Coarse mesh of a sphere

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

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


but result shows no diffenerence.

What could be the reason? Thanks!

• You need to shrink AccuracyGoal as well: DiscretizeRegion[Sphere[], MaxCellMeasure -> 0.01, AccuracyGoal -> 0]. Jun 24 at 14:08
• @rhemans Astonishing because Volume[Sphere[]]gives Undefined Jun 24 at 15:11
• 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.
– Syed
Jun 24 at 15:37
• What @Syed said: Ball[] and Disk[] are "full" regions, while Sphere[] and Circle[] are a dimension less than their embedding dimension. Jun 24 at 15:38
• That doesn't change the fact that the default figure for MaxCellMeasure  is "Volume" both for Ball and Sphere. Jun 24 at 15:40

In this case DiscretizeGraphics does what you want:

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


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

• 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} Jul 4 at 6:31
• 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. Jul 4 at 12:27
• Probably yes, remains surprising that DiscretizeGraphics[Sphere[], MaxCellMeasure -> {"Volume"-> .1}] is accepted without error message Jul 4 at 12:41
• Also surprising the default isn’t the dimension of the region. Jul 4 at 12:44

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

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