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@mrrclb48z

正三角形の辺の長さ「高校入試チャレンジ問題 正三角形ABCの高さは？」をsympyとFreeCADでやってみたい。

Last updated at Posted at 2024-10-20

・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。
・以下に私の勘違いもあります。
・(別件)???皆様が待望のFreeCADのマクロで寸法線表示ができました。(未、角度寸法表示)
https://qiita.com/mrrclb48z/items/a330f05a8e6946ea842c

オリジナル

・YUUU0123 様 (0:00〜3:02)

sympyで(オリジナル 様の方法を参考に)

ver0.1 ステキです。

from sympy import *
var('a,h',real=True,positive=True)
print("#",solve(Eq(3*a/2+4*a/2+5*a/2,a*h/2),h)[0])
# 12

sympyで(いつもの方法で)　以下は、いつもの勘違いです。

・良いように言えば、???作図のためです。
　「正三角形をつくる問題」として解きました。
　この課題は、奥が深いみたいです。省略。

ver0.2 連立方程式で

・３オフセットの共通点。最初に浮かんだのがコレです。

# ver0.2
from sympy import *
var('a,Gx,Gy',real=True,positive=True)
A,B,C,G=map(Point,[(a*Rational(1,2),a*Rational(1,2)*sqrt(3)),(0,0),(a,0),(Gx,Gy)])
sol_a,sol_Gx,sol_Gy=solve([Eq(Line(A,B).distance(G),3),
                           Eq(Line(B,C).distance(G),4),
                           Eq(Line(C,A).distance(G),5)],
                          [a,Gx,Gy])[1]
print("#",sol_a*Rational(1,2)*sqrt(3))
# 12

ver0.3 CAD風に。

・左下から、???片押し。いいですネ。普通はCAD風コレかも。
・直線のオフセットで良さそうなのが見つからなかったので、自作です。???以下でも。
parallel_line(p)
https://docs.sympy.org/latest/modules/geometry/lines.html#sympy.geometry.line.LinearEntity.parallel_line

# ver0.3
from sympy import *
def myLine_Offset(P1,P2,d):
    myOffset=d*(P2-P1).rotate(pi/2).unit
    return Line(P1+myOffset,P2+myOffset)
a=10  # 仮りの辺の長さ
A,B,C=map(Point,[(a*Rational(1,2),a*Rational(1,2)*sqrt(3)),(0,0),(a,0)])
G =myLine_Offset(B,C,4).intersection(myLine_Offset(B,A,-3))[0]
G2=Line(B,((C-B).unit+(A-B).unit)*Rational(1,2)).projection(G)
print("#",B.distance(G2)+5)
# 12

FreeCADのマクロで作図

・問題文は2次元ですが、３次元FreeCADのマクロで、XY平面に作図しました。
・計算部分は、Ver.0.2 の コピー貼り付けです。
・???皆様が待望のFreeCADのマクロで寸法線表示ができました。(未、角度寸法表示)

import FreeCAD
import Part
import DraftTools
import Draft
import Mesh
############################################################################
# ver0.2
from sympy import *
var('a,Gx,Gy',real=True,positive=True)
A,B,C,G=map(Point,[(a*Rational(1,2),a*Rational(1,2)*sqrt(3)),(0,0),(a,0),(Gx,Gy)])
sol_a,sol_Gx,sol_Gy=solve([Eq(Line(A,B).distance(G),3),
                           Eq(Line(B,C).distance(G),4),
                           Eq(Line(C,A).distance(G),5)],
                          [a,Gx,Gy])[1]
print("#",sol_a*Rational(1,2)*sqrt(3))
# 12
###########################################################################
rep={a:sol_a,Gx:sol_Gx,Gy:sol_Gy}
A=A.subs(rep)
B=B.subs(rep)
C=C.subs(rep)
G=G.subs(rep)
D=Line(A,B).projection(G)
E=Line(B,C).projection(G)
F=Line(C,A).projection(G)
############################################################################
# 3D作図 z=0 XY平面に作図しました。
# 2024-10-08 fontsize 追加しました。従来と互換性がありません。 
# 2024-10-20 HR 
############################################################################
def myDimension(fontsize,myExtOvershoot,start_point, end_point,HVP):
    x1, y1 = start_point.args
    x2, y2 = end_point.args
    myFlipText = True
    if HVP=="PL":
       myP1  =Point(float(x1),float(y1))
       myP2  =Point(float(x2),float(y2))
       myFlipText = False
       myExtOvershoot1=abs(myExtOvershoot)
    elif HVP=="PR":
       myP1  =Point(float(x1),float(y1))
       myP2  =Point(float(x2),float(y2))
       myFlipText = False
       myExtOvershoot1=-abs(myExtOvershoot)
    elif HVP=="VL":
       if x1<x2 and y1<y2:
          myP1  =Point(float(x1),float(y1))
          myP2  =Point(float(x1),float(y2))
          myExtOvershoot1= abs(myExtOvershoot)
          myFlipText = False
       elif x1<x2 and y1>y2:
          myP1  =Point(float(x1),float(y1))
          myP2  =Point(float(x1),float(y2))
          myExtOvershoot1=-abs(myExtOvershoot)
       elif x1>x2 and y1<y2:
          myP1  =Point(float(x2),float(y1))
          myP2  =Point(float(x2),float(y2))
          myExtOvershoot1= abs(myExtOvershoot)
          myFlipText = False
       else:
          myP1  =Point(float(x2),float(y1))
          myP2  =Point(float(x2),float(y2))
          myExtOvershoot1=-abs(myExtOvershoot)
    elif HVP=="VR":
       if x1<x2 and y1<y2:
          myP1  =Point(float(x2),float(y1))
          myP2  =Point(float(x2),float(y2))
          myExtOvershoot1=-abs(myExtOvershoot)
          myFlipText = False
       elif x1<x2 and y1>y2:
          myP1  =Point(float(x2),float(y1))
          myP2  =Point(float(x2),float(y2))
          myExtOvershoot1= abs(myExtOvershoot)
       elif x1>x2 and y1<y2:
          myP1  =Point(float(x1),float(y1))
          myP2  =Point(float(x1),float(y2))
          myExtOvershoot1=-abs(myExtOvershoot)
       else:
          myP1  =Point(float(x1),float(y1))
          myP2  =Point(float(x1),float(y2))
          myExtOvershoot1= abs(myExtOvershoot)
    elif HVP=="HL":
       if x1 < x2 and y1<y2:
          myP1  =Point(float(x1),float(y2))
          myP2  =Point(float(x2),float(y2))
          myExtOvershoot1= abs(myExtOvershoot)
          myFlipText = False
       elif x1 < x2 and y1>y2:
          myP1  =Point(float(x1),float(y1))
          myP2  =Point(float(x2),float(y1))
          myExtOvershoot1= abs(myExtOvershoot)
          myFlipText = False
       elif x1 > x2 and y1<y2:
          myP1  =Point(float(x1),float(y1))
          myP2  =Point(float(x2),float(y1))
          myExtOvershoot1= abs(myExtOvershoot)
       else:
          myP1  =Point(float(x1),float(y2))
          myP2  =Point(float(x2),float(y2))
          myExtOvershoot1= abs(myExtOvershoot)
    elif HVP=="HR":
       #if x1<x2 and y1<y2: # 2024-10-20 HR
       if x1<x2 and y1<=y2:
          myP1  =Point(float(x1),float(y1))
          myP2  =Point(float(x2),float(y1))
          myExtOvershoot1=-abs(myExtOvershoot)
          myFlipText = False
       elif x1<x2 and y1>y2:
          myP1  =Point(float(x1),float(y2))
          myP2  =Point(float(x2),float(y2))
          myExtOvershoot1=-abs(myExtOvershoot)
          myFlipText = False
       elif x1>x2 and y1<y2:
          myP1  =Point(float(x1),float(y2))
          myP2  =Point(float(x2),float(y2))
          myExtOvershoot1=-abs(myExtOvershoot)
       else:
          myP1  =Point(float(x1),float(y1))
          myP2  =Point(float(x2),float(y1))
          myExtOvershoot1=-abs(myExtOvershoot)
    else:  
      print("")

