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/*=========================================================================
Program: Visualization Toolkit
Module: vtkHexahedron.cxx
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or http://www.kitware.com/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 notice for more information.
=========================================================================*/
#include "vtkHexahedron.h"
#include "vtkCellArray.h"
#include "vtkCellData.h"
#include "vtkLine.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include "vtkPointData.h"
#include "vtkIncrementalPointLocator.h"
#include "vtkPoints.h"
#include "vtkQuad.h"
vtkStandardNewMacro(vtkHexahedron);
static const double VTK_DIVERGED = 1.e6;
//----------------------------------------------------------------------------
// Construct the hexahedron with eight points.
vtkHexahedron::vtkHexahedron()
{
this->Points->SetNumberOfPoints(8);
this->PointIds->SetNumberOfIds(8);
for (int i = 0; i < 8; i++)
{
this->Points->SetPoint(i, 0.0, 0.0, 0.0);
this->PointIds->SetId(i,0);
}
this->Line = vtkLine::New();
this->Quad = vtkQuad::New();
}
//----------------------------------------------------------------------------
vtkHexahedron::~vtkHexahedron()
{
this->Line->Delete();
this->Quad->Delete();
}
//----------------------------------------------------------------------------
// Method to calculate parametric coordinates in an eight noded
// linear hexahedron element from global coordinates.
//
static const int VTK_HEX_MAX_ITERATION=10;
static const double VTK_HEX_CONVERGED=1.e-03;
int vtkHexahedron::EvaluatePosition(double x[3], double* closestPoint,
int& subId, double pcoords[3],
double& dist2, double *weights)
{
int iteration, converged;
double params[3];
double fcol[3], rcol[3], scol[3], tcol[3];
int i, j;
double d, pt[3];
double derivs[24];
// set initial position for Newton's method
subId = 0;
pcoords[0] = pcoords[1] = pcoords[2] = params[0] = params[1] = params[2]=0.5;
// enter iteration loop
for (iteration=converged=0;
!converged && (iteration < VTK_HEX_MAX_ITERATION); iteration++)
{
// calculate element interpolation functions and derivatives
this->InterpolationFunctions(pcoords, weights);
this->InterpolationDerivs(pcoords, derivs);
// calculate newton functions
for (i=0; i<3; i++)
{
fcol[i] = rcol[i] = scol[i] = tcol[i] = 0.0;
}
for (i=0; i<8; i++)
{
this->Points->GetPoint(i, pt);
for (j=0; j<3; j++)
{
fcol[j] += pt[j] * weights[i];
rcol[j] += pt[j] * derivs[i];
scol[j] += pt[j] * derivs[i+8];
tcol[j] += pt[j] * derivs[i+16];
}
}
for (i=0; i<3; i++)
{
fcol[i] -= x[i];
}
// compute determinants and generate improvements
d=vtkMath::Determinant3x3(rcol,scol,tcol);
if ( fabs(d) < 1.e-20)
{
return -1;
}
pcoords[0] = params[0] - vtkMath::Determinant3x3 (fcol,scol,tcol) / d;
pcoords[1] = params[1] - vtkMath::Determinant3x3 (rcol,fcol,tcol) / d;
pcoords[2] = params[2] - vtkMath::Determinant3x3 (rcol,scol,fcol) / d;
// check for convergence
if ( ((fabs(pcoords[0]-params[0])) < VTK_HEX_CONVERGED) &&
((fabs(pcoords[1]-params[1])) < VTK_HEX_CONVERGED) &&
((fabs(pcoords[2]-params[2])) < VTK_HEX_CONVERGED) )
{
converged = 1;
}
// Test for bad divergence (S.Hirschberg 11.12.2001)
else if ((fabs(pcoords[0]) > VTK_DIVERGED) ||
(fabs(pcoords[1]) > VTK_DIVERGED) ||
(fabs(pcoords[2]) > VTK_DIVERGED))
{
return -1;
}
