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/*=========================================================================
Program: Visualization Toolkit
Module: vtkPyramid.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 "vtkPyramid.h"
#include "vtkCellArray.h"
#include "vtkCellData.h"
#include "vtkLine.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include "vtkPointData.h"
#include "vtkIncrementalPointLocator.h"
#include "vtkQuad.h"
#include "vtkTriangle.h"
#include "vtkUnstructuredGrid.h"
vtkStandardNewMacro(vtkPyramid);
static const double VTK_DIVERGED = 1.e6;
//----------------------------------------------------------------------------
//
// Construct the pyramid with five points.
//
vtkPyramid::vtkPyramid()
{
this->Points->SetNumberOfPoints(5);
this->PointIds->SetNumberOfIds(5);
for (int i = 0; i < 5; i++)
{
this->Points->SetPoint(i, 0.0, 0.0, 0.0);
this->PointIds->SetId(i,0);
}
this->Line = vtkLine::New();
this->Triangle = vtkTriangle::New();
this->Quad = vtkQuad::New();
}
//----------------------------------------------------------------------------
vtkPyramid::~vtkPyramid()
{
this->Line->Delete();
this->Triangle->Delete();
this->Quad->Delete();
}
static const int VTK_MAX_ITERATION=10;
static const double VTK_CONVERGED=1.e-03;
//----------------------------------------------------------------------------
int vtkPyramid::EvaluatePosition(double x[3], double closestPoint[3],
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[15];
// set initial position for Newton's method
subId = 0;
pcoords[0] = pcoords[1] = pcoords[2] = 0.5;
params[0] = params[1] = params[2] = 0.3333333;
// enter iteration loop
for (iteration=converged=0; !converged && (iteration < VTK_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<5; 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+5];
tcol[j] += pt[j] * derivs[i+10];
}
}
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_CONVERGED) &&
((fabs(pcoords[1]-params[1])) < VTK_CONVERGED) &&
((fabs(pcoords[2]-params[2])) < VTK_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 pyramid
}
return 1;
}
else
{
double pc[3], w[5];
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 vtkPyramid::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<5; i++)
{
this->Points->GetPoint(i, pt);
for (j=0; j<3; j++)
{
x[j] += pt[j] * weights[i];
}
}
}
//----------------------------------------------------------------------------
// Returns the closest face to the point specified. Closeness is measured
// parametrically.
int vtkPyramid::CellBoundary(int vtkNotUsed(subId), double pcoords[3],
vtkIdList *pts)
{
int i;
// define 6 planes that separate regions
static double normals[6][3] = {
{0.0,-0.5547002,0.8320503}, {0.5547002,0.0,0.8320503}, {0.0,0.5547002,0.8320503},
{-0.5547002,0.0,0.8320503}, {0.70710670,-0.70710670,0.0}, {0.70710670,0.70710670,0.0} };
static double point[3] = {0.5,0.5,0.3333333};
double vals[6];
// evaluate 6 plane equations
for (i=0; i<6; i++)
{
vals[i] = normals[i][0]*(pcoords[0]-point[0]) +
normals[i][1]*(pcoords[1]-point[1]) + normals[i][2]*(pcoords[2]-point[2]);
}
// compare against six planes in parametric space that divide element
// into five pieces (each corresponding to a face).