    myM   =myP1.midpoint(myP2)
    myT   =myM+myExtOvershoot1*((myP1-myM).unit).rotate( -pi/2 )
    dimension = Draft.makeDimension(
        FreeCAD.Vector(myP1.x, myP1.y, 0),           # 点1の座標
        FreeCAD.Vector(myP2.x, myP2.y, 0),           # 点2の座標
        FreeCAD.Vector(float(myT.x),float(myT.y),0)  # 矢印の位置を中央に設定
    )
    # Ext Overshootを設定
    dimension.ViewObject.ExtOvershoot = -float(myExtOvershoot)
    
    dimension.ViewObject.FlipText = myFlipText

    # 矢印のスタイルを設定
    dimension.ViewObject.ArrowType    = "Arrow"  # 矢印のタイプを "Arrow" に設定
    dimension.ViewObject.ArrowSize    = fontsize/5
    dimension.ViewObject.TextSpacing  = 0
    dimension.ViewObject.LineColor    = (0.0, 1.0, 0.0)  # 緑色
    dimension.ViewObject.FontSize     = fontsize  # フォントサイズを指定
def myXYZ2Txt_2D(A):
    return ""
def myXYZ2Txt_XY_2D(A):
    return '(' + str(A.x) + ',' + str(A.y) +  ')'
def myTxtXYZ_2D(fontsize,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 = str(fontsize,)+' mm'
    return
def myTxtXYZ_S_2D(fontsize,*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 myTxtXYZ_XY_S_2D(fontsize,*xy_tx):
    for i in range(1,int(len(xy_tx)/2)+1):
        myTxtXYZ_2D(fontsize,xy_tx[2*i-2],xy_tx[2*i-1]+myXYZ2Txt_XY_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
####################################################################################
myLine_C_2D     (A,B,C)  
myLine_S_2D     (G,D)
myLine_S_2D     (G,E)
myLine_S_2D     (G,F)
#
# myFontsize =0.25
myFontsize =0.5*2.0
myOvershoot=1.0*2.0
myDimension(myFontsize,myOvershoot,B,A,"PL")
myDimension(myFontsize,myOvershoot,B,C,"HR")
myDimension(myFontsize,myOvershoot,A,C,"PL")
myDimension(myFontsize,myOvershoot,D,G,"PL")
myDimension(myFontsize,myOvershoot,E,G,"PL")
myDimension(myFontsize,myOvershoot,G,F,"PL")
#
myTxtXYZ_XY_S_2D(myFontsize,A,"A",B,"B",C,"C")
myTxtXYZ_XY_S_2D(myFontsize,D,"D",E,"E",F,"F",G,"G")
####################################################################################
doc = App.activeDocument()
#App.ActiveDocument.addObject("App::Origin", "Origin")
#App.ActiveDocumen!t.getObject('Origin').Visibility = True
App.ActiveDocument.recompute()
Gui.activeDocument().activeView().viewAxonometric()
Gui.SendMsgToActiveView("ViewFit")

isometric方向?です。(省略)
拡大図
111.png

いつものリンク? sympyの実行環境と 参考のおすすめです。

(テンプレート)

・以下ができたら、助かります。指定と全部です

いつもと違うリンクのおすすめです。

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