Dear sage community, find below a small interact example of the Weierstrass representation of minimal surfaces. Maybe you find it suited for the sage-interact collection. I constructed it as a visualization example for my differential geometry class.
Best, Tobias ######################################################### Calculates Weierstrass-Enneper parametrization of a minimal surface (see http://en.wikipedia.org/wiki/Weierstrass%E2%80%93Enneper_parameterization) Enter two holomorphic functions f and g. The Weierstrass-Enneper parametrization then consists of a family (parmetrized by the parameter c) of isometric minimal surfaces, i.e. surfaces with zero mean curvature. Via "plotp" and "rng" the plotpoints and plot range of the 3d-plot can be adjusted. The default values correspond to the Enneper surface. Another interesting example is given by $$f=-i/z^2, g=z$$ which corresponds to the heliocid/catenoid family (http://en.wikipedia.org/wiki/Helicoid). For this example one has to play around a little bit with the plot ranges in order to have a reasonable image as the parametrization by real an imaginary parts are not really adapted in this case. ##################################################################################### var('a,b,z') @interact def WeierStrass(f=1, g=z, c=slider([0.05*pi*m for m in range(0,11)],default=0), plotp=slider(range(0,80),default=20) ,rng=slider(range(0,30),default=10)): Psi_1=f/2*(1-g^2) Psi_2=i*f/2*(1+g^2) Psi_3=f*g Phi_1=Psi_1.integrate(z) Phi_2=Psi_2.integrate(z) Phi_3=Psi_3.integrate(z) def FF1(a,b): return real_part(exp(i*c)*Phi_1(z=a+i*b)) def FF2(a,b): return real_part(exp(i*c)*Phi_2(z=a+i*b)) def FF3(a,b): return real_part(exp(i*c)*Phi_3(z=a+i*b)) P=parametric_plot3d([FF1,FF2,FF3],(a,-rng,rng),(b,-rng,rng), plot_points=[plotp,plotp]) P.show() -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
