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/*=========================================================================
Program: Visualization Toolkit
Module: vtkQuadraticLinearWedge.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.
=========================================================================*/
//Thanks to Soeren Gebbert who developed this class and
//integrated it into VTK 5.0.
#include "vtkQuadraticLinearWedge.h"
#include "vtkObjectFactory.h"
#include "vtkDoubleArray.h"
#include "vtkWedge.h"
#include "vtkLine.h"
#include "vtkMath.h"
#include "vtkQuadraticEdge.h"
#include "vtkQuadraticLinearQuad.h"
#include "vtkQuadraticTriangle.h"
#include "vtkPoints.h"
vtkStandardNewMacro (vtkQuadraticLinearWedge);
//----------------------------------------------------------------------------
// Construct the quadratic linear wedge with 12 points
vtkQuadraticLinearWedge::vtkQuadraticLinearWedge ()
{
this->Points->SetNumberOfPoints (12);
this->PointIds->SetNumberOfIds (12);
for (int i = 0; i < 12; i++)
{
this->Points->SetPoint(i, 0.0, 0.0, 0.0);
this->PointIds->SetId(i,0);
}
this->QuadEdge = vtkQuadraticEdge::New ();
this->Edge = vtkLine::New ();
this->Face = vtkQuadraticLinearQuad::New ();
this->TriangleFace = vtkQuadraticTriangle::New ();
this->Wedge = vtkWedge::New ();
this->Scalars = vtkDoubleArray::New ();
this->Scalars->SetNumberOfTuples (6); //num of linear wedge vetices
}
//----------------------------------------------------------------------------
vtkQuadraticLinearWedge::~vtkQuadraticLinearWedge ()
{
this->QuadEdge->Delete ();
this->Edge->Delete ();
this->Face->Delete ();
this->TriangleFace->Delete ();
this->Wedge->Delete ();
this->Scalars->Delete ();
}
//----------------------------------------------------------------------------
// We are using 4 linear wedge
static int LinearWedges[4][6] = {
{0, 6, 8, 3, 9, 11},
{6, 7, 8, 9, 10, 11},
{6, 1, 7, 9, 4, 10},
{8, 7, 2, 11, 10, 5}
};
// We use 2 quadratic triangles and 3 quadratic-linear quads
static int WedgeFaces[5][6] = {
{0, 1, 2, 6, 7, 8}, // first quad triangle
{3, 5, 4, 11, 10, 9}, // second quad triangle
{1, 0, 3, 4, 6, 9}, // 1. quad-linear quad
{2, 1, 4, 5, 7,10}, // 2. quad-linear quad
{0, 2, 5, 3, 8,11} // 3. quad-linear quad
};
// We have 6 quadratic and 3 linear edges
static int WedgeEdges[9][3] = {
{0, 1, 6}, {1, 2, 7}, {2, 0, 8}, // quadratic edges
{3, 4, 9}, {4, 5, 10}, {5, 3, 11},
{0, 3, 0}, {1, 4, 0}, {2, 5, 0} // linear edges
};
//----------------------------------------------------------------------------
int *vtkQuadraticLinearWedge::GetEdgeArray(int edgeId)
{
return WedgeEdges[edgeId];
}
//----------------------------------------------------------------------------
int *vtkQuadraticLinearWedge::GetFaceArray(int faceId)
{
return WedgeFaces[faceId];
}
//----------------------------------------------------------------------------
vtkCell * vtkQuadraticLinearWedge::GetEdge (int edgeId)
{
edgeId = (edgeId < 0 ? 0 : (edgeId > 8 ? 8 : edgeId));
//We have 6 quadratic edges and 3 linear edges
if (edgeId < 6)
{
for (int i = 0; i < 3; i++)
{
this->QuadEdge->PointIds->SetId (i, this->PointIds->GetId (WedgeEdges[edgeId][i]));
this->QuadEdge->Points->SetPoint (i, this->Points->GetPoint (WedgeEdges[edgeId][i]));
}
return this->QuadEdge;
}
else
{
for (int i = 0; i < 2; i++)
{
this->Edge->PointIds->SetId (i, this->PointIds->GetId (WedgeEdges[edgeId][i]));
this->Edge->Points->SetPoint (i, this->Points->GetPoint (WedgeEdges[edgeId][i]));
}
return this->Edge;
}
}
//----------------------------------------------------------------------------
