gusucode.com > demos工具箱matlab源码程序 > demos/xpklein.m
%% Klein Bottle % This example shows how to display a self-intersecting Klein bottle. % % A Klein bottle is a nonorientable surface in four-dimensional space. It % is formed by attaching two Mobius strips along their common boundary. % % Klein bottles cannot be constructed without intersection in % three-dimensional space. % % Thanks to Davide Cervone, University of Minnesota. % Copyright 1984-2014 The MathWorks, Inc. %% Generate The Klein Bottle % Define Klein bottle parameters n = 12; a = .2; % the diameter of the small tube c = .6; % the diameter of the bulb t1 = pi/4 : pi/n : 5*pi/4; % parameter along the tube t2 = 5*pi/4 : pi/n : 9*pi/4; % angle around the tube u = pi/2 : pi/n : 5*pi/2; [X,Z1] = meshgrid(t1,u); [Y,Z2] = meshgrid(t2,u); % The handle len = sqrt(sin(X).^2 + cos(2*X).^2); x1 = c*ones(size(X)).*(cos(X).*sin(X) ... - 0.5*ones(size(X))+a*sin(Z1).*sin(X)./len); y1 = a*c*cos(Z1).*ones(size(X)); z1 = ones(size(X)).*cos(X) + a*c*sin(Z1).*cos(2*X)./len; handleHndl = surf(x1,y1,z1,X); set(handleHndl,'EdgeColor',[.5 .5 .5]); hold on; % The bulb r = sin(Y) .* cos(Y) - (a + 1/2) * ones(size(Y)); x2 = c * sin(Z2) .* r; y2 = - c * cos(Z2) .* r; z2 = ones(size(Y)) .* cos(Y); bulbHndl = surf(x2,y2,z2,Y); set(bulbHndl,'EdgeColor',[.5 .5 .5]) colormap(hsv); axis vis3d view(-37,30); axis off light('Position',[2 -4 5]) light hold off %% Half of The Bottle shading interp c = X; [row, col] = size(c); c(1:floor(row/2),:) = NaN*ones(floor(row/2),col); set(handleHndl,'CData',c); c = Y; [row, col] = size(c); c(1:floor(row/2),:) = NaN*ones(floor(row/2),col); set(bulbHndl,'CData',c); set([handleHndl bulbHndl],'FaceAlpha',1); %% Transparent Bottle shading faceted; set(handleHndl,'CData',X); set(bulbHndl,'CData',Y); set([handleHndl bulbHndl], ... 'EdgeColor',[.5 .5 .5], ... 'FaceAlpha',.5);