// if not converged, repeat
else
{
params[0] = pcoords[0];
params[1] = pcoords[1];
params[2] = pcoords[2];
}
}
// if not converged, set the parametric coordinates to arbitrary values
// outside of element
if ( !converged )
{
return -1;
}
this->InterpolationFunctions(pcoords, weights);
if ( pcoords[0] >= -0.001 && pcoords[0] <= 1.001 &&
pcoords[1] >= -0.001 && pcoords[1] <= 1.001 &&
pcoords[2] >= -0.001 && pcoords[2] <= 1.001 )
{
if (closestPoint)
{
closestPoint[0] = x[0]; closestPoint[1] = x[1]; closestPoint[2] = x[2];
dist2 = 0.0; //inside hexahedron
}
return 1;
}
else
{
double pc[3], w[8];
if (closestPoint)
{
for (i=0; i<3; i++) //only approximate, not really true for warped hexa
{
if (pcoords[i] < 0.0)
{
pc[i] = 0.0;
}
else if (pcoords[i] > 1.0)
{
pc[i] = 1.0;
}
else
{
pc[i] = pcoords[i];
}
}
this->EvaluateLocation(subId, pc, closestPoint,
static_cast<double *>(w));
dist2 = vtkMath::Distance2BetweenPoints(closestPoint,x);
}
return 0;
}
}
//----------------------------------------------------------------------------
// Compute iso-parametric interpolation functions
//
void vtkHexahedron::InterpolationFunctions(double pcoords[3], double sf[8])
{
double rm, sm, tm;
rm = 1. - pcoords[0];
sm = 1. - pcoords[1];
tm = 1. - pcoords[2];
sf[0] = rm*sm*tm;
sf[1] = pcoords[0]*sm*tm;
sf[2] = pcoords[0]*pcoords[1]*tm;
sf[3] = rm*pcoords[1]*tm;
sf[4] = rm*sm*pcoords[2];
sf[5] = pcoords[0]*sm*pcoords[2];
sf[6] = pcoords[0]*pcoords[1]*pcoords[2];
sf[7] = rm*pcoords[1]*pcoords[2];
}
//----------------------------------------------------------------------------
void vtkHexahedron::InterpolationDerivs(double pcoords[3], double derivs[24])
{
double rm, sm, tm;
rm = 1. - pcoords[0];
sm = 1. - pcoords[1];
tm = 1. - pcoords[2];
// r-derivatives
derivs[0] = -sm*tm;
derivs[1] = sm*tm;
derivs[2] = pcoords[1]*tm;
derivs[3] = -pcoords[1]*tm;
derivs[4] = -sm*pcoords[2];
derivs[5] = sm*pcoords[2];
derivs[6] = pcoords[1]*pcoords[2];
derivs[7] = -pcoords[1]*pcoords[2];
// s-derivatives
derivs[8] = -rm*tm;
derivs[9] = -pcoords[0]*tm;
derivs[10] = pcoords[0]*tm;
derivs[11] = rm*tm;
derivs[12] = -rm*pcoords[2];
derivs[13] = -pcoords[0]*pcoords[2];
derivs[14] = pcoords[0]*pcoords[2];
derivs[15] = rm*pcoords[2];
// t-derivatives
derivs[16] = -rm*sm;
derivs[17] = -pcoords[0]*sm;
derivs[18] = -pcoords[0]*pcoords[1];
derivs[19] = -rm*pcoords[1];
derivs[20] = rm*sm;
derivs[21] = pcoords[0]*sm;
derivs[22] = pcoords[0]*pcoords[1];
derivs[23] = rm*pcoords[1];
}
//----------------------------------------------------------------------------
void vtkHexahedron::EvaluateLocation(int& vtkNotUsed(subId), double pcoords[3],
double x[3], double *weights)
{
int i, j;
double pt[3];
this->InterpolationFunctions(pcoords, weights);
x[0] = x[1] = x[2] = 0.0;
for (i=0; i<8; i++)
{
this->Points->GetPoint(i, pt);
for (j=0; j<3; j++)
{
x[j] += pt[j] * weights[i];
}
}
}
//----------------------------------------------------------------------------
int vtkHexahedron::CellBoundary(int vtkNotUsed(subId), double pcoords[3],
vtkIdList *pts)
{
double t1=pcoords[0]-pcoords[1];
double t2=1.0-pcoords[0]-pcoords[1];
double t3=pcoords[1]-pcoords[2];
double t4=1.0-pcoords[1]-pcoords[2];
double t5=pcoords[2]-pcoords[0];
double t6=1.0-pcoords[2]-pcoords[0];
pts->SetNumberOfIds(4);
// compare against six planes in parametric space that divide element
// into six pieces.
