Re: Color according to concavity

*To*: mathgroup at smc.vnet.net*Subject*: [mg128867] Re: Color according to concavity*From*: "djmpark" <djmpark at comcast.net>*Date*: Sat, 1 Dec 2012 04:34:30 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20121129110446.BF9AD688F@smc.vnet.net> <16863931.66693.1354273348933.JavaMail.root@m06>

Bob Hanlon got the trick by setting ColorFunctionScaling to False. But one thing I notice is that the curve no longer has antialiasing. I don't know if the following qualifies as brute force, but it is rather intuitively simple with Presentations and one obtains better looking curves with antialiasing. << Presentations` f[x_] := x^2 - x^3 + 10 x Draw2D[ {Red, Draw[f[x], {x, -5, 5}, RegionFunction -> (f''[#] > 0 &)], Blue, Draw[f[x], {x, -5, 5}, RegionFunction -> (f''[#] < 0 &)]}, Frame -> True, AspectRatio -> 1/2] For Bob Hanlon's example: g[x_] := Sin[x] Cos[2 x] Draw2D[ {Red, Draw[g[x], {x, -5, 5}, RegionFunction -> (g''[#] > 0 &)], Blue, Draw[g[x], {x, -5, 5}, RegionFunction -> (g''[#] < 0 &)]}, Frame -> True, AspectRatio -> 1/GoldenRatio] Or do it with a Show. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/index.html From: Murray Eisenberg [mailto:murray at math.umass.edu] On Nov 29, 2012, at 6:04 AM, Sergio Miguel Terrazas Porras <sterraza at uacj.mx> wrote: > > I want to plot a function with the color of the parts of the curve according to concavity, say Red when concve down an blue when concave up. > > I can do it by brute force, finding whwn the second derivative is cero, and then finding the sign of it in the different intervals, etc. This for particular examples. > > But, is there a way to use the second derivative as part of a ColorFunction, or something like that? One might think the following would work, but it doesn't. (The color erroneously remains constant after the local minimum.) f[x_] := x^2 - x^3 + 10 x Plot[f[x], {x, -5, 5}, ColorFunction -> Function[{x, y}, If[f''[x] < 0, Red, Blue]] ] --- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2838 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305