/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  dev
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    object      blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

vertices
(
    // (truncated) Cone
    (-1 0 0) (0 -1 0) (1 0 0) (0 1 0)
    (0 -2 2) (2 0 2) (0 2 2) (-2 0 2)

    // (quarter) Torus
    (3 0 0) (4 -1 0) (5 0 0) (4 1 0)
    (6 0 3) (6 -1 2) (6 0 1) (6 1 2)

    // Sphere
    (7 -1 0) (7 1 0) (7 1 2) (7 -1 2)
    (9 -1 0) (9 1 0) (9 1 2) (9 -1 2)
);

blocks
(
    hex (1 0 4 5 2 3 7 6) cone (9 10 11) simpleGrading (1 1 1)
    hex (8 9 10 11 12 13 14 15) torus (6 6 12) simpleGrading (1 1 1)
    hex (16 17 18 19 20 21 22 23) sphere (10 10 10) simpleGrading (1 1 1)
);

// A cone geometry is needed to project the edges to because we twist the block
// through the height of the cone. It would not be needed otherwise.
geometry
{
    cone
    {
        type    triSurface;
        file    "cone.obj";
    }
}

edges
(
    // (truncated) Cone
    arc 0 1 90 (0 0 1)
    arc 1 2 90 (0 0 1)
    arc 2 3 90 (0 0 1)
    arc 3 0 90 (0 0 1)

    arc 4 5 90 (0 0 1)
    arc 5 6 90 (0 0 1)
    arc 6 7 90 (0 0 1)
    arc 7 4 90 (0 0 1)

    project 0 4 (cone)
    project 1 5 (cone)
    project 2 6 (cone)
    project 3 7 (cone)

    // (quarter) Torus
    arc  8  9 90 (0 0 1)
    arc  9 10 90 (0 0 1)
    arc 10 11 90 (0 0 1)
    arc 11  8 90 (0 0 1)

    arc 12 13 90 (1 0 0)
    arc 13 14 90 (1 0 0)
    arc 14 15 90 (1 0 0)
    arc 15 12 90 (1 0 0)

    arc 8 12 90 (0 1 0)
    arc 9 13 90 (0 1 0)
    arc 10 14 90 (0 1 0)
    arc 11 15 90 (0 1 0)

    // Sphere
    arc 16 17 70.52877936550932 (1 0 -1)
    arc 17 18 70.52877936550932 (1 1 0)
    arc 18 19 70.52877936550932 (1 0 1)
    arc 19 16 70.52877936550932 (1 -1 0)

    arc 20 21 70.52877936550932 (1 0 1)
    arc 21 22 70.52877936550932 (1 -1 0)
    arc 22 23 70.52877936550932 (1 0 -1)
    arc 23 20 70.52877936550932 (1 1 0)

    arc 16 20 70.52877936550932 (0 -1 1)
    arc 17 21 70.52877936550932 (0 -1 -1)
    arc 18 22 70.52877936550932 (0 1 -1)
    arc 19 23 70.52877936550932 (0 1 1)
);

faces
(
    // (truncated) Cone. This is exact, and it also appears to be insensitive
    // to the direction of sweeping, which is somewhat surprising given that
    // the block also twists 90 degrees over the height of the cone.
    sweep (0 1 5 4) 1
    sweep (1 2 6 5) 1
    sweep (2 3 7 6) 1
    sweep (3 0 4 7) 1

    // (quarter) Torus. This is exact, but it is also sensitive to the
    // direction of sweeping. If the minor edges are swept (the more intuitive
    // option) then the rotation factor must be 1. If the major edges are swept
    // (the less intuitive option) then the rotation factor must be 0. The
    // swept edges are the first and third edges of the faces listed.
    sweep (8 9 13 12) 1
    sweep (9 10 14 13) 1
    sweep (10 11 15 14) 1
    sweep (11 8 12 15) 1
    // ... or ...
    /*
    sweep (9 13 12 8) 0
    sweep (10 14 13 9) 0
    sweep (11 15 14 10) 0
    sweep (8 12 15 11) 0
    */

    // Sphere. This is not exact. The positions are better than the basic
    // algorithm, but the projection still falls short of the sphere surface.
    // That's because, unlike the other two shapes, the "rows" of points in one
    // of the faces of the sphere are not geometrically similar (i.e., just
    // rotated and scaled). The angle spanned by the arc varies with each row.
    sweep (16 17 18 19) 1
    sweep (16 17 21 20) 1
    sweep (17 18 22 21) 1
    sweep (18 19 23 22) 1
    sweep (19 16 20 23) 1
    sweep (20 21 22 23) 1
);

defaultPatch
{
    name    walls;
    type    wall;
}

boundary
();

// ************************************************************************* //