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/*=========================================================================
Program: Insight Segmentation & Registration Toolkit
Module: itkFEMElement3DC0LinearHexahedron.cxx
Language: C++
Date: $Date$
Version: $Revision$
Copyright (c) Insight Software Consortium. All rights reserved.
See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.
This software is distributed WITHOUT ANY WARRANTY; without even
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE. See the above copyright notices for more information.
=========================================================================*/
// disable debug warnings in MS compiler
#ifdef _MSC_VER
#pragma warning(disable: 4786)
#endif
#include "itkFEMElement3DC0LinearHexahedron.h"
#include "vnl/vnl_math.h"
namespace itk {
namespace fem {
void
Element3DC0LinearHexahedron
::GetIntegrationPointAndWeight(unsigned int i, VectorType& pt, Float& w, unsigned int order) const
{
// FIXME: range checking
// default integration order=2
if (order==0) { order=2; }
pt.set_size(3);
pt[0] = gaussPoint[order][i%order];
pt[1] = gaussPoint[order][(i/order)%order];
pt[2] = gaussPoint[order][(i/(order*order))];
w=gaussWeight[order][i%order]*gaussWeight[order][(i/order)%order]*gaussWeight[order][(i/(order*order))];
}
unsigned int
Element3DC0LinearHexahedron
::GetNumberOfIntegrationPoints(unsigned int order) const
{
// FIXME: range checking
// default integration order=2
if (order==0) { order=2; }
return order*order*order;
}
Element3DC0LinearHexahedron::VectorType
Element3DC0LinearHexahedron
::ShapeFunctions( const VectorType& pt ) const
{
/* Linear hexahedral element has eight shape functions */
VectorType shapeF(8);
/**
* Linear hexahedral element has local coordinates
* (-1,-1,-1), (1,-1,-1), (1,1,-1), (-1,1,-1), (-1,-1,1), (1,-1,1), (1,1,1), (-1,1,1)
*/
/* given local point x=(r,s,t), where -1 <= r,s,t <= 1 and */
/** N_1 = ((1-r) * (1-s) * (1-t)) / 8 */
shapeF[0] = (1 - pt[0]) * (1 - pt[1]) * (1 - pt[2]) * 0.125;
/** N_2 = ((1+r) * (1-s) * (1-t)) / 8 */
shapeF[1] = (1 + pt[0]) * (1 - pt[1]) * (1 - pt[2]) * 0.125;
/** N_3 = ((1+r) * (1+s) * (1-t)) / 8 */
shapeF[2] = (1 + pt[0]) * (1 + pt[1]) * (1 - pt[2]) * 0.125;
/** N_4 = ((1-r) * (1+s) * (1-t)) / 8 */
shapeF[3] = (1 - pt[0]) * (1 + pt[1]) * (1 - pt[2]) * 0.125;
/** N_5 = ((1-r) * (1-s) * (1+t)) / 8 */
shapeF[4] = (1 - pt[0]) * (1 - pt[1]) * (1 + pt[2]) * 0.125;
/** N_6 = ((1+r) * (1-s) * (1+t)) / 8 */
shapeF[5] = (1 + pt[0]) * (1 - pt[1]) * (1 + pt[2]) * 0.125;
/** N_7 = ((1+r) * (1+s) * (1+t)) / 8 */
shapeF[6] = (1 + pt[0]) * (1 + pt[1]) * (1 + pt[2]) * 0.125;
/** N_8 = ((1-r) * (1+s) * (1+t)) / 8 */
shapeF[7] = (1 - pt[0]) * (1 + pt[1]) * (1 + pt[2]) * 0.125;
return shapeF;
}
void
Element3DC0LinearHexahedron
::ShapeFunctionDerivatives( const VectorType& pt, MatrixType& shapeD ) const
{
/** functions at directions r and s. */
shapeD.set_size(3,8);
// d(N_1) / d(r)
shapeD[0][0] = (-1) * (1 - pt[1]) * (1 - pt[2]) * 0.125;
// d(N_1) / d(s)
shapeD[1][0] = (-1) * (1 - pt[0]) * (1 - pt[2]) * 0.125;
// d(N_1) / d(t)
