- The arc will frequently enclose an angle less than 180 degrees.
  For the case, it is possible to define the arc by its endpoints
  and its centre (origin) point. For example,

      arc 0 1 origin (0 0 0);

  When defined in the way, any discrepancy in the arc radius for the
  endpoints is resolved by adjusting the origin to ensure that the
  average radius is satisfied.

  It is also possible to specify a \em flatness factor as a multiplier
  of the radius. For example,

      arc 0 1 origin 1.1 (0 0 0);

ENH: minor code cleanup for block edges

ENH: expose point appending as polyList::concat

- avoid potential ambiguities in naming of mesh faces/edges
  vs. block faces/edges

- additional methods characterizing the number of faces
  (internal, boundary, total) associated with a blockDescriptor

- cellLabel() accessor and checkIndex() methods

- restore demand-driven behaviour of block, cache the calculated cells
  and refactor generation of block boundary faces to improve potential
  reuse.

New functionality contributed by Mattijs Janssens:
  - new edge projection: projectCurve for use with new geometry
    'searchableCurve'
  - new tutorial 'pipe'
  - naming of vertices and blocks (see pipe tutorial). Including back
    substitution for error messages.

For example, to mesh a sphere with a single block the geometry is defined in the
blockMeshDict as a searchableSurface:

    geometry
    {
        sphere
        {
            type searchableSphere;
            centre (0 0 0);
            radius 1;
        }
    }

The vertices, block topology and curved edges are defined in the usual
way, for example

    v 0.5773502;
    mv -0.5773502;

    a 0.7071067;
    ma -0.7071067;

    vertices
    (
        ($mv $mv $mv)
        ( $v $mv $mv)
        ( $v  $v $mv)
        ($mv  $v $mv)
        ($mv $mv  $v)
        ( $v $mv  $v)
        ( $v  $v  $v)
        ($mv  $v  $v)
    );

    blocks
    (
        hex (0 1 2 3 4 5 6 7) (10 10 10) simpleGrading (1 1 1)
    );

    edges
    (
        arc 0 1 (0 $ma $ma)
        arc 2 3 (0 $a $ma)
        arc 6 7 (0 $a $a)
        arc 4 5 (0 $ma $a)

        arc 0 3 ($ma 0 $ma)
        arc 1 2 ($a 0 $ma)
        arc 5 6 ($a 0 $a)
        arc 4 7 ($ma 0 $a)

        arc 0 4 ($ma $ma 0)
        arc 1 5 ($a $ma 0)
        arc 2 6 ($a $a 0)
        arc 3 7 ($ma $a 0)
    );

which will produce a mesh in which the block edges conform to the sphere
but the faces of the block lie somewhere between the original cube and
the spherical surface which is a consequence of the edge-based
transfinite interpolation.

Now the projection of the block faces to the geometry specified above
can also be specified:

    faces
    (
        project (0 4 7 3) sphere
        project (2 6 5 1) sphere
        project (1 5 4 0) sphere
        project (3 7 6 2) sphere
        project (0 3 2 1) sphere
        project (4 5 6 7) sphere
    );

which produces a mesh that actually conforms to the sphere.

See OpenFOAM-dev/tutorials/mesh/blockMesh/sphere

This functionality is experimental and will undergo further development
and generalization in the future to support more complex surfaces,
feature edge specification and extraction etc.  Please get involved if
you would like to see blockMesh become a more flexible block-structured
mesher.

Henry G. Weller, CFD Direct.

This reverts commit c5bea524.

This reverts commit b18f6cc1.

- the blockMesh interface is splineEdge.H, selectable as "spline"

The first tests look fine - it works as expected for the case with
buggy polySpline reported on the forum. Should of course do some more
extensive testing.

The advantages compared to the current B-Spline implementation:

- Doesn't need a matrix solver.
- The coding resembles something that can be found in the literature.
- In contrast to the B-Spline implementation, it is fairly clear what
  is actually going on. I don't even know if the B-Spline are actually
  B-Spline, Beta-Splines or something else.
- Catmull-Rom splines seem to be what all the graphics people have as
  their stable workhorse.

We now have 3 different names for splines in blockMesh:
- "spline" - *new* Catmull-Rom for arbitrary segments.
- "simpleSpline" - B-Spline for a single segment
- "polySpline" - B-Spline for a multiple segments

Assuming the Catmull-Rom splines continue to behave nicely, there is
no reason to keep the other (broken) B-Splines. This would help clean
up the blockMesh interface too.

Placed the older ones under legacy/ for easier identification in the
future.

TODO:
- currently no handling of non-zero end tangents
- could be extended to handle closed loops, which might be useful
  for feature edges from CAD (eg, for the cvm mesher)

- slightly better code isolation, dropped unneed variables, changed
  vector -> point in the appropriate places

- the spline stuff is still horribly broken.
  Needs a complete rewrite or needs to get chucked.

- also sifted through code to find out why polySplineEdge is going wrong

  It doesn't seem to be a virtual/non-virtual issue, but appears to
  be an issue with how BSpline is solving for the new points.

- Unless the points(), cells(), patches() methods are called, the classes
  should know maintain a lightweight representation for as long as possible.

- bugfix: old-code used xferMove() instead of xferCopy() when creating the
  topology mesh - causing const pointField& to break if the code order was
  changed

- relocate blockMesh from src/meshing -> src/mesh