vtkCell * vtkQuadraticLinearWedge::GetFace (int faceId)
{
faceId = (faceId < 0 ? 0 : (faceId > 4 ? 4 : faceId));
// load point id's and coordinates
// be carefull with the last two one:
if (faceId < 2)
{
for (int i = 0; i < 6; i++)
{
this->TriangleFace->PointIds->SetId (i, this->PointIds->GetId (WedgeFaces[faceId][i]));
this->TriangleFace->Points->SetPoint (i, this->Points->GetPoint (WedgeFaces[faceId][i]));
}
return this->TriangleFace;
}
else
{
for (int i = 0; i < 6; i++)
{
this->Face->PointIds->SetId (i, this->PointIds->GetId (WedgeFaces[faceId][i]));
this->Face->Points->SetPoint (i, this->Points->GetPoint (WedgeFaces[faceId][i]));
}
return this->Face;
}
}
//----------------------------------------------------------------------------
static const double VTK_DIVERGED = 1.e6;
static const int VTK_WEDGE_MAX_ITERATION = 30;
static const double VTK_WEDGE_CONVERGED = 1.e-03;
int vtkQuadraticLinearWedge::EvaluatePosition (double *x,
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[3 * 12];
// 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_WEDGE_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 < 12; 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 + 12];
tcol[j] += pt[j] * derivs[i + 24];
}
}
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] - 0.5 * vtkMath::Determinant3x3 (fcol, scol, tcol) / d;
pcoords[1] = params[1] - 0.5 * vtkMath::Determinant3x3 (rcol, fcol, tcol) / d;
pcoords[2] = params[2] - 0.5 * vtkMath::Determinant3x3 (rcol, scol, fcol) / d;
// check for convergence
if (((fabs (pcoords[0] - params[0])) < VTK_WEDGE_CONVERGED) &&
((fabs (pcoords[1] - params[1])) < VTK_WEDGE_CONVERGED) &&
((fabs (pcoords[2] - params[2])) < VTK_WEDGE_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 wedge
}
return 1;
}
else
{
double pc[3], w[12];
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;
}
}
//----------------------------------------------------------------------------
void vtkQuadraticLinearWedge::EvaluateLocation (int &vtkNotUsed (subId),
double pcoords[3], double x[3], double *weights)
{
double pt[3];
this->InterpolationFunctions (pcoords, weights);
x[0] = x[1] = x[2] = 0.0;
for (int i = 0; i < 12; i++)
{
this->Points->GetPoint (i, pt);
for (int j = 0; j < 3; j++)
{
x[j] += pt[j] * weights[i];
}
}
}
//----------------------------------------------------------------------------
int vtkQuadraticLinearWedge::CellBoundary (int subId, double pcoords[3], vtkIdList * pts)
{
return this->Wedge->CellBoundary (subId, pcoords, pts);
}
//----------------------------------------------------------------------------
void vtkQuadraticLinearWedge::Contour (double value,
vtkDataArray * cellScalars,
vtkIncrementalPointLocator * locator,
vtkCellArray * verts,
vtkCellArray * lines,
vtkCellArray * polys,
vtkPointData * inPd,
vtkPointData * outPd, vtkCellData * inCd,
vtkIdType cellId, vtkCellData * outCd)
{
//contour each linear wedge separately
for (int i=0; i<4; i++) //for each wedge
{
for (int j=0; j<6; j++) //for each point of wedge
{
this->Wedge->Points->SetPoint(j,this->Points->GetPoint(LinearWedges[i][j]));
this->Wedge->PointIds->SetId(j,this->PointIds->GetId(LinearWedges[i][j]));
this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearWedges[i][j]));
}
this->Wedge->Contour(value,this->Scalars,locator,verts,lines,polys,
inPd,outPd,inCd,cellId,outCd);
}
}
//----------------------------------------------------------------------------
// Clip this quadratic-linear wedge using scalar value provided. Like contouring,
// except that it cuts the wedge to produce tetrahedra.
