Re: Any way to get gradient lines as well as contour lines?

*To*: mathgroup at smc.vnet.net*Subject*: [mg129672] Re: Any way to get gradient lines as well as contour lines?*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Sun, 3 Feb 2013 20:21:16 -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*: <20130203074823.CADA568AF@smc.vnet.net>

Grad[Sin[x + y^2], {x, y}] {Cos[x + y^2], 2*y*Cos[x + y^2]} Plot3D[Sin[x + y^2], {x, -Pi, Pi}, {y, -2, 2}, MeshFunctions -> { Cos[#1 + #2^2] &, 2 #2 Cos[#1 + #2^2] &}, Mesh -> {10, 20}, PlotPoints -> 35] Bob Hanlon On Sun, Feb 3, 2013 at 2:48 AM, Chris Young <cy56 at comcast.net> wrote: > I'd like to be able to plot "gradient lines", i.e., lines of steepest > descent, on plots of functions of x and y, f(x, y). The contour lines > can be obtained via MeshFunctions, as in > > Plot3D[Sin[x + y^2], {x, -3, 3}, {y, -2, 2}, MeshFunctions -> {#3 &}, > Mesh -> 5]. > > I'd like all the lines at right angles to these contours. > > There must be some way to use the gradient function and then integrate > to the get the gradient lines. > > Maybe this is difficult to do, in general. Also, maybe in general the > "gradient lines" wouldn't be continuous. > > But I wonder if it could be done for some simple examples. > > Any suggestions appreciated. > > Chris Young > cy56 at comcast.net > >

**References**:**Any way to get gradient lines as well as contour lines?***From:*Chris Young <cy56@comcast.net>