shapeD[2][0] = (-1) * (1 - pt[0]) * (1 - pt[1]) * 0.125;
// d(N_2) / d(r)
shapeD[0][1] = (+1) * (1 - pt[1]) * (1 - pt[2]) * 0.125;
// d(N_2) / d(s)
shapeD[1][1] = (-1) * (1 + pt[0]) * (1 - pt[2]) * 0.125;
// d(N_2) / d(t)
shapeD[2][1] = (-1) * (1 + pt[0]) * (1 - pt[1]) * 0.125;
// d(N_3) / d(r)
shapeD[0][2] = (+1) * (1 + pt[1]) * (1 - pt[2]) * 0.125;
// d(N_3) / d(s)
shapeD[1][2] = (+1) * (1 + pt[0]) * (1 - pt[2]) * 0.125;
// d(N_3) / d(t)
shapeD[2][2] = (-1) * (1 + pt[0]) * (1 + pt[1]) * 0.125;
// d(N_4) / d(r)
shapeD[0][3] = (-1) * (1 + pt[1]) * (1 - pt[2]) * 0.125;
// d(N_4) / d(s)
shapeD[1][3] = (+1) * (1 - pt[0]) * (1 - pt[2]) * 0.125;
// d(N_4) / d(t)
shapeD[2][3] = (-1) * (1 - pt[0]) * (1 + pt[1]) * 0.125;
// d(N_5) / d(r)
shapeD[0][4] = (-1) * (1 - pt[1]) * (1 + pt[2]) * 0.125;
// d(N_5) / d(s)
shapeD[1][4] = (-1) * (1 - pt[0]) * (1 + pt[2]) * 0.125;
// d(N_5) / d(t)
shapeD[2][4] = (+1) * (1 - pt[0]) * (1 - pt[1]) * 0.125;
// d(N_6) / d(r)
shapeD[0][5] = (+1) * (1 - pt[1]) * (1 + pt[2]) * 0.125;
// d(N_6) / d(s)
shapeD[1][5] = (-1) * (1 + pt[0]) * (1 + pt[2]) * 0.125;
// d(N_6) / d(t)
shapeD[2][5] = (+1) * (1 + pt[0]) * (1 - pt[1]) * 0.125;
// d(N_7) / d(r)
shapeD[0][6] = (+1) * (1 + pt[1]) * (1 + pt[2]) * 0.125;
// d(N_7) / d(s)
shapeD[1][6] = (+1) * (1 + pt[0]) * (1 + pt[2]) * 0.125;
// d(N_7) / d(t)
shapeD[2][6] = (+1) * (1 + pt[0]) * (1 + pt[1]) * 0.125;
// d(N_8) / d(r)
shapeD[0][7] = (-1) * (1 + pt[1]) * (1 + pt[2]) * 0.125;
// d(N_8) / d(s)
shapeD[1][7] = (+1) * (1 - pt[0]) * (1 + pt[2]) * 0.125;
// d(N_8) / d(t)
shapeD[2][7] = (+1) * (1 - pt[0]) * (1 + pt[1]) * 0.125;
}
bool
Element3DC0LinearHexahedron
::GetLocalFromGlobalCoordinates( const VectorType& globalPt , VectorType& localPt ) const
{
// Float x1, x2, x3, x4, y1, y2, y3, y4, xce, yce, xb, yb, xcn, ycn,
// A, J1, J2, x0, y0, dx, dy, be, bn, ce, cn;
localPt=globalPt;
localPt.set_size(3);
localPt.fill(0.0);
// FIXME!
// x1 = this->m_node[0]->GetCoordinates()[0]; y1 = this->m_node[0]->GetCoordinates()[1];
// x2 = this->m_node[1]->GetCoordinates()[0]; y2 = this->m_node[1]->GetCoordinates()[1];
// x3 = this->m_node[2]->GetCoordinates()[0]; y3 = this->m_node[2]->GetCoordinates()[1];
// x4 = this->m_node[3]->GetCoordinates()[0]; y4 = this->m_node[3]->GetCoordinates()[1];
// xb = x1 - x2 + x3 - x4;
// yb = y1 - y2 + y3 - y4;
// xce = x1 + x2 - x3 - x4;
// yce = y1 + y2 - y3 - y4;
// xcn = x1 - x2 - x3 + x4;
// ycn = y1 - y2 - y3 + y4;
// A = 0.5 * (((x3 - x1) * (y4 - y2)) - ((x4 - x2) * (y3 - y1)));
// J1 = ((x3 - x4) * (y1 - y2)) - ((x1 - x2) * (y3 - y4));
// J2 = ((x2 - x3) * (y1 - y4)) - ((x1 - x4) * (y2 - y3));
// x0 = 0.25 * (x1 + x2 + x3 + x4);
// y0 = 0.25 * (y1 + y2 + y3 + y4);
// dx = globalPt[0] - x0;
// dy = globalPt[1] - y0;
// be = A - (dx * yb) + (dy * xb);
// bn = -A - (dx * yb) + (dy * xb);
// ce = (dx * yce) - (dy * xce);
// cn = (dx * ycn) - (dy * xcn);
// localPt[0] = (2 * ce) / (-sqrt((be * be) - (2 * J1 * ce)) - be);
// localPt[1] = (2 * cn) / ( vcl_sqrt((bn * bn) + (2 * J2 * cn)) - bn);
// FIXME
bool IsInside=false;
return IsInside;
}
/**
* Draw the element on device context pDC.
