ParametricPlot3D, color with function ?

*Subject*: [mg2787] ParametricPlot3D, color with function ?*From*: crobc at epix.net (Christopher R. Carlen)*Date*: Sun, 17 Dec 1995 02:06:43 -0500*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: epix.net

I am finding minima of the function M(x,y,z)=6x-y^2+xz+60 over the constraint x^2+y^2+z^2=36 . I plotted the top half of the sphere as z=Sqrt[36-x^2-y^2] over {x,-6,6}, {y,-6,6} however this clips the surface with a jagged edge wherever (x,y) is not in the domain of z(x,y) . But nonetheless, with this plot I added: Hue[(6x-y^2+x Sqrt[36-x^2-y^2])/100] which allowed me to visualize the value of the function M over the constraining sphere. Question: Can one color a surface in ParametricPlot3D with a function of (x,y,z) or (t,u) , so that that function, such as M above, may be visualized as a color change over the constraint domain which is the surface. I want to use ParametricPlot3D because it allows me to show the entire sphere, which I currently parameterized as: x(t,u)=Sqrt[36-u^2] Cos[t] y(t,u)=Sqrt[36-u^2] Sin[t] z(t,u)=u t=[0,2Pi] I can write M in terms of t and u using the parametrics, but is there a coloring function like Hue[] to which to feed the resulting value ? Is there any other way to do this sort of thing, perhaps through ContourPlot3D or other functions ? _____________________ Christopher R. Carlen crobc at epix.net carlenC at cs.moravian.edu