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geometry_utils.hh
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geometry_utils.hh
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/**
* Copyright (©) 2019-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This file is part of Akantu
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*/
/* -------------------------------------------------------------------------- */
#include "aka_common.hh"
#include "fe_engine.hh"
#include "mesh.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_GEOMETRY_UTILS_HH_
#define AKANTU_GEOMETRY_UTILS_HH_
namespace akantu {
class GeometryUtils {
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
static Vector<Real> outsideDirection(const Mesh & mesh,
const Element & element);
/// computes the normal on an element (assuming elements is flat)
template <class Derived>
static Vector<Real> normal(const Mesh & mesh,
const Eigen::MatrixBase<Derived> & coords,
const Element & element, bool outward = true);
// computes normal at given covariant basis
template <class Derived>
static Vector<Real> normal(const Mesh & mesh, const Element & element,
Eigen::MatrixBase<Derived> & tangents,
bool outward = true);
/// computes the orthogonal projection on a set of elements and
/// returns natural projection and normal gap and index of element
template <class Derived1, class Derived2, class Derived3, class Derived4,
class ElementList>
static Element orthogonalProjection(
const Mesh & mesh, const Array<Real> & positions,
const Eigen::MatrixBase<Derived1> & slave, const ElementList & elements,
Real & gap, Eigen::MatrixBase<Derived2> & natural_projection,
Eigen::MatrixBase<Derived3> & normal,
Eigen::MatrixBase<Derived4> & tangent, Real alpha,
Int max_iterations = 100, Real projection_tolerance = 1e-10,
Real extension_tolerance = 1e-5);
/// computes the natural projection on an element
template <class Derived1, class Derived2>
static std::pair<Vector<Real>, Vector<Real>>
naturalProjection(const Eigen::MatrixBase<Derived1> & coords,
const Element & element,
const Eigen::MatrixBase<Derived2> & slave_coords,
Int max_iterations = 100, Real tolerance = 1e-10);
/// computes the real projection on an element
template <class Derived1, class Derived2, class Derived3>
static Vector<Real>
realProjection(const Eigen::MatrixBase<Derived1> & coords,
const Eigen::MatrixBase<Derived2> & slave,
const Eigen::MatrixBase<Derived3> & normal);
/// computes the real projection from a natural coordinate
template <class Derived1, class Derived2>
static Vector<Real>
realProjection(const Eigen::MatrixBase<Derived1> & coords,
const Element & element,
const Eigen::MatrixBase<Derived2> & natural_coord);
/// computes the covariant basis/ local surface basis/ tangents on projection
/// point
template <class Derived1, class Derived2>
static Matrix<Real>
covariantBasis(const Eigen::MatrixBase<Derived1> & coords,
const Element & element,
Eigen::MatrixBase<Derived2> & natural_coord);
/// computes the covariant basis/ local surface basis/ tangents on projection
/// point
template <class Derived1, class Derived2, class Derived3>
static Matrix<Real>
covariantBasis(const Eigen::MatrixBase<Derived1> & coords,
const Element & element,
const Eigen::MatrixBase<Derived2> & normal,
Eigen::MatrixBase<Derived3> & natural_coord);
// computes the curvature on projection
template <class Derived1, class Derived2>
static Matrix<Real>
curvature(const Eigen::MatrixBase<Derived1> & coords, const Element & element,
const Eigen::MatrixBase<Derived2> & natural_coord);
/// computes the contravariant basis on projection point
template <class Derived>
static Matrix<Real>
contravariantBasis(const Eigen::MatrixBase<Derived> & covariant);
/// computes metric tesnor with covariant components
template <class Derived>
static Matrix<Real>
covariantMetricTensor(const Eigen::MatrixBase<Derived> & covariant_bases);
/// computes metric tensor with contravariant components
template <class Derived>
static Matrix<Real>
contravariantMetricTensor(const Eigen::MatrixBase<Derived> & covariant_bases);
// computes curvature tensor with convariant components
template <class Derived1, class Derived2, class Derived3>
static Matrix<Real>
covariantCurvatureTensor(const Eigen::MatrixBase<Derived1> & coords,
const Element & element,
const Eigen::MatrixBase<Derived2> & natural_coord,
const Eigen::MatrixBase<Derived3> & normal);
/// checks if the element is truly a boundary element or not
inline static bool isBoundaryElement(const Mesh & mesh,
const Element & element);
/// checks if the natural projection is valid for not
template <class Derived>
inline static bool
isValidProjection(const Eigen::MatrixBase<Derived> & projection,
Real extension_tolerance = 1e-5);
};
} // namespace akantu
#include "geometry_utils_inline_impl.hh"
#endif /* AKANTU_GEOMETRY_UTILS_HH_ */

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