triangular pyramid, trigonal pyramid offset-3d-Plane-Intersection By vbasolver - vba

Question

triangular pyramid, trigonal pyramid offset-3d-Plane-Intersection By vbasolver
x=0.250 y=0.250 z=0.250　Inscribed sphere　Center
each plane offset 0.25 I challenge vba solver
why ALL-Row 0.250 0.250 0.250
I want ALL-Row 0.250 0.250 0.250
why 6row 8row error
The result is strange
Please tell me how to fix it.
Const x0 = 0
Const y0 = 0
Const z0 = 2
Const x1 = 0
Const y1 = 0
Const z1 = 0
Const x2 = 1
Const y2 = 0
Const z2 = 0
Const x3 = 0
Const y3 = 1
Const z3 = 0
Const r0 = 0.25
Const r1 = 0.25
Const r2 = 0.25
Const r3 = 0.25
Function myR1C1toA1(i, j)
myR1C1toA1 = Application.ConvertFormula("R" & i & "C" & j, xlR1C1, xlA1)
End Function
Function myPlane(Ax, Ay, Az, Bx, By, Bz, Cx, Cy, Cz)
a = (By - Ay) * (Cz - Az) - (Cy - Ay) * (Bz - Az)
b = (Bz - Az) * (Cx - Ax) - (Cz - Az) * (Bx - Ax)
c = (Bx - Ax) * (Cy - Ay) - (Cx - Ax) * (By - Ay)
d = -(a * Ax + b * Ay + c * Az)
myPlane = Array(a, b, c, d)
End Function
Function myOffset3PlaneIntersection(irow, x0, y0, z0, x1, y1, z1, x2, y2, z2, x3, y3, z3, r1, r2, r3)
Dim v1 As Variant
Dim v2 As Variant
Dim v3 As Variant
'
v1 = myPlane(x0, y0, z0, x2, y2, z2, x3, y3, z3)
v2 = myPlane(x0, y0, z0, x3, y3, z3, x1, y1, z1)
v3 = myPlane(x0, y0, z0, x1, y1, z1, x2, y2, z2)
'
my1 = "(Abs(" & v1(0) & " * " & myR1C1toA1(irow, 1) & "+ " & v1(1) & " * " & myR1C1toA1(irow, 2) & "+ " & v1(2) & " * " & myR1C1toA1(irow, 3) & "+ " & v1(3) & ") / Sqrt(" & v1(0) & " ^ 2 + " & v1(1) & " ^ 2 +" & v1(2) & " ^ 2) - " & myR1C1toA1(irow, 1) & ")"
my2 = "(Abs(" & v2(0) & " * " & myR1C1toA1(irow, 1) & "+ " & v2(1) & " * " & myR1C1toA1(irow, 2) & "+ " & v2(2) & " * " & myR1C1toA1(irow, 3) & "+ " & v2(3) & ") / Sqrt(" & v2(0) & " ^ 2 + " & v2(1) & " ^ 2 +" & v2(2) & " ^ 2) - " & myR1C1toA1(irow, 2) & ")"
my3 = "(Abs(" & v3(0) & " * " & myR1C1toA1(irow, 1) & "+ " & v3(1) & " * " & myR1C1toA1(irow, 2) & "+ " & v3(2) & " * " & myR1C1toA1(irow, 3) & "+ " & v3(3) & ") / Sqrt(" & v3(0) & " ^ 2 + " & v3(1) & " ^ 2 +" & v3(2) & " ^ 2) - " & myR1C1toA1(irow, 3) & ")"
Range(myR1C1toA1(irow, 5)).Formula = "=" & my1 & "^ 2 +" & my2 & "^ 2 +" & my3 & "^ 2"
'
Dim ws As Worksheet: Set ws = ActiveSheet
SolverReset
SolverOk setCell:=ws.Range(myR1C1toA1(irow, 5)), _
MaxMinVal:=3, _
ByChange:=ws.Range(myR1C1toA1(irow, 1) & ":" & myR1C1toA1(irow, 3)), _
EngineDesc:="GRG Nonlinear"
SolverSolve UserFinish:=True
End Function
Sub myFormat()
Columns("A:E").Select