if ( t3 >= 0.0 && t4 >= 0.0 && t5 < 0.0 && t6 >= 0.0 )
{
pts->SetId(0,this->PointIds->GetId(0));
pts->SetId(1,this->PointIds->GetId(1));
pts->SetId(2,this->PointIds->GetId(2));
pts->SetId(3,this->PointIds->GetId(3));
}
else if ( t1 >= 0.0 && t2 < 0.0 && t5 < 0.0 && t6 < 0.0 )
{
pts->SetId(0,this->PointIds->GetId(1));
pts->SetId(1,this->PointIds->GetId(2));
pts->SetId(2,this->PointIds->GetId(6));
pts->SetId(3,this->PointIds->GetId(5));
}
else if ( t1 >= 0.0 && t2 >= 0.0 && t3 < 0.0 && t4 >= 0.0 )
{
pts->SetId(0,this->PointIds->GetId(0));
pts->SetId(1,this->PointIds->GetId(1));
pts->SetId(2,this->PointIds->GetId(5));
pts->SetId(3,this->PointIds->GetId(4));
}
else if ( t3 < 0.0 && t4 < 0.0 && t5 >= 0.0 && t6 < 0.0 )
{
pts->SetId(0,this->PointIds->GetId(4));
pts->SetId(1,this->PointIds->GetId(5));
pts->SetId(2,this->PointIds->GetId(6));
pts->SetId(3,this->PointIds->GetId(7));
}
else if ( t1 < 0.0 && t2 >= 0.0 && t5 >= 0.0 && t6 >= 0.0 )
{
pts->SetId(0,this->PointIds->GetId(0));
pts->SetId(1,this->PointIds->GetId(4));
pts->SetId(2,this->PointIds->GetId(7));
pts->SetId(3,this->PointIds->GetId(3));
}
else // if ( t1 < 0.0 && t2 < 0.0 && t3 >= 0.0 && t6 < 0.0 )
{
pts->SetId(0,this->PointIds->GetId(2));
pts->SetId(1,this->PointIds->GetId(3));
pts->SetId(2,this->PointIds->GetId(7));
pts->SetId(3,this->PointIds->GetId(6));
}
if ( pcoords[0] < 0.0 || pcoords[0] > 1.0 ||
pcoords[1] < 0.0 || pcoords[1] > 1.0 ||
pcoords[2] < 0.0 || pcoords[2] > 1.0 )
{
return 0;
}
else
{
return 1;
}
}
//----------------------------------------------------------------------------
static int edges[12][2] = { {0,1}, {1,2}, {3,2}, {0,3},
{4,5}, {5,6}, {7,6}, {4,7},
{0,4}, {1,5}, {3,7}, {2,6}};
static int faces[6][4] = { {0,4,7,3}, {1,2,6,5},
{0,1,5,4}, {3,7,6,2},
{0,3,2,1}, {4,5,6,7} };
// Marching cubes case table
//
#include "vtkMarchingCubesCases.h"
void vtkHexahedron::Contour(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator,
vtkCellArray *verts,
vtkCellArray *lines,
vtkCellArray *polys,
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId,
vtkCellData *outCd)
{
static int CASE_MASK[8] = {1,2,4,8,16,32,64,128};
vtkMarchingCubesTriangleCases *triCase;
EDGE_LIST *edge;
int i, j, index, *vert;
int v1, v2, newCellId;
vtkIdType pts[3];
double t, x1[3], x2[3], x[3], deltaScalar;
vtkIdType offset = verts->GetNumberOfCells() + lines->GetNumberOfCells();
// Build the case table
for ( i=0, index = 0; i < 8; i++)
{
if (cellScalars->GetComponent(i,0) >= value)
{
index |= CASE_MASK[i];
}
}
triCase = vtkMarchingCubesTriangleCases::GetCases() + index;
edge = triCase->edges;
for ( ; edge[0] > -1; edge += 3 )
{
for (i=0; i<3; i++) // insert triangle
{
vert = edges[edge[i]];
// calculate a preferred interpolation direction
deltaScalar = (cellScalars->GetComponent(vert[1],0)
- cellScalars->GetComponent(vert[0],0));
if (deltaScalar > 0)
{
v1 = vert[0]; v2 = vert[1];
}
else
{
v1 = vert[1]; v2 = vert[0];
deltaScalar = -deltaScalar;
}
// linear interpolation
t = ( deltaScalar == 0.0 ? 0.0 :
(value - cellScalars->GetComponent(v1,0)) / deltaScalar );
this->Points->GetPoint(v1, x1);
this->Points->GetPoint(v2, x2);
for (j=0; j<3; j++)
{
x[j] = x1[j] + t * (x2[j] - x1[j]);
}
if ( locator->InsertUniquePoint(x, pts[i]) )
{
if ( outPd )
{
