Timeline for Support Functions Of 3D Convex Bodies In Spherical Polar Coordinates

4 events

when toggle format	what		by	license	comment
Mar 7, 2013 at 16:39	vote	accept	Ian Calvert
Mar 7, 2013 at 16:10	comment	added	Deane Yang		To be honest, I haven't worked out the details myself, so some trial and error is probably needed. It seems to me easier to use the formulas that give $x$, $y$, and $z$ in terms of $r$, $\theta$, and $\phi$. These can be used to write the function of $\theta$ and $\phi$ in terms of the homogeneous function $x$, $y$, and $z$. If you calculate the Hessian of the function of $\theta$ and $\phi$, you will get a formula that involves the Hessian of the homogeneous function, which you know is positive definite. You use this to try to infer what the corresponding condition is for the first function.
Mar 7, 2013 at 16:06	comment	added	Ian Calvert		Thanks very much for your answer. As you suggest I was considering functions defined on the unit sphere such as h = 0.5 + (1/16)Cos(3Theta) + (1/8)Cos(Phi)Sin(Theta). I understand the extended function idea but I am still unclear that "differentiating twice" gives the simple solution I was, perhaps foolishly, seeking. I do know of the quadratic form tests for convexity of functions at a point in Eggleston's book "Convexity"
Mar 7, 2013 at 13:40	history	answered	Deane Yang	CC BY-SA 3.0