moab::Element::SphericalTri Class Reference

Shape function space for linear triangle on sphere, obtained from the canonical linear (affine) functions. It is mapped using gnomonic projection to a plane tangent at the first vertex It works well for edges that are great circle arcs; RLL meshes do not have this property, but HOMME or MPAS meshes do have it. More...

#include <ElemUtil.hpp>

Inheritance diagram for moab::Element::SphericalTri:

Collaboration diagram for moab::Element::SphericalTri:

Public Member Functions
	SphericalTri (const std::vector< CartVect > &vertices)
virtual	~SphericalTri ()
virtual bool	inside_box (const CartVect &pos, double &tol) const
CartVect	ievaluate (const CartVect &x, double tol=1e-6, const CartVect &x0=CartVect(0.0)) const
	Evaluate the inverse map (calculate \(\vec \xi = F^-1($\vec x)\) to given tolerance)
Protected Attributes
CartVect	v1
Matrix3	transf

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Detailed Description

Shape function space for linear triangle on sphere, obtained from the canonical linear (affine) functions. It is mapped using gnomonic projection to a plane tangent at the first vertex It works well for edges that are great circle arcs; RLL meshes do not have this property, but HOMME or MPAS meshes do have it.

Definition at line 382 of file ElemUtil.hpp.

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Constructor & Destructor Documentation

moab::Element::SphericalTri::SphericalTri

(

const std::vector< CartVect > &

vertices

)

Definition at line 553 of file ElemUtil.cpp.

References moab::CartVect::length(), moab::Element::LinearTri::set_vertices(), transf, and v1.

    {
        vertex.resize( vertices.size() );
        vertex = vertices;
        // project the vertices to the plane tangent at first vertex
        v1          = vertex[0];  // member data
        double v1v1 = v1 % v1;    // this is 1, in general, for unit sphere meshes
        for( int j = 1; j < 3; j++ )
        {
            // first, bring all vertices in the gnomonic plane
            //  the new vertex will intersect the plane at vnew
            //   so that (vnew-v1)%v1 is 0 ( vnew is in the tangent plane, i.e. normal to v1 )
            // pos is the old position of the vertex, and it is in general on the sphere
            // vnew = alfa*pos;  (alfa*pos-v1)%v1 = 0  <=> alfa*(pos%v1)=v1%v1 <=> alfa =
            // v1v1/(pos%v1)
            //  <=> vnew = ( v1v1/(pos%v1) )*pos
            CartVect vnew = v1v1 / ( vertex[j] % v1 ) * vertex[j];
            vertex[j]     = vnew;
        }
        // will compute a transf matrix, such that a new point will be transformed with
        // newpos =  transf * (vnew-v1), and it will be a point in the 2d plane
        // the transformation matrix will be oriented in such a way that orientation will be
        // positive
        CartVect vx = vertex[1] - v1;  // this will become Ox axis
        // z axis will be along v1, in such a way that orientation of the quad is positive
        // look at the first 2 edges
        CartVect vz = vx * ( vertex[2] - vertex[1] );
        vz          = vz / vz.length();

        vx = vx / vx.length();

        CartVect vy = vz * vx;
        transf      = Matrix3( vx[0], vx[1], vx[2], vy[0], vy[1], vy[2], vz[0], vz[1], vz[2] );
        vertex[0]   = CartVect( 0. );
        for( int j = 1; j < 3; j++ )
            vertex[j] = transf * ( vertex[j] - v1 );

        LinearTri::set_vertices( vertex );
    }

virtual moab::Element::SphericalTri::~SphericalTri

(

)

[inline, virtual]

Definition at line 386 of file ElemUtil.hpp.

{};

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Member Function Documentation

CartVect moab::Element::SphericalTri::ievaluate	(	const CartVect &	x,
		double	tol = 1e-6,
		const CartVect &	x0 = CartVect( 0.0 )
	)		const [virtual]

Evaluate the inverse map (calculate \(\vec \xi = F^-1($\vec x)\) to given tolerance)

Reimplemented from moab::Element::LinearTri.

Definition at line 593 of file ElemUtil.cpp.

References transf, and v1.

Referenced by moab::Coupler::nat_param(), and test_spherical_tri().

    {
        // project to the plane tangent at first vertex (gnomonic projection)
        double v1v1   = v1 % v1;
        CartVect vnew = v1v1 / ( x % v1 ) * x;  // so that (vnew-v1)%v1 is 0
        vnew          = transf * ( vnew - v1 );
        // det will be positive now
        return LinearTri::ievaluate( vnew );
    }

bool moab::Element::SphericalTri::inside_box	(	const CartVect &	pos,
		double &	tol
	)		const [virtual]

Reimplemented from moab::Element::Map.

Definition at line 603 of file ElemUtil.cpp.

References transf, and v1.

Referenced by test_spherical_tri().

    {
        // project to the plane tangent at first vertex
        // CartVect v1=vertex[0];
        double v1v1   = v1 % v1;
        CartVect vnew = v1v1 / ( pos % v1 ) * pos;  // so that (x-v1)%v1 is 0
        vnew          = transf * ( vnew - v1 );
        return Map::inside_box( vnew, tol );
    }

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Member Data Documentation

Matrix3 moab::Element::SphericalTri::transf [protected]

Definition at line 392 of file ElemUtil.hpp.

Referenced by ievaluate(), inside_box(), and SphericalTri().

CartVect moab::Element::SphericalTri::v1 [protected]

Definition at line 391 of file ElemUtil.hpp.

Referenced by ievaluate(), inside_box(), and SphericalTri().

List of all members.

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The documentation for this class was generated from the following files:

• ElemUtil.hpp
• ElemUtil.cpp