最小二乘法平面拟合Word格式文档下载.docx
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Theanglebetweentheplane’snormalvectorandthez-axisofthecurrentcoordinatesystem.（Z-Angle=arccosinem）.Thez-angleisapositivenumberbetween0and180degrees.
Flatness:
Flatnessisaconditionforwhichanelementofasurfaceisinaplane.
Flatnessisreportedasthewidthofthezoneformedbytwoclosestparallelplanesthatfullycontainthepointsetusedtofittheplanefeature.Avalueofzeroindicatesperfectflatness.
Flatness（minimum）:
Thedistancefromthefittedplanetothemeasuredpointfarthestbelowthefittedplaininthepointset.Aboveandbelowaredeterminedbythedirectionoftheplanevector.SeeExplanationofMax/Mindistanceindifferentcases.
Flatness（maximum）:
Thedistancefromthefittedplanetothemeasuredpointfarthestabovethefittedplaininthepointset.Aboveandbelowaredeterminedbythedirectionoftheplanevector.SeeExplanationofMax/Mindistanceindifferentcases.
Parallelism:
Theconditionofafeature,projectedtoacertainplane,beingequidistantatallelementsfromadatum（reference）.Quantitatively,parallelismisdefinedastheabsolutedistantdifferencebetweenthefarthestandclosestpointsfromthedatum.
Parallelismisevaluatedrelativetoareferencelineorxy-plane.Whenevaluatingasetofpointswithareferenceline,parallelismusestheprojectionsofthepointsandreferencelineontothexy-planeinthecurrentcoordinatesystem,orz/refplanefeature,andisspecifiedasazonetolerance.Thez/refplanefeatureisaplaneincludingthereferencelineandparallelto（orincluding）thez-axis.Whenevaluatingasetofpointswithaxy-plane,parallelismiscalculatedinthree-dimensionalspace.
Parallelism（minimum）:
Thedistancefromthereferencedlineorplanetothepointinthepointsetwiththeleastvalue（leastpositivevalueifallevaluatedpointsarepositive,ormostnegativevalueifevaluatedpointsincludenegativevalues）.SeeExplanationofMax/Mindistanceindifferentcases.
Parallelism（maximum）:
Thedistancefromthereferencelineorplanetothepointinthepointsetwiththegreatestvalue（mostpositivevalueifevaluatedpointsincludepositivevalues,orleastnegativevalueifallevaluatedpointsarenegative）.SeeExplanationofMax/Mindistanceindifferentcases.
平面相关知识：
算法如下：
VB源代码：
OptionExplicit
PublicConstPI=3.1415926535897
PublicTypetagPoint
xAsDouble
yAsDouble
zAsDouble
EndType
PublicTypetagLine2D
kAsDouble
'
Slope,Kis
the"
K"
of"
y=kx+b"
bAsDouble
intercept,Bis
B"
AngleAsDouble
arctg（k）
0to180deg
StraightnessAsDouble
RSQAsDouble
PublicTypetagLine3D
'
3Dline'
sformulaisshowingasfollowing.
1）|Ax+By+Z+D=0
|A1x+B1y+z+D1=0
2）（x-x0）/m=（y-y0）/n=（z-z0）/p----（x-x0）/m=（y-y0）/n=z/1
3）x=mt+x0,y=nt+y0,z=pt+z0
Onlypoint'
scoordinateis（a+b*Z,c+d*Z,Z）,sotheline'
svectoris{b,d,1}
x0AsDouble'
AddedonJul.1st,2009
y0AsDouble'
z0AsDouble
mAsDouble
（x-x0）/m=（y-y0）/n=（z-z0）/p,sameas:
z=a+bx,z=c+dy
nAsDouble
pAsDouble
vectors={m,n,p}
AngleAsDouble
xAnAsDouble
yAnAsDouble
zAnAsDouble
MinStAsDouble
MaxStAsDouble
PublicTypetagCircle
rAsDouble
dAsDouble
CircularAsDouble
PublicTypetagVector
aAsDouble
bAsDouble
cAsDouble
TypetagPlane
xAsDouble
Thedistancefromtheorigintothecentroid,asmeasuredalongthex-axis.
