最小二乘法平面拟合word精品文档17页Word文档下载推荐.docx
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最小二乘法平面拟合word精品文档17页Word文档下载推荐.docx
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X:
Thedistancefromtheorigintothecentroid,asmeasuredalongthex-axis.
Y:
Thedistancefromtheorigintothecentroid,asmeasuredalongthey-axis.
Z:
Thedistancefromtheorigintothecentroid,asmeasuredalongthez-axis.
IfmeasuredinaCylindricalcoordinatesystem,thecoordinatesoftheplane'
R:
Thedistancefromthez-axisofthecoordinatesystemtothecentroid,asmeasuredwithinaplanewhichcontainsthecentroidandisorthogonaltothez-axisofthecoordinatesystem.
A:
Thedirection,measuredasanangle,betweenareferenceradiusvectorandaradiusvectorthatcontainsthecentroidandisprojectedontothexy-plane.Thereferenceradiusvectormaybeconsideredtobethex-axis.
Theheightfromtheorigintothecentroidinthecylindricalcoordinatesystem,asmeasuredalongthez-axis.
Theotherattributesoftheplanefeatureare:
Angle:
Theanglebetweentheprojectionoftheplane’snormalvectorontothexy-planeandthex-axisofthecurrentcoordinatesystem.
X-angle:
Theanglebetweentheplane’snormalvectorandthex-axisofthecurrentcoordinatesystem.(X-Angle=arccosinek).Thex-angleisapositivenumberbetween0and180degrees.
Y-angle:
Theanglebetweentheplane’snormalvectorandthey-axisofthecurrentcoordinatesystem.(Y-Angle=arccosinel).They-angleisapositivenumberbetween0and180degrees.
Z-angle:
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),sothe
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