% 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_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 right;lighting phong;shading interpline(x,y,z,'marker','.','markersize',4,'linestyle','none');title 'Use topographic contours to recreate a surface'%% Fitting 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];y = [[0 1 0 1]';y;1-y;y;1-y];figureplot(x,y,'.')title 'Data locations in the x-y plane'%%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);figuresurf(xi,xi,zgd)colormap(hot(256))camlight rightlighting phongtitle 'Griddata on trig surface'% Note the wing-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 = xi/100;ys = y*100;yis = xi*100;% griddata has problems with badly scaled data[xg,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 = 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 surface'%% Fitting the "peaks" surfaceclearn = 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');figuresurf(xi,xi,zpgd)colormap(jet(256))camlight rightlighting phongtitle 'Griddata (method == cubic) on peaks surface'figuresurf(xi,xi,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. I'll generate a large amount of data,% and hope to model a fairly large grid - 800 x 800. This% would normally require gridfit to 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) overlap 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'%%