Selection.NumberFormatLocal = "0.000_ "
Range("A5").Select
End Sub
Sub aaa_Main()
Dim myXYZ As Variant
ActiveSheet.Cells.Clear
MsgBox "Solver Start"
Cells(1, 1) = x0
Cells(1, 2) = y0
Cells(1, 3) = z0
Cells(2, 1) = x1
Cells(2, 2) = y1
Cells(2, 3) = z1
Cells(3, 1) = x2
Cells(3, 2) = y2
Cells(3, 3) = z2
Cells(4, 1) = x3
Cells(4, 2) = y3
Cells(4, 3) = z3
'-----------------------------------------------------------------------------------------------------
irow = 5
Cells(irow + 0, 4) = r0
Cells(irow + 1, 4) = r1
Cells(irow + 2, 4) = r2
Cells(irow + 3, 4) = r3
myXYZ = myOffset3PlaneIntersection(irow + 0, x0, y0, z0, x1, y1, z1, x2, y2, z2, x3, y3, z3, r1, r2, r3)
myXYZ = myOffset3PlaneIntersection(irow + 1, x1, y1, z1, x2, y2, z2, x3, y3, z3, x0, y0, z0, r2, r3, r0)
myXYZ = myOffset3PlaneIntersection(irow + 2, x2, y2, z2, x3, y3, z3, x0, y0, z0, x1, y1, z1, r3, r0, r1)
myXYZ = myOffset3PlaneIntersection(irow + 3, x3, y3, z3, x0, y0, z0, x1, y1, z1, x2, y2, z2, r0, r1, r2)
myFormat
End Sub
'1 0.000 0.000 2.000
'2 0.000 0.000 0.000
'3 1.000 0.000 0.000
'4 0.000 1.000 0.000
'5 0.250 0.250 0.250 0.250 0.000
'6 0.000 0.000 0.000 0.250 0.000 ???? I want 0.250 0.250 0.250
'7 0.250 0.250 0.250 0.250 0.000
'8 0.102 0.339 0.102 0.250 0.000 ???? I want 0.250 0.250 0.250
(2021-11-15)I try sympy
from sympy import *
def myVol(PTO,PTA,PTB,PTC):
return Matrix([[PTA.x-PTO.x, PTA.y-PTO.y, PTA.z-PTO.z], [PTB.x-PTO.x, PTB.y-PTO.y, PTB.z-PTO.z], [PTC.x-PTO.x, PTC.y-PTO.y, PTC.z-PTO.z]]).det()/6
def myUnitVector(myPoint3D):
myL=myPoint3D.distance((0, 0))
return Point3D(myPoint3D.x/myL,myPoint3D.y/myL,myPoint3D.z/myL)
def myHtoP(myHairetu):
return Point3D(myHairetu[0],myHairetu[1],myHairetu[2])
def my3PLaneIntersection(PTO,PTA,PTB,PTC,RA,RB,RC):
vA =myUnitVector(myHtoP(Plane(PTO, PTB, PTC).normal_vector))
PLA=Plane(PTO + RA * vA, normal_vector=vA)
vB =myUnitVector(myHtoP(Plane(PTO, PTC, PTA).normal_vector))
PLB=Plane(PTO + RB * vB, normal_vector=vB)
vC =myUnitVector(myHtoP(Plane(PTO, PTA, PTB).normal_vector))
PLC=Plane(PTO + RC * vC, normal_vector=vC)
return PLC.intersection(PLB.intersection(PLA)[0])
PTO,PTA,PTB,PTC=Point3D(0,0,0),Point3D(1,0,0),Point3D(0,1,0),Point3D(0,0,2)
print("#",myVol(PTO,PTA,PTB,PTC))
myRO,myRA,myRB,myRC=0,0,0,0
print("#",myVol(
my3PLaneIntersection(PTO,PTA,PTB,PTC,myRO,myRO,myRO)[0],
my3PLaneIntersection(PTA,PTC,PTB,PTO,myRA,myRA,myRA)[0],
my3PLaneIntersection(PTB,PTC,PTO,PTA,myRB,myRB,myRB)[0],
my3PLaneIntersection(PTC,PTB,PTA,PTO,myRC,myRC,myRC)[0]))
