stdellipsoid.zip_matlab 3D

function h=stdellipsoid(data,scale,varargin) % h=stdellipsoid(data,scale,varargin) % -h is the handle of the standard deviation ellipsoid surface object % -data is a nx3 matrix, where n is the number of observations % -scale is the scale factor of the semi-axis lengths measured in standard deviation % -further inputs are the properties set for surface object h % % example: % figure; hold on; % for ii=1:3 % pts=10*ones(100,1)*randn(1,3)+randn(100,1)*ceil(3*rand(1,3)).*randn(100,3); % scatter3(pts(:,1),pts(:,2),pts(:,3),'x'); % h(1)=stdellipsoid(pts,1,'EdgeColor','r','EdgeAlpha',.5,'FaceAlpha',0.2,'FaceColor','r'); % h(2)=stdellipsoid(pts,2,'EdgeColor','g','EdgeAlpha',.5,'FaceAlpha',0.2,'FaceColor','g'); % h(3)=stdellipsoid(pts,3,'EdgeColor','b','EdgeAlpha',.5,'FaceAlpha',0.2,'FaceColor','b'); % h(4)=stdellipsoid(pts,4,'EdgeColor',[.5,.5,.5],'EdgeAlpha',.5,'FaceAlpha',0); % end % axis equal; axis tight; if nargin<2 scale=1; % default scale value is one standard deviation end if nargin<1 %generate data if not given data=10*ones(100,1)*randn(1,3)+randn(100,1)*ceil(3*rand(1,3)).*randn(100,3); end [V,D]=eig(cov(data)); %eigenvectors V, eigenvalues D (diagonal) of the covariance matrix lengths=scale*sqrt(diag(abs(D))); % the square root of the eigenvalues are the standard deviations along the eigenvectors [X,Y,Z]=ellipsoid(0,0,0,lengths(1),lengths(2),lengths(3)); %X,Y,Z is an ellipsoid furface aligned to the axis of base coordinate system tmp=[X(:) Y(:) Z(:)]/V; %aligns the ellipsoid surface data to the covariance matrix eigenvectors mdata=mean(data); %mdata is the center of the data set X(:)=tmp(:,1)+mdata(1); %shifting the surface data towards to the expected value Y(:)=tmp(:,2)+mdata(2); Z(:)=tmp(:,3)+mdata(3); h=surfl(X,Y,Z); % draw the ellipsoid set(h,varargin{:}); % set surface properties