vtkIdType p1 = this->PointIds->GetId(v1);
vtkIdType p2 = this->PointIds->GetId(v2);
outPd->InterpolateEdge(inPd,pts[i],p1,p2,t);
}
}
}
// check for degenerate triangle
if ( pts[0] != pts[1] && pts[0] != pts[2] && pts[1] != pts[2] )
{
newCellId = offset + polys->InsertNextCell(3,pts);
outCd->CopyData(inCd,cellId,newCellId);
}
}
}
//----------------------------------------------------------------------------
int *vtkHexahedron::GetEdgeArray(int edgeId)
{
return edges[edgeId];
}
//----------------------------------------------------------------------------
vtkCell *vtkHexahedron::GetEdge(int edgeId)
{
int *verts;
verts = edges[edgeId];
// load point id's
this->Line->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
this->Line->PointIds->SetId(1,this->PointIds->GetId(verts[1]));
// load coordinates
this->Line->Points->SetPoint(0,this->Points->GetPoint(verts[0]));
this->Line->Points->SetPoint(1,this->Points->GetPoint(verts[1]));
return this->Line;
}
//----------------------------------------------------------------------------
int *vtkHexahedron::GetFaceArray(int faceId)
{
return faces[faceId];
}
//----------------------------------------------------------------------------
vtkCell *vtkHexahedron::GetFace(int faceId)
{
int *verts, i;
verts = faces[faceId];
for (i=0; i<4; i++)
{
this->Quad->PointIds->SetId(i,this->PointIds->GetId(verts[i]));
this->Quad->Points->SetPoint(i,this->Points->GetPoint(verts[i]));
}
return this->Quad;
}
//----------------------------------------------------------------------------
//
// Intersect hexa faces against line. Each hexa face is a quadrilateral.
//
int vtkHexahedron::IntersectWithLine(double p1[3], double p2[3], double tol,
double &t, double x[3], double pcoords[3],
int& subId)
{
int intersection=0;
double pt1[3], pt2[3], pt3[3], pt4[3];
double tTemp;
double pc[3], xTemp[3];
int faceNum;
t = VTK_DOUBLE_MAX;
for (faceNum=0; faceNum<6; faceNum++)
{
this->Points->GetPoint(faces[faceNum][0], pt1);
this->Points->GetPoint(faces[faceNum][1], pt2);
this->Points->GetPoint(faces[faceNum][2], pt3);
this->Points->GetPoint(faces[faceNum][3], pt4);
this->Quad->Points->SetPoint(0,pt1);
this->Quad->Points->SetPoint(1,pt2);
this->Quad->Points->SetPoint(2,pt3);
this->Quad->Points->SetPoint(3,pt4);
if ( this->Quad->IntersectWithLine(p1, p2, tol, tTemp, xTemp, pc, subId) )
{
intersection = 1;
if ( tTemp < t )
{
t = tTemp;
x[0] = xTemp[0]; x[1] = xTemp[1]; x[2] = xTemp[2];
switch (faceNum)
{
case 0:
pcoords[0] = 0.0; pcoords[0] = pc[0]; pcoords[1] = 0.0;
break;
case 1:
pcoords[0] = 1.0; pcoords[0] = pc[0]; pcoords[1] = 0.0;
break;
case 2:
pcoords[0] = pc[0]; pcoords[1] = 0.0; pcoords[2] = pc[1];
break;
case 3:
pcoords[0] = pc[0]; pcoords[1] = 1.0; pcoords[2] = pc[1];
break;
case 4:
pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 0.0;
break;
case 5:
pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 1.0;
break;
}
}
}
}
return intersection;
}
//----------------------------------------------------------------------------
int vtkHexahedron::Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts)
{
int p[4], i;
ptIds->Reset();
pts->Reset();
// Create five tetrahedron. Triangulation varies depending upon index. This
// is necessary to insure compatible voxel triangulations.