myRO,myRA,myRB,myRC=1/4,1/4,1/4,1/4
print("#",myVol(
my3PLaneIntersection(PTO,PTA,PTB,PTC,myRO,myRO,myRO)[0],
my3PLaneIntersection(PTA,PTC,PTB,PTO,myRA,myRA,myRA)[0],
my3PLaneIntersection(PTB,PTC,PTO,PTA,myRB,myRB,myRB)[0],
my3PLaneIntersection(PTC,PTB,PTA,PTO,myRC,myRC,myRC)[0]))
myRO,myRA,myRB,myRC=-1/4,-1/4,-1/4,-1/4
print("#",myVol(
my3PLaneIntersection(PTO,PTA,PTB,PTC,myRO,myRO,myRO)[0],
my3PLaneIntersection(PTA,PTC,PTB,PTO,myRA,myRA,myRA)[0],
my3PLaneIntersection(PTB,PTC,PTO,PTA,myRB,myRB,myRB)[0],
my3PLaneIntersection(PTC,PTB,PTA,PTO,myRC,myRC,myRC)[0]))
# 1/3
# 1/3
# 0
# 8/3

Answer 1

I check
from sympy import *
var('m')
def myUnitVector(myPoint3D):
myL=myPoint3D.distance((0, 0))
return Point3D(myPoint3D.x/myL,myPoint3D.y/myL,myPoint3D.z/myL)
def myHtoP(myHairetu):
return Point3D(myHairetu[0],myHairetu[1],myHairetu[2])
def my3PLaneIntersection(PTO,PTA,PTB,PTC,RA,RB,RC):
vA =myUnitVector(myHtoP(Plane(PTO, PTB, PTC).normal_vector))
PLA=Plane(PTO + RA * vA, normal_vector=vA)
vB =myUnitVector(myHtoP(Plane(PTO, PTC, PTA).normal_vector))
PLB=Plane(PTO + RB * vB, normal_vector=vB)
vC =myUnitVector(myHtoP(Plane(PTO, PTA, PTB).normal_vector))
PLC=Plane(PTO + RC * vC, normal_vector=vC)
return PLC.intersection(PLB.intersection(PLA)[0])
def myProjection(PTO,PTA,PTC,PTOO):
v = myUnitVector(myHtoP(Plane(PTO, PTA, PTC).normal_vector))
return solve(PTOO - Plane(PTO, PTA, PTC).projection(PTOO) - m * v, m)[m] * (-1)
PTO,PTA,PTB,PTC=Point3D(0,0,0),Point3D(1,0,0),Point3D(0,1,0),Point3D(0,0,2)
myRO,myRA,myRB,myRC=-1/4,-1/4,-1/4,-1/4
PTOO= my3PLaneIntersection(PTO, PTA,PTB,PTC,myRO,myRO,myRO)[0]
PTAA= my3PLaneIntersection(PTA, PTC,PTB,PTO,myRA,myRA,myRA)[0]
PTBB= my3PLaneIntersection(PTB, PTC,PTO,PTA,myRB,myRB,myRB)[0]
PTCC= my3PLaneIntersection(PTC, PTB,PTA,PTO,myRC,myRC,myRC)[0]
print("#",PTOO,"\n#",PTAA,"\n#",PTBB,"\n#",PTCC,)
print("#",myProjection(PTO,PTB,PTA,PTOO),
myProjection(PTO,PTA,PTC,PTOO),
myProjection(PTO,PTC,PTB,PTOO))
print("#",myProjection(PTA,PTO,PTB,PTAA),
myProjection(PTA,PTC,PTO,PTAA),
myProjection(PTA,PTB,PTC,PTAA))
print("#",myProjection(PTB,PTA,PTO,PTBB),
myProjection(PTB,PTO,PTC,PTBB),
myProjection(PTB,PTC,PTA,PTBB))
print("#",myProjection(PTC,PTO,PTA,PTCC),
myProjection(PTC,PTB,PTO,PTCC),
myProjection(PTC,PTA,PTB,PTCC))
# Point3D(-1/4, -1/4, -1/4)
# Point3D(7/4, -1/4, -1/4)
# Point3D(-1/4, 7/4, -1/4)
# Point3D(-1/4, -1/4, 15/4)
# -1/4 -1/4 -1/4
# -1/4 -1/4 -1/4
# -1/4 -1/4 -1/4
# -1/4 -1/4 -1/4