matlab程序曲面拟合.docx

matlab程序曲面拟合.docx

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%Gridfitdemoscript

%Thisscriptfileisdesignedtobeusedincellmode

%fromthematlabeditor,orbestofall,usethepublish

%toHTMLfeaturefromthematlabeditor.Olderversions

%ofmatlabcancopyandpasteentireblocksofcodeinto

%theMatlabcommandwindow.

Topographicdata

loadbluff_data;

x=bluff_data（:

1）;

y=bluff_data（:

2）;

z=bluff_data（:

3）;

%Tworavinesonahillside.Scannedfroma

%topographicmapofanareainupstateNewYork.

plot3（x,y,z,'.'）

%Turnthescannedpointdataintoasurface

gx=0:

4:

264;

gy=0:

4:

400;

g=gridfit（x,y,z,gx,gy）;

figure

colormap（hot（256））;

surf（gx,gy,g）;

camlightright;

lightingphong;

shadinginterp

line（x,y,z,'marker','.','markersize',4,'linestyle','none'）;

title'Usetopographiccontourstorecreateasurface'

Fittingatrigonometricsurface

clear

n1=15;

n2=15;

theta=rand（n1,1）*pi/2;

r=rand（1,n2）;

x=cos（theta）*r;

y=sin（theta）*r;

x=x（:

）;

y=y（:

）;

x=[[0011]';x;x;1-x;1-x];

y=[[0101]';y;1-y;y;1-y];

figure

plot（x,y,'.'）

title'Datalocationsinthex-yplane'

z=sin（4*x+5*y）.*cos（7*（x-y））+exp（x+y）;

xi=linspace（0,1,51）;

[xg,yg]=meshgrid（xi,xi）;

zgd=griddata（x,y,z,xg,yg）;

figure

surf（xi,xi,zgd）

colormap（hot（256））

camlightright

lightingphong

title'Griddataontrigsurface'

%Notethewing-likeartifactsalongtheedges,due

%totheuseofaDelaunaytriangulationingriddata.

zgrid=gridfit（x,y,z,xi,xi）;

figure

surf（xi,xi,zgrid）

colormap（hot（256））

camlightright

lightingphong

title（'Gridfittotrigsurface'）

Thetrigsurfacewithhighlydifferentscalingsonthexandyaxes

xs=x/100;

xis=xi/100;

ys=y*100;

yis=xi*100;

%griddatahasproblemswithbadlyscaleddata

[xg,yg]=meshgrid（xis,yis）;

zgd=griddata（xs,ys,z,xg,yg）;

figure

surf（xg,yg,zgd）

colormap（hot（256））

camlightright

lightingphong

title'Seriousproblemsforgriddataonbadlyscaledtrigsurface'

%autoscalingon（thedefault）

zgrids=gridfit（xs,ys,z,xis,yis,'autoscale','on'）;

%plottheautoscaledresult

figure

surf（xis,yis,zgrids）

colormap（hot（256））

camlightright

lightingphong

title'Gridfit（automaticallyscaled）ontrigsurface'

Warning:

Duplicatex-ydatapointsdetected:

usingaverageofthezvalues.

Fittingthe"peaks"surface

clear

n=100;

x=（rand（n,1）-.5）*6;

y=（rand（n,1）-.5）*6;

z=peaks（x,y）;

xi=linspace（-3,3,101）;

zpgf=gridfit（x,y,z,xi,xi）;

[xg,yg]=meshgrid（xi,xi）;

zpgd=griddata（x,y,z,xg,yg,'cubic'）;

figure

surf（xi,xi,zpgd）

colormap（jet（256））

camlightright

lightingphong

title'Griddata（method==cubic）onpeakssurface'

figure

surf（xi,xi,zpgf）

colormap（hsv（256））

camlightright

lightingphong

title（'Gridfittopeakssurface'）

Usingtilesingridfit

%Usersofgridfitwhohavereallyhugeproblemsnowhave

%anoption.I'llgeneratealargeamountofdata,

%andhopetomodelafairlylargegrid-800x800.This

%wouldnormallyrequiregridfittosolveasystemof

%equationswith640,000unknowns.Itwouldprobablybetoo

%largeofaproblemformycomputer,wereItousegridfit

%onthefullproblem.Gridfitallowsyoutobreaktheproblem

%intosmallertilesifyouchoose.Inthiscaseeachtile

%is120x120,witha25%（30element）overlapbetweentiles.

%Relax,thisdemomaytakeacoupleofminutestorun!

!

!

!

n=100000;

x=rand（n,1）;

y=rand（n,1）;

z=x+y+sin（（x.^2+y.^2）*10）;

xnodes=0:

.00125:

1;

ynodes=xnodes;

[zg,xg,yg]=gridfit（x,y,z,xnodes,ynodes,'tilesize',120,'overlap',0.25）;

surf（xg,yg,zg）

shadinginterp

colormap（jet（256））

camlightright

lightingphong

title'Tiledgridfit'