Re: How to get plot Exclusions for a numerical function?

*To*: mathgroup at smc.vnet.net*Subject*: [mg102563] Re: How to get plot Exclusions for a numerical function?*From*: antononcube <antononcube at gmail.com>*Date*: Fri, 14 Aug 2009 05:58:52 -0400 (EDT)*References*: <h60ert$pj8$1@smc.vnet.net>

You might find the following code to be useful: (* This defines a numerical function with a discontinuity *) f[x_?NumericQ, y_?NumericQ, z_?NumericQ] := If[x^2 + y^3 - 2 x y + 0.1 > x z, 0, 1]; (* Using NIntegrate to get the sampling points of a global adaptive integrator. The sampling points will be clustered around the discontinuity. *) Clear[c, x, y, z] c = 2; rng = Rescale[Range[1, 2], {-c, c}]; pnts = Reap[ NIntegrate[ f[x, y, z], {x, -c, c}, {y, -c, c}, {z, -c, c} // Evaluate, MinRecursion -> 3, MaxRecursion -> 4, PrecisionGoal -> 4, EvaluationMonitor :> Sow[{x, y, z}, Method -> {GlobalAdaptive, SingularityHandler -> None, Method -> {TrapezoidalRule, Points -> 5}, SymbolicProcessing -> 0}]]][[2, 1]]; // AbsoluteTiming (* Plot the points using small point size. Rotate the plot... *) Graphics3D[{PointSize[0.00051], Point[pnts]}] On Aug 13, 3:20 am, asdf qwerty <bradc355... at yahoo.com> wrote: > I have a complex analytic function that I'm computing numerically, and > it has branch cuts along arbitrary curves that I can't know > beforehand. Does anyone have any ideas on how I can get Exclusions- > like functionality from Plot3D for this case? > > With the allowed form "Exclusions -> {{lhs = rhs, ineqs}, ...}", I > can't think of an easy way to do it numerically... maybe something > like "Exclusions -> {{True, <something clever>}}"? Has anyone tackled > this problem before?