Changing Sqrt{(z-1)(z-2)(z-3)} to coffee mug

*To*: mathgroup at smc.vnet.net*Subject*: [mg82698] Changing Sqrt{(z-1)(z-2)(z-3)} to coffee mug*From*: chuck009 <dmilioto at comcast.com>*Date*: Mon, 29 Oct 2007 05:30:48 -0500 (EST)

I sure would like to see animation of this over the Riemann sphere: Take two Riemann spheres corresponing to the two branches of sqrt showing the two branch cuts on each. Now: open up the branch cuts, stretch them into necks, join the necks, form the double flask, double neck, transform this into a donut, indent the donut into a coffee mug. Would make a nice addition to the Wolfram demonstration project. I can only get as far as using ContourPlot3D with the two holes in the sphere: r2 = ContourPlot3D[x^2 + y^2 + z^2 == 2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, RegionFunction -> Function[{x, y, z}, (x - 0.2)^2 + (y - 0.2)^2 > 0.05 && (x - 0.7)^2 + (y - 0.7)^2 > 0.05], BoundaryStyle -> Directive[Red, Thick], Boxed -> False, Axes -> None] Anyone know of this being done or how one might do this? Thanks, Chuck