yAsDouble
Thedistancefromtheorigintothecentroid,asmeasuredalongthey-axis
zAsDouble
Thedistancefromtheorigintothecentroid,asmeasuredalongthez-axis
Z+A*x+B*y+C=0
z'
scoefficientisjust1
axAsDouble
coefficient
ofX
byAsDouble
ofY
czAsDouble
dAsDouble
ConstantC
xAnAsDouble
YAnasDouble
zAnAsDouble
FlatAsDouble
MinFlatAsDouble
*************************************************************
函数名：
PlaneSet
功能：
求拟合平面（相关参数）
参数：
dataRaw
-tagPoint型
自定义点类型（x,y,z），数组
PlaneSet–tagPlane
其值返回为平面圆相关参数
返回值：
Long型，失败为0，成功为-1
PublicFunctionPlaneSet（dataRaw（）AstagPoint,PlaneAstagPlane）AsLong'
z+Ax+BY+C=0
PlaneSet=0
DimlbAsLong,ubAsLong,MaxFAsDouble,MinFAsDouble,tmpAsDouble
lb=LBound（dataRaw）:
ub=UBound（dataRaw）
Ifub-lb+1<
4ThenExitFunction
DimiAsLong,nAsLong
n=ub-lb+1
DimxAsDouble,yAsDouble,zAsDouble
DimXYAsDouble,XZAsDouble,YZAsDouble
DimX2AsDouble,Y2AsDouble
DimaAsDouble,bAsDouble,cAsDouble,dAsDouble
Dima1AsDouble,b1AsDouble,z1AsDouble
Dima2AsDouble,b2AsDouble,z2AsDouble
Dimn1AstagVector'
{.ax,by,1}
s1
Dimn2AstagVector'
{0,0,N}XYplane
s2
Dimn3AstagVector'
lineprojectedplane
DimSLineAstagVector
DimxLineAstagVector'
{1,0,0}
DimyLineAstagVector'
DimzLineAstagVector'
DimVectorPlaneAstagVector
xLine.a=1:
xLine.b=0:
xLine.c=0
yLine.a=0:
yLine.b=1:
yLine.c=0
zLine.a=0:
zLine.b=0:
zLine.c=1
Fori=lbToub
WithdataRaw（i）
x=x+.x
y=y+.y
z=z+.z
XY=XY+.x*.y
XZ=XZ+.x*.z
YZ=YZ+.y*.z
X2=X2+.x^2
Y2=Y2+.y^2
EndWith
Nexti
z1=n*XZ-x*z
e=z-Ax-By-C
z=Ax+By+D
a1=n*X2-x^2
b1=n*XY-x*y
z2=n*YZ-y*z
a2=n*XY-x*y
b2=n*Y2-y^2
a=（z1*b2-z2*b1）/（a1*b2-a2*b1）
b=（a1*z2-a2*z1）/（a1*b2-a2*b1）
c=1
d=（z-a*x-b*y）/n
WithPlane
.x=x/（ub-lb+1）
.y=y/（ub-lb+1）
.z=z/（ub-lb+1）
sum（Mi*Ri）/sum（Mi）,Miismass.
here
Miissetedtobe1and.zisjusttheaverageofz
.Ax=-a
.By=-b
.Cz=1
.d=-d
z=Ax+By+D-----Ax+By+Z+D=0
VectorPlane.a=.Ax:
VectorPlane.b=.By:
VectorPlane.c=1
.xAn=Intersect（VectorPlane,xLine）
.yAn=Intersect（VectorPlane,yLine）
.zAn=Intersect（VectorPlane,zLine）
n1.a=.Ax:
n1.b=.By:
n1.c=1
SLine.a=.Ax:
SLine.b=.By:
SLine.c=0
.Angle=Intersect（xLine,SLine）
（xLine.A*SLine.A+xLine.A*SLine.B+xLine.C*SLine.C）
IfSLine.b<
0Then.Angle=360-.Angle
PointToPlanedataRaw（i）,Plane,tmp,0
Ifi=lbThen
MaxF=tmp:
MinF=tmp
Else
IfMaxF<
tmpThenMaxF=tmp
IfMinF>
tmpThenMinF=tmp
EndIf
.MaxFlat=MaxF
.MinFlat=MinF
.Flat=MaxF-MinF
PlaneSet=-1
EndFunction
VectorMulti
求两向量的积,结果存放于参数rtV3中
v1
-tagVector
v2
rtV3
-tagVector
PublicFunctionVectorMulti（v1AstagVector,v2AstagVector,rtv3AstagVector）AsLong
rtV3=v1*v2=|i
j
k
|
|v1.A
v1.B
v1.C|
|v2.A
v2.B
v2.C|
rtv3.A=（v1.B*v2.c-v2.B*v1.C）
i
rtV3.B=-（v1.A*v2.C-v2.A*v1.C）'
j
rtV3.C=（v1.A*v2.B-v2.A*V1.B）
k
rtv3.a=（v1.b*v2.c-v2.b*v1.c）
rtv3.b=-（
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