gmTriShape.h

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/************************************************************************
**
** Copyright (C) 2014 by Carlos Augusto Teixera Mendes
** All rights reserved.
**
** This file is part of the "GeMA" software. It's use should respect
** the terms in the license agreement that can be found together 
** with this source code.
** It is provided AS IS, with NO WARRANTY OF ANY KIND, 
** INCLUDING THE WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR 
** A PARTICULAR PURPOSE.
**
************************************************************************/

#ifndef _GEMA_TRI_SHAPE_H_
#define _GEMA_TRI_SHAPE_H_

#include "gmShape.h"


//--------------------------------------------------------------------------------------------------------------------------
//      Tri Elements
//--------------------------------------------------------------------------------------------------------------------------
class GMC_API_EXPORT GmTriShape : public GmShape
{
public:
  // See comments on the base class
  virtual int numNaturalCoord() const { return 3; }

  // See comments on the base class
  virtual int numCartesianCoord() const { return 2; }

  // See comments on the base class
  virtual void naturalCoordLimits(int coord, double* min, double* max) const { Q_UNUSED(coord); *min = 0.0; *max = 1.0; }

  // See comments on the base class
  virtual void naturalCenter(GmVector& coord) const { coord.set_size(3); coord.fill(1/3.0); } // Center = (1/3, 1/3, 1/3) for all triangles

  virtual bool translateEdgePoint(int edge, const GmVector& srcEdgeCoord, GmVector& elementCoord) const;

  // See comments on the base class. Undefined for surface elements.
  virtual bool translateFacePoint(int face, const GmVector& srcFaceCoord, GmVector& elementCoord) const
  {
    Q_UNUSED(face); Q_UNUSED(srcFaceCoord); Q_UNUSED(elementCoord); return false;
  }

  virtual double shapeCartesianPartialsFromPJ(const GmMatrix& P, const GmMatrix& J, GmMatrix& dN, bool transposed = false) const;

  // See comments on the base class
  virtual double scaledJacobianDet(const GmMatrix& J) const { return 0.5 * arma::det(J); }

  // See comments on the base class
  virtual void jacobianAndPartials(const GmVector& ncoord, const GmMatrix& X, GmMatrix& J, GmMatrix& P, bool transposed = false) const
  {
    jacDependentNatCoord(ncoord, X, J, P, transposed);
  }

  // See comments on the base class
  virtual double borderScalingFactor(int border, const GmVector& borderCoord, const GmVector& elementCoord,
                                     const GmMatrix& X, bool transposed = false) const
  {
    return edgeScalingFactor(border, borderCoord, elementCoord, X, transposed);
  }

  // See comments on the base class. Undefined for 2D elements.
  virtual double faceScalingFactor(int border, const GmVector& borderCoord, const GmVector& elementCoord,
                                   const GmMatrix& X, bool transposed = false) const
  {
    Q_UNUSED(border); Q_UNUSED(borderCoord); Q_UNUSED(elementCoord); Q_UNUSED(X); Q_UNUSED(transposed);
    return 0.0;
  }

  // fixedEdgeCoord() is made static since it is "reused" by Int3DTFace shape functions
  static int fixedEdgeCoord(int border);

protected:

  // See comments on the base class. Calls the default algorithm for Tri / Tet elements
  virtual bool gradientBasedCartesianToNatural(const GmVector& coord, const GmMatrix& X, double tol,
                                               int maxIter, double natTol, GmVector& ncoord, bool* inside) const
  {
    return gradientBasedCartesianToNaturalTriTet(coord, X, tol, maxIter, natTol, ncoord, inside);
  }
};

class GMC_API_EXPORT GmTri3Shape: public GmTriShape
{
public:
  // See comments on the base class
  virtual GmCellType elemType() const { return GM_TRI3; }

  // See comments on the base class
  virtual int numFunctions() const { return 3; }

  virtual void nodeNaturalCoord(int node, GmVector& coord) const;

  virtual void shapeValues(const GmVector& ncoord, GmVector& N) const;
  virtual void shapePartials(const GmVector& ncoord, GmMatrix& dN, bool transposed = false) const;

  virtual double edgeScalingFactor(int border, const GmVector& borderCoord, const GmVector& elementCoord, 
                                   const GmMatrix& X, bool transposed = false) const;

protected:
  // See comments on the base class
  virtual bool hasGeometryBasedCartesianToNatural() const { return true; }

  virtual bool geometryBasedCartesianToNatural(const GmVector& coord, const GmMatrix& X, double natTol,
                                               GmVector& ncoord, bool* inside) const;
};

class GMC_API_EXPORT GmTri6Shape: public GmTriShape
{
public:
  // See comments on the base class
  virtual GmCellType elemType() const { return GM_TRI6; }

  // See comments on the base class
  virtual int numFunctions() const { return 6; }

  virtual void nodeNaturalCoord(int node, GmVector& coord) const;

  virtual void shapeValues(const GmVector& ncoord, GmVector& N) const;
  virtual void shapePartials(const GmVector& ncoord, GmMatrix& dN, bool transposed = false) const;

  virtual double edgeScalingFactor(int border, const GmVector& borderCoord, const GmVector& elementCoord, 
                                   const GmMatrix& X, bool transposed = false) const;
};

class GMC_API_EXPORT GmTri3D3Shape : public GmTri3Shape
{
public:
  // See comments on the base class
  virtual GmCellType elemType() const { return GM_TRI3D3; }
  virtual int numCartesianCoord() const { return 3; }

  virtual void jacDependentNatCoord(const GmVector& ncoord, const GmMatrix& X, GmMatrix& J, GmMatrix& P, bool transposed) const;

protected:
  // Implementation of the geometric cartesian to natural method for Tri3 only works with 2D coordinates
  virtual bool hasGeometryBasedCartesianToNatural() const { return false; }

  // See comments on the base class. At the moment we don't have a working version for 3D triangles
  virtual bool gradientBasedCartesianToNatural(const GmVector& coord, const GmMatrix& X, double tol,
                                               int maxIter, double natTol, GmVector& ncoord, bool* inside) const
  {
    Q_UNUSED(coord); Q_UNUSED(X); Q_UNUSED(tol); Q_UNUSED(maxIter); Q_UNUSED(natTol); Q_UNUSED(ncoord); Q_UNUSED(inside);
    return false;
  }
};

class GMC_API_EXPORT GmTri3D6Shape : public GmTri6Shape
{
public:
  // See comments on the base class
  virtual GmCellType elemType() const { return GM_TRI3D6; }
  virtual int numCartesianCoord() const { return 3; }

  virtual void jacDependentNatCoord(const GmVector& ncoord, const GmMatrix& X, GmMatrix& J, GmMatrix& P, bool transposed) const;

protected:
  // See comments on the base class. At the moment we don't have a working version for 3D triangles
  virtual bool gradientBasedCartesianToNatural(const GmVector& coord, const GmMatrix& X, double tol,
                                               int maxIter, double natTol, GmVector& ncoord, bool* inside) const
  {
    Q_UNUSED(coord); Q_UNUSED(X); Q_UNUSED(tol); Q_UNUSED(maxIter); Q_UNUSED(natTol); Q_UNUSED(ncoord); Q_UNUSED(inside);
    return false;
  }
};

#endif