference / pi) / 2.0
    elif area != 0:                                        # with area
        radius =  sqrt((area / pi))
    elif (cord != 0) and (arrow != 0):                     # with cord and arrow
        radius = ((arrow**2) + (cord**2) / 4.0) / (arrow*2) 
    elif (arc != 0) and (anglecenter != 0):                # with arc and anglecenter central in degrees
        radius = ((360/anglecenter)*arc) / pi/2.0
        if endangle != 0:
            startangle  = endangle - anglecenter
        endangle   = anglecenter + startangle
        startangle  = endangle - anglecenter
    if radius != 0:
        try:
            Draft.makeCircle(radius,placement=pl,face=False,startangle=startangle,endangle=endangle,support=None)
            if center != 0:
                x=pl.Base.x
                y=pl.Base.y
                z=pl.Base.z
                Draft.makePoint(x,y,z)
        except Exception:
            App.Console.PrintError("Unexpected keyword argument" + "\n")
        App.ActiveDocument.recompute()
    else:
        App.Console.PrintMessage("Unexpected keyword argument" + "\n")
        App.Console.PrintMessage("circle(x,y,z,radius,diameter,circumference,area,startangle,endangle,[arc,anglecenter],[cord,arrow],center,placemObject)" + "\n")
        App.Console.PrintMessage("circle(radius=10.0,placemObject=App.Placement(App.Vector(11,20,30), App.Rotation(30,40,0), App.Vector(0,0,0)))" + "\n")
    return
def myCircle_2D(myCi):
    x=myCi.center.x
    y=myCi.center.y
    r=myCi.radius
    Freecad3D_circle(
           x=float(x),y=float(y),z=0.0,
           radius=float(abs(r)),
           center=1,
           placemObject=App.Placement(App.Vector(float(x),float(y),0),
           App.Rotation(0,0,0),App.Vector(0,0,0)))
    return
############################################################################
def myXYZ2Txt_2D(A):
    return '(' + str(A.x) + ',' + str(A.y) +  ')'
    #return ""
def myTxtXYZ_2D(A,myWedgei):
    P5x=float(A.x)
    P5y=float(A.y)
    P5z=0.0
    p5 = FreeCAD.Vector(P5x, P5y, P5z)
    myText = Draft.makeText(myWedgei, p5)
    myText.Label = myWedgei
    FreeCADGui.ActiveDocument.ActiveObject.FontSize = '0.15 mm'
    return
def myTxtXYZ_S_2D(*xy_tx):
    for i in range(1,int(len(xy_tx)/2)+1):
        myTxtXYZ_2D(xy_tx[2*i-2],xy_tx[2*i-1]+myXYZ2Txt_2D(xy_tx[2*i-2]) )
    return
def myLine_2D(A,B):
    Ax,Ay,Az=float(A.x),float(A.y),0.0
    Bx,By,Bz=float(B.x),float(B.y),0.0
    pl = FreeCAD.Placement()
    pl.Rotation.Q = (0.4247081540122249, 0.17592004639554645, 0.33985110062924484, 0.8204732460821097)
    pl.Base = FreeCAD.Vector(-3.9166066876399563, -2.1670824762243774, 1.7495260956243028)
    points = [FreeCAD.Vector(Ax,Ay,Az), FreeCAD.Vector(Bx,By,Bz)]
    line = Draft.make_wire(points, placement=pl, closed=False, face=True, support=None)
    Draft.autogroup(line)
    return
def myLine_S_2D(*args):
    for i in range(1,len(args)):
        myLine_2D(args[i-1],args[i])
    return
def myLine_C_2D(*args):
    for i in range(1,len(args)):
        myLine_2D(args[i-1],args[i])
    myLine_2D(args[i],args[0])
    return
#######################################################################################
myCircle_2D  ( myCi )
myLine_C_2D  ( A,B,C,D)
myLine_S_2D  ( B2,O)
myLine_S_2D  ( A ,O)
myLine_S_2D  ( D2,O)
myTxtXYZ_S_2D( O,"O",A,"A",B,"B",C,"C",D,"D" )
myTxtXYZ_S_2D( B2,"B2",D2,"D2" )
#######################################################################################
doc = App.activeDocument()
App.ActiveDocument.addObject("App::Origin", "Origin")
App.ActiveDocument.getObject('Origin').Visibility = True
![1png.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/109698/7ca4cf9d-2045-712b-cad2-6d621e87ee9d.png)
![0png.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/109698/a1b13033-87e8-b652-8228-fbf0d9859f21.png)
App.ActiveDocument.recompute()
Gui.activeDocument().activeView().viewAxonometric()
Gui.SendMsgToActiveView("ViewFit")

・isometric方向?です。
0png.png

・上空から?です。
・ちょっと気になる、点Aのｙ座標。マイナスでした。
・ベクトルAOをベクトルAB2とベクトルAD2に分解しました。

1png.png

sympyの実行環境

①私の環境は,pycharmです。
②よく聞くのは、Jupyterです。
③web上で、上記のソースを「SymPy Live shell」に、コピー貼り付けでもできました。
黒背景の右上に、マウスを移動すると、コピーマークが発生します。
???　タブレット環境で、コピー貼り付けが実行できませんでした。???

参考

以下、いつもの?おすすめです。

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