#1251 AddedPointset andGrid.#1090 also proposesTriangularMesh, but with the refactoring seen in#1251, that seemed like a bit of extra work for minimal benefit to the transformations use-case. This PR re-adds triangular meshes.

Overall, the approach of multiple names feels clunky and pushes the concerns of surface families into pointsets.#1251 removed that, and this PR extends this by keepingTriangularMesh focused on the base data structure and movesTriangularMeshFamily logic into aCoordinateFamilyMixin class that permits swapping out coordinates with a.with_name() method (open to bikeshedding). Hence, we would change:

left_surfaces.get_coords(name='pial')

to:

left_surfaces.with_name('pial').get_coords()

It also follows the lead ofGrid and gets rid of the omni-__init__ in favor of targeted factory classmethods.

Notes from previous discussion:

• @oesteban wrote: "As a note, if some time we support other meshes with more than three edges, then n_triangles should be better named n_faces."
  • This was part of early discussions of BIAP9. IIRC the universality of triangular meshes makes them worth special-casing for now. FreeSurfer has old formats that use non-triangular meshes, and both FreeSurfer and we convert them to triangular on load:

    nibabel/nibabel/freesurfer/io.py

    Lines 145 to 168 in590b226

    	ifmagicin (QUAD_MAGIC,NEW_QUAD_MAGIC):# Quad file
    	nvert=_fread3(fobj)
    	nquad=_fread3(fobj)
    	(fmt,div)= ('>i2',100.0)ifmagic==QUAD_MAGICelse ('>f4',1.0)
    	coords=np.fromfile(fobj,fmt,nvert*3).astype(np.float64)/div
    	coords=coords.reshape(-1,3)
    	quads=_fread3_many(fobj,nquad*4)
    	quads=quads.reshape(nquad,4)
    	#
    	# Face splitting follows
    	#
    	faces=np.zeros((2*nquad,3),dtype=int)
    	nface=0
    	forquadinquads:
    	if (quad[0]%2)==0:
    	faces[nface]=quad[0],quad[1],quad[3]
    	nface+=1
    	faces[nface]=quad[2],quad[3],quad[1]
    	nface+=1
    	else:
    	faces[nface]=quad[0],quad[1],quad[2]
    	nface+=1
    	faces[nface]=quad[0],quad[2],quad[3]
    	nface+=1