基于vbasolver的三角棱锥体、三角棱锥体偏移-三维平面-相交 [英] triangular pyramid, trigonal pyramid offset-3d-Plane-Intersection By vbasolver
本文介绍了基于vbasolver的三角棱锥体、三角棱锥体偏移-三维平面-相交的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！
问题描述
用vbasolver实现三角棱锥体、三角棱锥体偏移-三维平面相交
x=0.250 y=0.250 z=0.250内接球心
每个平面偏移0.25I挑战VBA求解器
为什么整行0.250 0.250 0.250
我要全排0.250 0.250 0.250
为什么6row 8 row错误
结果很奇怪
请告诉我如何修复它。
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)我尝试症状
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
推荐答案
我检查
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,"
#",PTAA,"
#",PTBB,"
#",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
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