
Re: Any way to get gradient lines as well as contour lines?
Posted:
Feb 3, 2013 8:19 PM


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@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@comcast.net > >

