How to get a larger triangle when we discretize a sphere?

Question

In order to solve this problem,I want to get larger triangles (Of course less amount). But I don't know how to do this. I have tried MaxCellMeasure and MeshRefinementFunction, but this doesn't work

DiscretizeRegion[Sphere[], MaxCellMeasure -> 10]

and

DiscretizeRegion[Sphere[], 
 MeshRefinementFunction -> Function[{vertices, area}, area > 10]]

Always gives

Any suggestions ?

Think about it: can you cover a sphere with three triangles? — J. M.'s missing motivation, Mar 31 '17 at 05:56
That's an icosahedron (twenty triangles), so still far away from the limit of four. ;) — J. M.'s missing motivation, Mar 31 '17 at 06:00

Dunlop · Accepted Answer · 2017-03-31T06:00:00.770

6

How about the following:

a = BoundaryDiscretizeRegion[Ball[{0, 0, 0}, 1], 
  MaxCellMeasure -> {"Length" -> 3}, PrecisionGoal -> 0.01]

Length determines the size of the triangulation

which gives:

edited Mar 31 '17 at 06:00

answered Mar 31 '17 at 05:56

Dunlop

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Amazing,I don't know we can use MaxCellMeasure like this.. – yode Mar 31 '17 at 05:59
I still haven't figured out how to force it to show an octahedron, much less a tetrahedron. – J. M.'s missing motivation Mar 31 '17 at 05:59
Why not DiscretizeRegion[Sphere[]...] :) – yode Mar 31 '17 at 06:01
1

True ;) i.e. DiscretizeRegion[Sphere[{0, 0, 0}, 1], MaxCellMeasure -> {"Length" -> 3}, PrecisionGoal -> 0.01] would also work – Dunlop Mar 31 '17 at 06:04
1

or DiscretizeRegion[Sphere[], MaxCellMeasure -> 1, PrecisionGoal -> 1] – halmir Mar 31 '17 at 15:14

How to get a larger triangle when we discretize a sphere?

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