void vtkQuadraticLinearWedge::Clip (double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator * locator, vtkCellArray * tets,
vtkPointData * inPd, vtkPointData * outPd,
vtkCellData * inCd, vtkIdType cellId, vtkCellData * outCd, int insideOut)
{
//clip each linear wedge separately
for (int i=0; i<4; i++) //for each wedge
{
for (int j=0; j<6; j++) //for each of the six vertices of the wedge
{
this->Wedge->Points->SetPoint(j,this->Points->GetPoint(LinearWedges[i][j]));
this->Wedge->PointIds->SetId(j,this->PointIds->GetId(LinearWedges[i][j]));
this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearWedges[i][j]));
}
this->Wedge->Clip(value,this->Scalars,locator,tets,inPd,outPd,
inCd,cellId,outCd,insideOut);
}
}
//----------------------------------------------------------------------------
// Line-wedge intersection. Intersection has to occur within [0,1] parametric
// coordinates and with specified tolerance.
int vtkQuadraticLinearWedge::IntersectWithLine (double *p1, double *p2,
double tol, double &t, double *x, double *pcoords, int &subId)
{
int intersection = 0;
double tTemp;
double pc[3], xTemp[3];
int faceNum;
int inter;
t = VTK_DOUBLE_MAX;
for (faceNum = 0; faceNum < 5; faceNum++)
{
// We have 6 nodes on quad-linear face
// and 6 on triangle faces
if (faceNum < 2)
{
for (int i = 0; i < 6; i++)
{
this->TriangleFace->PointIds->SetId (i, this->PointIds->GetId (WedgeFaces[faceNum][i]));
this->TriangleFace->Points->SetPoint (i, this->Points->GetPoint (WedgeFaces[faceNum][i]));
}
inter = this->TriangleFace->IntersectWithLine (p1, p2, tol, tTemp, xTemp, pc, subId);
}
else
{
for (int i = 0; i < 6; i++)
{
this->Face->Points->SetPoint (i, this->Points->GetPoint (WedgeFaces[faceNum][i]));
}
inter = this->Face->IntersectWithLine (p1, p2, tol, tTemp, xTemp, pc, subId);
}
if (inter)
{
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[1] = pc[1];
pcoords[2] = pc[0];
break;
case 1:
pcoords[0] = 1.0;
pcoords[1] = pc[0];
pcoords[2] = pc[1];
break;
case 2:
pcoords[0] = pc[0];
pcoords[1] = 0.0;
pcoords[2] = pc[1];
break;
case 3:
pcoords[0] = pc[1];
pcoords[1] = 1.0;
pcoords[2] = pc[0];
break;
case 4:
pcoords[0] = pc[1];
pcoords[1] = pc[0];
pcoords[2] = 0.0;
break;
case 5:
pcoords[0] = pc[0];
pcoords[1] = pc[1];
pcoords[2] = 1.0;
break;
}
}
}
}
return intersection;
}
//----------------------------------------------------------------------------
int vtkQuadraticLinearWedge::Triangulate (int vtkNotUsed (index),
vtkIdList * ptIds, vtkPoints * pts)
{
pts->Reset ();
ptIds->Reset ();
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 6; j++)
{
ptIds->InsertId (6 * i + j, this->PointIds->GetId (LinearWedges[i][j]));
pts->InsertPoint (6 * i + j, this->Points->GetPoint (LinearWedges[i][j]));
}
}
return 1;
}
//----------------------------------------------------------------------------
// Given parametric coordinates compute inverse Jacobian transformation
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
// function derivatives.
