ConvexHullMesh, setting the options.

Questions
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1

Hi,

I am using ConvexHullMesh, but have problems setting the right options.

pts = {{3.`, 0.95`, 10.07`}, {3.`, -0.61`, 11.63`}, {-1.97`, 0.95`, 
    15.04`}, {-1.97`, -0.61`, 16.6`}, {6.68`, -0.13`, 
    11.15`}, {6.2`, -0.61`, 11.63`}, {-0.99`, -0.13`, 
    18.82`}, {-1.47`, -0.61`, 19.3`}, {5.55`, 3.5`, 7.52`}, {6.68`, 
    3.5`, 7.52`}, {-0.99`, 4.63`, 14.06`}, {-1.97`, 3.65`, 
    15.04`}, {-1.97`, -0.61`, 19.3`}, {5.55`, 4.63`, 7.52`}};

CH = ConvexHullMesh[pts, Axes -> True, 
  Ticks -> {{-5, 0, 5}, {-5, 0, 5}, {0, 10, 20}}, Boxed -> True, 
  AxesLabel -> {y1, y2, y3}, PlotTheme -> "Scientific"]

This does give me a convexhullmesh, as it should. However, I do not know how to:

  • change the axis range, such that they include all the ticks that I stated. For instance, right now y3 does not include 0. Another way to say this: I want the box to be larger. Right now it seems like Mathematica seeks to make the box as small as possible.

  • make sure that the three axis have the same steps (i.e. the length of 1 unit is the same on all three axes).

  • change opacity to 0.5

  • change the color to, say, yellow

In the next step I will use Show to illustrate CH and some points and lines in 3D, so the specified options should remain when I will use CH later in Show.

Thank you very much for your time and consideration!

2

Have you looked at the options for ConvexHullMesh in docs? It does have MeshCellHighlight and MeshCellStyle - and you can look up those in docs too and related functions. Please look too at the rest of options I list below and read carefully examples in docs on them, this will help you a lot in future.

ConvexHullMesh[pts, Axes -> True, FrameTicks -> {{-5, 0, 5}, {-5, 0, 5}, {0, 10, 20}}, 
 Boxed -> True, AxesLabel -> {y1, y2, y3}, PlotTheme -> "Scientific", MeshCellStyle -> 
{{2, All} -> Opacity[0.5, Yellow]}, PlotRangePadding -> 1, SphericalRegion -> True]

sdfewa5r34qt5thrwdfas.gif

3

Thank you so much for your answer, Vitaliy. I did read the examples, but unfortunately could not find a way of solving all the problems in one line. For instance, I did not know about the option PlotRangePadding. So, I solved the problem by first drawing invisible points in a 3d diagram (to set the axes) and then using Show where I first ask to show these points, and then the convexhullmesh.
Once again, thank you!