*/
#ifdef FEM_BUILD_VISUALIZATION
void
Element3DC0LinearHexahedron
::Draw(CDC* pDC, Solution::ConstPointer sol) const
{
int x1=m_node[0]->GetCoordinates()[0]*DC_Scale;
int y1=m_node[0]->GetCoordinates()[1]*DC_Scale;
int z1=m_node[0]->GetCoordinates()[2]*DC_Scale;
int x2=m_node[1]->GetCoordinates()[0]*DC_Scale;
int y2=m_node[1]->GetCoordinates()[1]*DC_Scale;
int z2=m_node[1]->GetCoordinates()[2]*DC_Scale;
int x3=m_node[2]->GetCoordinates()[0]*DC_Scale;
int y3=m_node[2]->GetCoordinates()[1]*DC_Scale;
int z3=m_node[2]->GetCoordinates()[2]*DC_Scale;
int x4=m_node[3]->GetCoordinates()[0]*DC_Scale;
int y4=m_node[3]->GetCoordinates()[1]*DC_Scale;
int z4=m_node[3]->GetCoordinates()[2]*DC_Scale;
int x5=m_node[4]->GetCoordinates()[0]*DC_Scale;
int y5=m_node[4]->GetCoordinates()[1]*DC_Scale;
int z5=m_node[4]->GetCoordinates()[2]*DC_Scale;
int x6=m_node[5]->GetCoordinates()[0]*DC_Scale;
int y6=m_node[5]->GetCoordinates()[1]*DC_Scale;
int z6=m_node[5]->GetCoordinates()[2]*DC_Scale;
int x7=m_node[6]->GetCoordinates()[0]*DC_Scale;
int y7=m_node[6]->GetCoordinates()[1]*DC_Scale;
int z7=m_node[6]->GetCoordinates()[2]*DC_Scale;
int x8=m_node[7]->GetCoordinates()[0]*DC_Scale;
int y8=m_node[7]->GetCoordinates()[1]*DC_Scale;
int z8=m_node[7]->GetCoordinates()[2]*DC_Scale;
x1 += sol->GetSolutionValue(this->m_node[0]->GetDegreeOfFreedom(0))*DC_Scale;
y1 += sol->GetSolutionValue(this->m_node[0]->GetDegreeOfFreedom(1))*DC_Scale;
z1 += sol->GetSolutionValue(this->m_node[0]->GetDegreeOfFreedom(2))*DC_Scale;
x2 += sol->GetSolutionValue(this->m_node[1]->GetDegreeOfFreedom(0))*DC_Scale;
y2 += sol->GetSolutionValue(this->m_node[1]->GetDegreeOfFreedom(1))*DC_Scale;
z2 += sol->GetSolutionValue(this->m_node[1]->GetDegreeOfFreedom(2))*DC_Scale;
x3 += sol->GetSolutionValue(this->m_node[2]->GetDegreeOfFreedom(0))*DC_Scale;
y3 += sol->GetSolutionValue(this->m_node[2]->GetDegreeOfFreedom(1))*DC_Scale;
z3 += sol->GetSolutionValue(this->m_node[2]->GetDegreeOfFreedom(2))*DC_Scale;
x4 += sol->GetSolutionValue(this->m_node[3]->GetDegreeOfFreedom(0))*DC_Scale;
y4 += sol->GetSolutionValue(this->m_node[3]->GetDegreeOfFreedom(1))*DC_Scale;
z4 += sol->GetSolutionValue(this->m_node[3]->GetDegreeOfFreedom(2))*DC_Scale;
x5 += sol->GetSolutionValue(this->m_node[4]->GetDegreeOfFreedom(0))*DC_Scale;
y5 += sol->GetSolutionValue(this->m_node[4]->GetDegreeOfFreedom(1))*DC_Scale;
z5 += sol->GetSolutionValue(this->m_node[4]->GetDegreeOfFreedom(2))*DC_Scale;
x6 += sol->GetSolutionValue(this->m_node[5]->GetDegreeOfFreedom(0))*DC_Scale;
y6 += sol->GetSolutionValue(this->m_node[5]->GetDegreeOfFreedom(1))*DC_Scale;
z6 += sol->GetSolutionValue(this->m_node[5]->GetDegreeOfFreedom(2))*DC_Scale;
x7 += sol->GetSolutionValue(this->m_node[6]->GetDegreeOfFreedom(0))*DC_Scale;
y7 += sol->GetSolutionValue(this->m_node[6]->GetDegreeOfFreedom(1))*DC_Scale;
z7 += sol->GetSolutionValue(this->m_node[6]->GetDegreeOfFreedom(2))*DC_Scale;
x8 += sol->GetSolutionValue(this->m_node[7]->GetDegreeOfFreedom(0))*DC_Scale;
y8 += sol->GetSolutionValue(this->m_node[7]->GetDegreeOfFreedom(1))*DC_Scale;
z8 += sol->GetSolutionValue(this->m_node[7]->GetDegreeOfFreedom(2))*DC_Scale;
}
#endif
}} // end namespace itk::fem
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