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Re: Defective Mesh lines in ContourPlot3D

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  • Subject: [mg121129] Re: Defective Mesh lines in ContourPlot3D
  • From: "Alexey Popkov" <lehin.p at>
  • Date: Tue, 30 Aug 2011 06:36:05 -0400 (EDT)
  • Delivered-to:
  • References: <2011829151456.862365@jfultz3winlap>


The option

MeshStyle -> {{GrayLevel[.7], Tube[0.01]}}

solves the problem with overlapped Mesh lines. Now another problem: FrontEnd 
crashes when I add a set of 200 little non-tranparent spheres to the plot. I 
am forced to use Spheres instead of Points primarily because Points are not 
scaled with distance in 3D.
It seems that the crash happens because the number of 3D-objects becomes 
large when Mesh is also rendered as 3D. Crash also happens when I increase 
PlotPoints option:

 x^4 + y^4 + z^4 - (x^2 + y^2 + z^2)^2 + 3 (x^2 + y^2 + z^2) ==
  3, {x, -2, 2}, {y, -2, 2}, {z, -2, 2},
 BoundaryStyle -> Directive[Black, Thickness[.003]],
 ContourStyle ->
  Directive[Orange, Opacity[0.5], Specularity[White, 300]],
 Ticks -> None, PlotPoints -> 60,
 MeshStyle -> {{Glow[GrayLevel[.7]], Black, Tube[0.005]}},
 Lighting -> {{"Directional",
    RGBColor[1, 1, 1], {ImageScaled@{1, 0, 1},
     ImageScaled@{0, 0, 0}}}}]

Is there any workaround for this (I need semi-transparent surface)?

(I use Lenove R500 laptop with 32bit Windows XP SP3 installed and 
Mathematica 7.0.1.)

Thank you for your help,

----- Original Message ----- 
From: "John Fultz" <jfultz at>
To: <lehin.p at>; <mathgroup at>
Sent: Tuesday, August 30, 2011 12:14 AM
Subject: [mg121129] Re: Defective Mesh lines in ContourPlot3D

Version 8 has three rendering methods, controlled by the
RenderingOptions->{"Graphics3DRenderingEngine"} option:

Advantage - very fast
Disadvantage - absolutely unusable with transparency

Advantage - renders everything
Disadvantage - divvies up the polygons into a bazillion sub-polygons, which 
reordered during rotation.  Most of this happens in the CPU, not the GPU. By
far, the slowest rendering method.

Advantage - renders most transparency fine, uses GPU hardware.
Disadvantage - some older video cards don't support it, a few (but rare)
outlying transparent cases don't work well.

V7 only had the first two options.  What you're seeing is a complication
stemming from the facts that:

* There's a great deal of polygonal subdividision
* The mesh is also highly subdivided
* The mesh and the polygons are nearly (or sometimes exactly) coplanar 

In v7, there are two ways out of this.  One is to prevent the BSPTree method
from being used by removing the transparency from the graphic.  The second 
is to
prevent the coplanarity by changing how the mesh is rendered.  There's an
undocumented usage of the MeshStyle option which would do this:

MeshStyle -> {{GrayLevel[.7], Tube[0.01]}}

In v8, the DepthPeeling method does a vastly better job with the transparent
version of the graphic.  And, if your hardware supports it, DepthPeeling is 
Mathematica will use by default.


John Fultz
jfultz at
User Interface Group
Wolfram Research, Inc.

On Mon, 29 Aug 2011 03:46:57 -0400 (EDT), Alexey Popkov wrote:
> Hello,
> I have a problem with rendering of Mesh lines on a 3D surface produced by
> ContourPlot3D in Mathematica 7.0.1:
> p=ContourPlot3D[x^4+y^4+z^4-(x^2+y^2+z^2)^2+3(x^2+y^2+z^2)==3,
> {x, -2,2}, {y, -2, 2}, {z,-2,2},
> BoundaryStyle->Directive[Black,Thickness[.003]],
> ContourStyle->Directive[Orange,Opacity[0.5],Specularity[White,300]],
> PlotPoints->90,Ticks->None,
> MeshStyle->Directive[GrayLevel[.7],Thickness[.001]],
> Lighting->{{"Directional",RGBColor[1,1,1],
> {ImageScaled@{1,0,1},ImageScaled@{0,0,0}}}}];
> p=Graphics[Inset[p,{0,0},Center,{1,1}],
> PlotRange->{{-.5,.5},{-.5,.5}},Frame->True]
> (see screenshot here: )
> Let us to look closer on Mesh lines:
> Show[p, PlotRange -> {{-.16, -.05}, {0, .1}}]
> (see screenshot here: )
> You can see that gray Mesh lines are overlapped by surface-forming
> triangles in many places and even look dashed. Is there a way to avoid
> this?

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