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geometry_utils.hh
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rAKA akantu
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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