void vtkQuadraticLinearWedge::JacobianInverse (double pcoords[3],
double **inverse, double derivs[36])
{
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 < 12; j++)
{
this->Points->GetPoint (j, x);
for (i = 0; i < 3; i++)
{
m0[i] += x[i] * derivs[j];
m1[i] += x[i] * derivs[12 + j];
m2[i] += x[i] * derivs[24 + j];
}
}
// now find the inverse
if (vtkMath::InvertMatrix (m, inverse, 3) == 0)
{
vtkErrorMacro (<<"Jacobian inverse not found");
return;
}
}
//----------------------------------------------------------------------------
void vtkQuadraticLinearWedge::Derivatives (int vtkNotUsed (subId),
double pcoords[3], double *values, int dim, double *derivs)
{
double *jI[3], j0[3], j1[3], j2[3];
double functionDerivs[3 * 12], 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 < 12; i++) //loop over interp. function derivatives
{
sum[0] += functionDerivs[i] * values[dim * i + k];
sum[1] += functionDerivs[12 + i] * values[dim * i + k];
sum[2] += functionDerivs[24 + 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];
}
}
}
//----------------------------------------------------------------------------
// Compute interpolation functions for the fifteen nodes.
void vtkQuadraticLinearWedge::InterpolationFunctions (double pcoords[3],
double weights[12])
{
// VTK needs parametric coordinates to be between (0,1). Isoparametric
// shape functions are formulated between (-1,1). Here we do a
// coordinate system conversion from (0,1) to (-1,1).
double x = 2*(pcoords[0]- 0.5);
double y = 2*(pcoords[1]- 0.5);
double z = 2*(pcoords[2]- 0.5);
// corners
weights[0] =(x + y) * 0.5 * (x + y + 1.0) * (1 - z) * 0.5;
weights[1] = x * (x + 1.0) * 0.5 * (1 - z) * 0.5;
weights[2] = y * (1.0 + y) * 0.5 * (1 - z) * 0.5;
weights[3] =(x + y) * 0.5 * (x + y + 1.0) * (1 + z) * 0.5;
weights[4] = x * (x + 1.0) * 0.5 * (1 + z) * 0.5;
weights[5] = y * (1.0 + y) * 0.5 * (1 + z) * 0.5;
// midsides of triangles
weights[6] = -(x + 1)*(x + y) * (1 - z) * 0.5;
weights[7] = (x + 1)*(y + 1) * (1 - z) * 0.5;
weights[8] = -(y + 1)*(x + y) * (1 - z) * 0.5;
weights[9] = -(x + 1)*(x + y) * (1 + z) * 0.5;
weights[10]= (x + 1)*(y + 1) * (1 + z) * 0.5;
weights[11]= -(y + 1)*(x + y) * (1 + z) * 0.5;
}
//----------------------------------------------------------------------------
// Derivatives in parametric space.
void vtkQuadraticLinearWedge::InterpolationDerivs (double pcoords[3],
double derivs[36])
{
//VTK needs parametric coordinates to be between (0,1). Isoparametric
//shape functions are formulated between (-1,1). Here we do a
//coordinate system conversion from (0,1) to (-1,1).
