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geometry_utils.hh
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/**
* @file geometry_utils.hh
*
* @author Mohit Pundir <mohit.pundir@epfl.ch>
*
* @date creation: Wed Oct 02 2019
* @date last modification: Sat Dec 12 2020
*
* @brief class to compute geometry related quantities
*
*
* @section LICENSE
*
* Copyright (©) 2018-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* 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:
/// computes the normal on an element (assuming elements is flat)
static void normal(const Mesh & mesh, const Array<Real> & positions,
const Element & element, Vector<Real> & normal,
bool outward = true);
// computes normal at given covariant basis
static void normal(const Mesh & mesh, const Element & element,
Matrix<Real> & tangents, Vector<Real> & normal,
bool outward = true);
/// computes the orthogonal projection on a set of elements and
/// returns natural projection and normal gap and index of element
static UInt
orthogonalProjection(const Mesh & mesh, const Array<Real> & positions,
const Vector<Real> & slave,
const Array<Element> & elements, Real & gap,
Vector<Real> & natural_projection, Vector<Real> & normal,
Real alpha, UInt max_iterations = 100,
Real tolerance = 1e-10, Real extension_tolerance = 1e-5);
/// computes the orthogonal projection on a set of elements and
/// returns natural projection and normal gap and index of element
static UInt orthogonalProjection(
const Mesh & mesh, const Array<Real> & positions,
const Vector<Real> & slave, const Array<Element> & elements, Real & gap,
Vector<Real> & natural_projection, Vector<Real> & normal,
Matrix<Real> & tangent, Real alpha, UInt max_iterations = 100,
Real tolerance = 1e-10, Real extension_tolerance = 1e-5);
/// computes the natural projection on an element
static void
naturalProjection(const Mesh & mesh, const Array<Real> & positions,
const Element & element, const Vector<Real> & slave_coords,
Vector<Real> & master_coords,
Vector<Real> & natural_projection,
UInt max_iterations = 100, Real tolerance = 1e-10);
/// computes the real projection on an element
static void realProjection(const Mesh & mesh, const Array<Real> & positions,
const Vector<Real> & slave,
const Element & element,
const Vector<Real> & normal,
Vector<Real> & projection);
/// computes the real projection from a natural coordinate
static void realProjection(const Mesh & mesh, const Array<Real> & positions,
const Element & element,
const Vector<Real> & natural_coord,
Vector<Real> & projection);
/// computes the covariant basis/ local surface basis/ tangents on projection
/// point
static void covariantBasis(const Mesh & mesh, const Array<Real> & positions,
const Element & element,
Vector<Real> & natural_coord,
Matrix<Real> & tangents);
/// computes the covariant basis/ local surface basis/ tangents on projection
/// point
static void covariantBasis(const Mesh & mesh, const Array<Real> & positions,
const Element & element,
const Vector<Real> & normal,
Vector<Real> & natural_coord,
Matrix<Real> & tangents);
// computes the curvature on projection
static void curvature(const Mesh & mesh, const Array<Real> & positions,
const Element & element,
const Vector<Real> & natural_coord,
Matrix<Real> & curvature);
/// computes the contravariant basis on projection point
static void contravariantBasis(const Matrix<Real> & covariant,
Matrix<Real> & contravariant);
/// computes metric tesnor with covariant components
static Matrix<Real>
covariantMetricTensor(const Matrix<Real> & /*covariant_bases*/);
/// computes metric tensor with contravariant components
static Matrix<Real>
contravariantMetricTensor(const Matrix<Real> & /*covariant_bases*/);
// computes curvature tensor with convariant components
static Matrix<Real> covariantCurvatureTensor(
const Mesh & /*mesh*/, const Array<Real> & /*positions*/,
const Element & /*element*/, const Vector<Real> & /*natural_coord*/,
const Vector<Real> & /*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
inline static bool isValidProjection(const Vector<Real> & projection,
Real extension_tolerance = 1e-5);
};
} // namespace akantu
#include "geometry_utils_inline_impl.cc"
#endif /* __AKANTU_GEOMETRY_UTILS_HH__ */

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