matlab程序曲面拟合.docx

1、% Gridfit demo script% This script file is designed to be used in cell mode% from the matlab editor, or best of all, use the publish% to HTML feature from the matlab editor. Older versions% of matlab can copy and paste entire blocks of code into% the Matlab command window.Topographic dataload bluff_

2、data;x=bluff_data(:,1);y=bluff_data(:,2);z=bluff_data(:,3);% Two ravines on a hillside. Scanned from a% topographic map of an area in upstate New York.plot3(x,y,z,.)% Turn the scanned point data into a surfacegx=0:4:264;gy=0:4:400;g=gridfit(x,y,z,gx,gy);figurecolormap(hot(256);surf(gx,gy,g);camlight

3、 right;lighting phong;shading interpline(x,y,z,marker,.,markersize,4,linestyle,none);title Use topographic contours to recreate a surfaceFitting a trigonometric surfaceclearn1 = 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 = 0 0 1 1;x;x;1-x;1-x;

4、y = 0 1 0 1;y;1-y;y;1-y;figureplot(x,y,.)title Data locations in the x-y planez = 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);figuresurf(xi,xi,zgd)colormap(hot(256)camlight rightlighting phongtitle Griddata on trig surface% Note the wing

5、-like artifacts along the edges, due% to the use of a Delaunay triangulation in griddata.zgrid = gridfit(x,y,z,xi,xi);figuresurf(xi,xi,zgrid)colormap(hot(256)camlight rightlighting phongtitle(Gridfit to trig surface)The trig surface with highly different scalings on the x and y axesxs = x/100;xis =

6、xi/100;ys = y*100;yis = xi*100;% griddata has problems with badly scaled dataxg,yg=meshgrid(xis,yis);zgd = griddata(xs,ys,z,xg,yg);figuresurf(xg,yg,zgd)colormap(hot(256)camlight rightlighting phongtitle Serious problems for griddata on badly scaled trig surface% autoscaling on (the default)zgrids =

7、gridfit(xs,ys,z,xis,yis,autoscale,on);% plot the autoscaled resultfiguresurf(xis,yis,zgrids)colormap(hot(256)camlight rightlighting phongtitle Gridfit (automatically scaled) on trig surfaceWarning: Duplicate x-y data points detected: using average of the z values.Fitting the peaks surfaceclearn = 10

8、0;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);figuresurf(xi,xi,zpgd)colormap(jet(256)camlight rightlighting phongtitle Griddata (method = cubic) on peaks surfacefiguresurf(xi,xi,

9、zpgf)colormap(hsv(256)camlight rightlighting phongtitle(Gridfit to peaks surface)Using tiles in gridfit% Users of gridfit who have really huge problems now have% an option. Ill generate a large amount of data,% and hope to model a fairly large grid - 800 x 800. This% would normally require gridfit t

10、o solve a system of% equations with 640,000 unknowns. It would probably be too% large of a problem for my computer, were I to use gridfit% on the full problem. Gridfit allows you to break the problem% into smaller tiles if you choose. In this case each tile% is 120x120, with a 25% (30 element) overl

11、ap between tiles.% Relax, this demo may take a couple of minutes to run!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)shading interpcolormap(jet(256)camlight rightlighting phongtitle Tiled gridfit