double x = 2*(pcoords[0]- 0.5);
double y = 2*(pcoords[1]- 0.5);
double z = 2*(pcoords[2]- 0.5);
//Derivatives in x-direction
// corners
derivs[0] = (2.0 * x + 2.0 * y + 1.0) * 0.5 * (1.0 - z) * 0.5;
derivs[1] = (1.0 + 2.0 * x) * 0.5 * (1.0 - z) * 0.5;
derivs[2] = 0;
derivs[3] = (2.0 * x + 2.0 * y + 1.0) * 0.5 * (1.0 + z) * 0.5;
derivs[4] = (1.0 + 2.0 * x) * 0.5 * (1.0 + z) * 0.5;
derivs[5] = 0;
// midsides of triangles
derivs[6] = -(2.0 * x + y + 1.0) * (1.0 - z) * 0.5;
derivs[7] = (y + 1.0) * (1.0 - z) * 0.5;
derivs[8] = -(y + 1.0) * (1.0 - z) * 0.5;
derivs[9] = -(2.0 * x + y + 1.0) * (1.0 + z) * 0.5;
derivs[10] = (y + 1.0) * (1.0 + z) * 0.5;
derivs[11] =-(y + 1.0) * (1.0 + z) * 0.5;
//Derivatives in y-direction
// corners
derivs[12] = (2.0 * x + 2.0 * y + 1.0) * 0.5 * (1.0 - z) * 0.5;
derivs[13] = 0;
derivs[14] = (1.0 + 2.0 * y) * 0.5 * (1.0 - z) * 0.5;
derivs[15] = (2.0 * x + 2.0 * y + 1.0) * 0.5 * (1.0 + z) * 0.5;
derivs[16] = 0;
derivs[17] = (1.0 + 2.0 * y) * 0.5 * (1.0 + z) * 0.5;
// midsides of triangles
derivs[18] = -(x + 1.0) * (1.0 - z) * 0.5;
derivs[19] = (x + 1.0) * (1.0 - z) * 0.5;
derivs[20] = -(x + 2.0 * y + 1.0) * (1.0 - z) * 0.5;
derivs[21] = -(x + 1.0) * (1.0 + z) * 0.5;
derivs[22] = (x + 1.0) * (1.0 + z) * 0.5;
derivs[23] = -(x + 2.0 * y + 1.0) * (1.0 + z) * 0.5;
//Derivatives in z-direction
// corners
derivs[24] =(x + y) * 0.5 * (x + y + 1.0) * -0.5;
derivs[25] = x * (x + 1.0) * 0.5 * -0.5;
derivs[26] = y * (1.0 + y) * 0.5 * -0.5;
derivs[27] =(x + y) * 0.5 * (x + y + 1.0) * 0.5;
derivs[28] = x * (x + 1.0) * 0.5 * 0.5;
derivs[29] = y * (1.0 + y) * 0.5 * 0.5;
// midsides of triangles
derivs[30] = -(x + 1.0) * (x + y) * -0.5;
derivs[31] = (x + 1.0) * (y + 1.0) * -0.5;
derivs[32] = -(y + 1.0) * (x + y) * -0.5;
derivs[33] = -(x + 1.0) * (x + y) * 0.5;
derivs[34] = (x + 1.0) * (y + 1.0) * 0.5;
derivs[35] = -(y + 1.0) * (x + y) * 0.5;
// we compute derivatives in in [-1; 1] but we need them in [ 0; 1]
for(int i = 0; i < 36; i++)
derivs[i] *= 2;
}
//----------------------------------------------------------------------------
static double vtkQWedgeCellPCoords[36] = {
0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0,
0.5, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.5, 0.0,
0.5, 0.0, 1.0, 0.5, 0.5, 1.0, 0.0, 0.5, 1.0
};
double * vtkQuadraticLinearWedge::GetParametricCoords ()
{
return vtkQWedgeCellPCoords;
}
//----------------------------------------------------------------------------
void vtkQuadraticLinearWedge::PrintSelf (ostream & os, vtkIndent indent)
{
this->Superclass::PrintSelf (os, indent);
os << indent << "Edge:\n";
this->Edge->PrintSelf (os, indent.GetNextIndent ());
os << indent << "TriangleFace:\n";
this->TriangleFace->PrintSelf (os, indent.GetNextIndent ());
os << indent << "Face:\n";
this->Face->PrintSelf (os, indent.GetNextIndent ());
os << indent << "Wedge:\n";
this->Wedge->PrintSelf (os, indent.GetNextIndent ());
os << indent << "Scalars:\n";
this->Scalars->PrintSelf (os, indent.GetNextIndent ());
}