# Spurious output from SliceDensityPlot3D with CenterCutBox

Bug introduced in 12.2 or earlier, persisting through 13.2.

I am modeling a simple system: the potential from a sphere of charge Q as a function of position. SliceDensityPlot3D with the "CenterCutBox" option almost gives a gorgeous output, and except for the clutter on the right facing surfaces it does exactly what I want: gives a sense of the potential both on the surface and interior to the cube. I have tried different PlotPoints, to no avail.

In the SliceDensityPlot3D documentation under "scope -> surfaces -> Standard boundary surfaces" a table with the three boundary surfaces is provided, and which looks fine in the documentation page (no surprise). When I use the exact same code in my own notebook, I get the same spurious output (!).

As another try, I used a cylinder, however I could not get that to appear smooth and also there is no centercut cylinder.

I am running version 12.2.0.0 on Win 10 pro. Thanks in advance!

a = 5 10^-5;
q1 = 1.602 * 10^-12;
eps0 = 8.85418781 * 10^-12;
qEnclosed1[r_] := If[r < a, (q1 r^3)/a^3, q1];
eField1[r_] := qEnclosed1[r]/(4 \[Pi] r^2 eps0);
potSphereTEMP[r_] = -Integrate[eField1[r], r ];
potInfinity = Limit[potSphereTEMP[r], {r -> \[Infinity]} ];
potSphere[r_] := potSphereTEMP[r] - potInfinity
potSphereCartesian[x_, y_, z_] := potSphere[Sqrt[x^2 + y^2 + z^2]]
SliceDensityPlot3D[
potSphereCartesian[x, y, z], "CenterCutBox" , {x, -3.0 a,
0.0 a}, {y, -1.5 a, 1.5 a}, {z, -1.5 a, 1.5 a},
ColorFunction -> "Rainbow"] (* my plot *)

SliceDensityPlot3D[potSphereCartesian[x, y, z],
Cylinder[{{-3. a, 0., 0.}, {0., 0., 0.}}, a], {x, -3.0 a,
0.0 a}, {y, -1.5 a, 1.5 a}, {z, -1.5 a, 1.5 a},
ColorFunction -> "Rainbow",
Method -> {"CylinderPoints" -> {200,
200}}]  (* another version of my plot *)

Table[SliceDensityPlot3D[Sin[x] + y^2 - z^3,
sl, {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
PlotLabel -> sl], {sl, {"CenterSphere", "CenterCutSphere",
"CenterCutBox"}}]  (* copied direction from documentation *)


• BoundaryStyle -> None. Jun 23, 2023 at 1:23
• This is a confirmed bug. (I mean the output of CenterCutBox. ) Jun 25, 2023 at 6:52

The issue with the Cylinder surface can be fixed using exact numbers:

SliceDensityPlot3D[potSphereCartesian[x, y, z],
Cylinder[{{0, 0, 0}, {-3 a, 0, 0}}, a],
{x, -3 a, 0}, {y, -3/2 a, 3/2 a}, {z, -3/2 a, 3/2 a},
ColorFunction -> "Rainbow",
Method -> {"CylinderPoints" -> {200, 200}}]


The issue with "CenterCutBox" can be fixed using BoundaryStyle -> None (as in this Q/A):

SliceDensityPlot3D[
potSphereCartesian[x, y, z], "CenterCutBox",
{x, -3.0 a, 0.0 a}, {y, -1.5 a, 1.5 a}, {z, -1.5 a, 1.5 a},
BoundaryStyle -> None, ColorFunction -> "Rainbow"]


SliceDensityPlot3D[Sin[x] + y^2 - z^3, "CenterCutBox",
{x, -1, 1}, {y, -1, 1}, {z, -1, 1}, BoundaryStyle -> None]


• This got me going again, @kglr, thanks so much. My only question, really out of curiosity more than necessity, is why I need to add "BoundaryStyle -> None" and that is not included in the docs. May there is a background setting I am not using? Jun 23, 2023 at 14:51
• @JackAdams, I could not find any reference in the docs either. I found by accident (using BoundaryStyle->Green) that those spurious lines are boundary lines.
– kglr
Jun 23, 2023 at 15:41