# Improve appearance of ListPointPlot3D with respect to Plot3D

I solve a PDE of which solution is physically a probability density $p$. Due to the algorithm the result is a $n\times m$-matrix which will be plotted by ListPointPlot3D and colored by a blend like this

f[x_, y_] := Exp[-x^2 - 100 y^2]

ListPointPlot3D[
Transpose[Table[f[x, y], {x, -3, 3, 0.05}, {y, -3, 3, 0.05}]],
ColorFunction -> (Blend[{Green, Yellow, Red}, #3] &),
Filling -> Axis, PlotStyle -> PointSize[0], PlotRange -> Full,
AxesLabel -> {"x", "y", "p"}, DataRange -> {{-3, 3}, {-3, 3}}
]


Let's say that there would be an analytical result, so no discretization is required, then this result could be represented with Plot3D:

Plot3D[f[x, y], {x, -3, 3}, {y, -3, 3},
ColorFunction -> (Blend[{Green, Yellow, Red}, #3] &),
PlotRange -> Full, AxesLabel -> {"x", "y", "p"}, Mesh -> None,
PlotPoints -> 100
]


The appearance of Plot3D is much better. How can i improve the appearance of the ListPointPlot3D so that there are no gaps between the discretized points?

EDIT: ListPlot3D is not an option. Let $m0$ be the data of the solution. E.G.

ListPlot3D[m0, ColorFunction -> (Blend[{Green, Yellow, Red}, #3] &),
Filling -> Axis, PlotRange -> Full, Mesh -> None
]


But an ListLinePlot3D has a much better visual outcome in this case.

ListPointPlot3D[m0,
ColorFunction -> (Blend[{Green, Yellow, Red}, #3] &),
Filling -> Axis, PlotStyle -> PointSize[0], PlotRange -> Full
]


But it is still not perfect. Depending on the ViewPoint (or ViewAngle) one can see gaps or a unsmooth transition.

• Try ListPlot3D. Apr 6 '15 at 20:42
• And PlotPoints-> 100 or the equivalent of increasing the number of $x$ and $y$ points in the iterators. Apr 6 '15 at 21:06

As suggested by @Pickett with minor, cosmetic tweaks:

 f[x_, y_] := Exp[-x^2. - 100. y^2.] + .0000001;

ListPlot3D[
Transpose[
Table[f[x, y], {x, -3, 3, 0.05}, {y, -3, 3, 0.05}]],
ColorFunction -> (Blend[{Green, Yellow, Red}, #3] &),
Filling -> Axis,
PlotStyle -> PointSize[0],
PlotRange -> Full,
AxesLabel -> {"x", "y", "p"},
DataRange -> {{-3, 3}, {-3, 3}},
Mesh -> None]


And you mentioned that your function is a probability density. As such, normalize your function first. Alternatively, notice that your function is a MultinormalDistribution:

 Plot3D[
PDF[MultinormalDistribution[{0, 0}, {{1, 0}, {0, .001}}],
{x, y}],
{x, -3, 3}, {y, -3, 3},
PlotRange -> All]

• In my case, this is not the better solution. I've oversimplified the problem. The matrix is actually a list of $(x,y,p)$-vectors which are on the $(x,y)$-plane dense. You can see an edit to my question. Apr 6 '15 at 23:45
• @Drakonomikon The ListPlot3D[m0, ...] solution looks great in version 10.1. But if the $(x, y, p)$ values obey your explicit Exp[ ] equation, then they do obey a MultinormalDistribution, so why not use such a distribution and avoid all your problems? Apr 6 '15 at 23:49
• Due to a licensing issue we have not received an update. This will take a few weeks. So i'm still using 10.0.1. Does that really make a difference? Apr 6 '15 at 23:52
• The problem is not the Exp[] function. The result of the PDE looks like an exponential-function but it isn't. Using MultinormalDistribution does not change the problem and it is even not possible. Apr 7 '15 at 9:41
• @Drakonomikon Did you post a Multinormal distribution (Exp[-ax^2 - by^2]) and then claim that the function you seek to plot isn't such a distribution? Apr 7 '15 at 15:52