8
$\begingroup$

I try to mesh a sphere (examplary) in different qualities, using MaxCellMeasure:

DiscretizeRegion[Sphere[], MaxCellMeasure -> #] & /@ {.1, 1, 10}

enter image description here

but result shows no diffenerence.

What could be the reason? Thanks!

Improve this question
$\endgroup$
19
  • 4
    $\begingroup$ You need to shrink AccuracyGoal as well: DiscretizeRegion[Sphere[], MaxCellMeasure -> 0.01, AccuracyGoal -> 0]. $\endgroup$
    – J. M.'s eventual burnout ♦
    Jun 24, 2022 at 14:08
  • 2
    $\begingroup$ @rhemans Astonishing because Volume[Sphere[]]gives Undefined $\endgroup$
    – Ulrich Neumann
    Jun 24, 2022 at 15:11
  • 2
    $\begingroup$ Volume[Ball[]] gives $\frac{4 \pi }{3}$. I think Sphere is surface only just like in 2D where Disk[] has area, but Circle[] doesn't. $\endgroup$
    – Syed
    Jun 24, 2022 at 15:37
  • 1
    $\begingroup$ What @Syed said: Ball[] and Disk[] are "full" regions, while Sphere[] and Circle[] are a dimension less than their embedding dimension. $\endgroup$
    – J. M.'s eventual burnout ♦
    Jun 24, 2022 at 15:38
  • 1
    $\begingroup$ That doesn't change the fact that the default figure for MaxCellMeasure is "Volume" both for Ball and Sphere. $\endgroup$
    – rhermans
    Jun 24, 2022 at 15:40

2 Answers 2

Reset to default
5
$\begingroup$

In this case DiscretizeGraphics does what you want:

DiscretizeGraphics[Sphere[], MaxCellMeasure -> {2 -> #}] & /@ {.01, .1, 1, 10}

enter image description here

Funnily enough the documentation for MaxCellMeasure has an example similar to this question. It doesn't work now either. https://wolfram.com/xid/0dqt848dvp2-ej8ci4

Improve this answer
$\endgroup$
4
  • 1
    $\begingroup$ Thanks, I was wondering too about this example, which doesn't evaluate as indicated. The problem with default of MaxCellMeasure still persists if you change your example to DiscretizeGraphics[Sphere[], MaxCellMeasure -> { #}] & /@ {.01, .1, 1, 10} $\endgroup$
    – Ulrich Neumann
    Jul 4, 2022 at 6:31
  • $\begingroup$ I think the default dimension for MaxCellMeasure is d for a MeshRegion and d-1 for a BoundaryMeshRegion, where d is the embedding dimension. Since Sphere has dimension 2, we need to specify it. $\endgroup$
    – Greg Hurst
    Jul 4, 2022 at 12:27
  • $\begingroup$ Probably yes, remains surprising that DiscretizeGraphics[Sphere[], MaxCellMeasure -> {"Volume"-> .1}] is accepted without error message $\endgroup$
    – Ulrich Neumann
    Jul 4, 2022 at 12:41
  • $\begingroup$ Also surprising the default isn’t the dimension of the region. $\endgroup$
    – Greg Hurst
    Jul 4, 2022 at 12:44
4
+50
$\begingroup$

You could use "SpherePoints" and "ConvexHull" like:

Table[ConvexHullRegion[SpherePoints[i]] // Region , {i, 50, 550, 
  100}]

enter image description here

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.