scvfnormal.hh

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
//
// SPDX-FileCopyrightText: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
// SPDX-License-Identifier: GPL-3.0-or-later
//
#ifndef DUMUX_DISCRETIZATION_SCVF_NORMAL_HH
#define DUMUX_DISCRETIZATION_SCVF_NORMAL_HH
 
#include <dumux/common/math.hh>
#include <dumux/geometry/normal.hh>
 
namespace Dumux::Detail {

template<class ElementGeometry, class CornerStorage>
inline auto scvfUnitNormal(const ElementGeometry& geo, const CornerStorage& corners)
{
    using GlobalPosition = typename ElementGeometry::GlobalCoordinate;
    static constexpr int dim = ElementGeometry::mydimension;
    static constexpr int dimWorld = ElementGeometry::coorddimension;
    static_assert(dim >= 1 && dim <= 3 && dimWorld <= 3);
 
    const auto normalize = [](GlobalPosition n){ n /= n.two_norm(); return n; };
 
    if constexpr (dim == 1)
        return normalize(GlobalPosition(geo.corner(1) - geo.corner(0)));
 
    else if constexpr (dim == 2 && dimWorld == 2)
        return Dumux::unitNormal(GlobalPosition(corners[1] - corners[0]));
 
    else if constexpr (dim == 2 && dimWorld == 3)
    {
        // A segment's two corners do not determine the element plane.
        const auto elementNormal = crossProduct(
            GlobalPosition(geo.corner(1) - geo.corner(0)),
            GlobalPosition(geo.corner(2) - geo.corner(0))
        );
        return normalize(crossProduct(elementNormal, GlobalPosition(corners[1] - corners[0])));
    }
 
    else
    {
        // mean normal of a possibly non-planar quadrilateral (lexicographic corner order):
        // the direction of its vector area
        if (corners.size() == 4)
            return normalize(crossProduct(
                GlobalPosition(corners[3] - corners[0]),
                GlobalPosition(corners[2] - corners[1])
            ));
 
        return normalize(crossProduct(
            GlobalPosition(corners[1] - corners[0]),
            GlobalPosition(corners[2] - corners[0])
        ));
    }
}
 
} // end namespace Dumux::Detail
 
#endif