if ( (index % 2) )
{
p[0] = 0; p[1] = 1; p[2] = 3; p[3] = 4;
for ( i=0; i < 4; i++ )
{
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
p[0] = 1; p[1] = 4; p[2] = 5; p[3] = 6;
for ( i=0; i < 4; i++ )
{
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
p[0] = 1; p[1] = 4; p[2] = 6; p[3] = 3;
for ( i=0; i < 4; i++ )
{
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
p[0] = 1; p[1] = 3; p[2] = 6; p[3] = 2;
for ( i=0; i < 4; i++ )
{
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
p[0] = 3; p[1] = 6; p[2] = 7; p[3] = 4;
for ( i=0; i < 4; i++ )
{
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
}
else
{
p[0] = 2; p[1] = 1; p[2] = 5; p[3] = 0;
for ( i=0; i < 4; i++ )
{
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
p[0] = 0; p[1] = 2; p[2] = 3; p[3] = 7;
for ( i=0; i < 4; i++ )
{
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
p[0] = 2; p[1] = 5; p[2] = 6; p[3] = 7;
for ( i=0; i < 4; i++ )
{
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
p[0] = 0; p[1] = 7; p[2] = 4; p[3] = 5;
for ( i=0; i < 4; i++ )
{
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
p[0] = 0; p[1] = 2; p[2] = 7; p[3] = 5;
for ( i=0; i < 4; i++ )
{
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
}
return 1;
}
//----------------------------------------------------------------------------
// Compute derivatives in x-y-z directions. Use chain rule in combination
// with interpolation function derivatives.
//
void vtkHexahedron::Derivatives(int vtkNotUsed(subId), double pcoords[3],
double *values, int dim, double *derivs)
{
double *jI[3], j0[3], j1[3], j2[3];
double functionDerivs[24], sum[3];
int i, j, k;
// compute inverse Jacobian and interpolation function derivatives
jI[0] = j0; jI[1] = j1; jI[2] = j2;
this->JacobianInverse(pcoords, jI, functionDerivs);
// now compute derivates of values provided
for (k=0; k < dim; k++) //loop over values per vertex
{
sum[0] = sum[1] = sum[2] = 0.0;
for ( i=0; i < 8; i++) //loop over interp. function derivatives
{
sum[0] += functionDerivs[i] * values[dim*i + k];
sum[1] += functionDerivs[8 + i] * values[dim*i + k];
sum[2] += functionDerivs[16 + i] * values[dim*i + k];
}
for (j=0; j < 3; j++) //loop over derivative directions
{
derivs[3*k + j] = sum[0]*jI[j][0] + sum[1]*jI[j][1] + sum[2]*jI[j][2];
}
}
}
//----------------------------------------------------------------------------
// Given parametric coordinates compute inverse Jacobian transformation
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
// function derivatives.
void vtkHexahedron::JacobianInverse(double pcoords[3], double **inverse,
double derivs[24])
{
int i, j;
double *m[3], m0[3], m1[3], m2[3];
double x[3];
// compute interpolation function derivatives
this->InterpolationDerivs(pcoords, derivs);
// create Jacobian matrix
m[0] = m0; m[1] = m1; m[2] = m2;
for (i=0; i < 3; i++) //initialize matrix
{
m0[i] = m1[i] = m2[i] = 0.0;
}
for ( j=0; j < 8; j++ )
{
this->Points->GetPoint(j, x);
for ( i=0; i < 3; i++ )
{
m0[i] += x[i] * derivs[j];
m1[i] += x[i] * derivs[8 + j];
m2[i] += x[i] * derivs[16 + j];
}
}
// now find the inverse
if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
{
vtkErrorMacro(<<"Jacobian inverse not found");
return;
}
}
//----------------------------------------------------------------------------
void vtkHexahedron::GetEdgePoints(int edgeId, int* &pts)
{
pts = this->GetEdgeArray(edgeId);
}
//----------------------------------------------------------------------------
void vtkHexahedron::GetFacePoints(int faceId, int* &pts)
{
pts = this->GetFaceArray(faceId);
}
//----------------------------------------------------------------------------
static double vtkHexahedronCellPCoords[24] = {0.0,0.0,0.0, 1.0,0.0,0.0,
1.0,1.0,0.0, 0.0,1.0,0.0,
0.0,0.0,1.0, 1.0,0.0,1.0,
1.0,1.0,1.0, 0.0,1.0,1.0};
double *vtkHexahedron::GetParametricCoords()
{
return vtkHexahedronCellPCoords;
}
//----------------------------------------------------------------------------
void vtkHexahedron::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os,indent);
os << indent << "Line:\n";
this->Line->PrintSelf(os,indent.GetNextIndent());
os << indent << "Quad:\n";
this->Quad->PrintSelf(os,indent.GetNextIndent());
}