if ( vals[4] >= 0.0 && vals[5] <= 0.0 && vals[0] >= 0.0 )
{
pts->SetNumberOfIds(3); //triangle face
pts->SetId(0,this->PointIds->GetId(0));
pts->SetId(1,this->PointIds->GetId(1));
pts->SetId(2,this->PointIds->GetId(4));
}
else if ( vals[4] >= 0.0 && vals[5] >= 0.0 && vals[1] >= 0.0 )
{
pts->SetNumberOfIds(3); //triangle face
pts->SetId(0,this->PointIds->GetId(1));
pts->SetId(1,this->PointIds->GetId(2));
pts->SetId(2,this->PointIds->GetId(4));
}
else if ( vals[4] <= 0.0 && vals[5] >= 0.0 && vals[2] >= 0.0 )
{
pts->SetNumberOfIds(3); //triangle face
pts->SetId(0,this->PointIds->GetId(2));
pts->SetId(1,this->PointIds->GetId(3));
pts->SetId(2,this->PointIds->GetId(4));
}
else if ( vals[4] <= 0.0 && vals[5] <= 0.0 && vals[3] >= 0.0 )
{
pts->SetNumberOfIds(3); //triangle face
pts->SetId(0,this->PointIds->GetId(3));
pts->SetId(1,this->PointIds->GetId(0));
pts->SetId(2,this->PointIds->GetId(4));
}
else
{
pts->SetNumberOfIds(4); //quad face
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));
}
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;
}
}
//----------------------------------------------------------------------------
// Marching pyramids (contouring)
//
static int edges[8][2] = { {0,1}, {1,2}, {2,3},
{3,0}, {0,4}, {1,4},
{2,4}, {3,4} };
static int faces[5][4] = { {0,3,2,1}, {0,1,4,-1},
{1,2,4,-1}, {2,3,4,-1}, {3,0,4,-1} };
typedef int EDGE_LIST;
typedef struct {
EDGE_LIST edges[13];
} TRIANGLE_CASES;
static TRIANGLE_CASES triCases[] = {
{{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, //0
{{ 3, 4, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, //1
{{ 5, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, //2
{{ 5, 1, 4, 1, 3, 4, -1, -1, -1, -1, -1, -1, -1}}, //3
{{ 6, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, //4
{{ 3, 4, 0, 6, 2, 1, -1, -1, -1, -1, -1, -1, -1}}, //5
{{ 5, 2, 0, 6, 2, 5, -1, -1, -1, -1, -1, -1, -1}}, //6
{{ 2, 3, 4, 2, 4, 6, 4, 5, 6, -1, -1, -1, -1}}, //7
{{ 2, 7, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, //8
{{ 2, 7, 4, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1}}, //9
{{ 5, 1, 0, 2, 7, 3, -1, -1, -1, -1, -1, -1, -1}}, //10
{{ 5, 7, 4, 1, 7, 5, 2, 7, 1, -1, -1, -1, -1}}, //11
{{ 6, 3, 1, 7, 3, 6, -1, -1, -1, -1, -1, -1, -1}}, //12
{{ 4, 6, 7, 0, 6, 4, 1, 6, 0, -1, -1, -1, -1}}, //13
{{ 7, 5, 6, 3, 5, 7, 0, 5, 3, -1, -1, -1, -1}}, //14
{{ 7, 4, 5, 7, 5, 6, -1, -1, -1, -1, -1, -1, -1}}, //15
{{ 5, 7, 4, 6, 7, 5, -1, -1, -1, -1, -1, -1, -1}}, //16
{{ 0, 5, 3, 5, 6, 3, 6, 7, 3, -1, -1, -1, -1}}, //17
{{ 0, 1, 4, 1, 7, 4, 1, 6, 7, -1, -1, -1, -1}}, //18
{{ 1, 6, 3, 6, 7, 3, -1, -1, -1, -1, -1, -1, -1}}, //19
{{ 7, 5, 4, 7, 1, 5, 7, 2, 1, -1, -1, -1, -1}}, //20
{{ 3, 7, 0, 7, 5, 0, 7, 2, 5, 2, 1, 5, -1}}, //21
{{ 4, 2, 0, 7, 2, 4, -1, -1, -1, -1, -1, -1, -1}}, //22
{{ 7, 2, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, //23
{{ 2, 4, 3, 5, 4, 2, 6, 5, 2, -1, -1, -1, -1}}, //24
{{ 2, 5, 0, 2, 6, 5, -1, -1, -1, -1, -1, -1, -1}}, //25
{{ 6, 1, 0, 4, 6, 0, 3, 6, 4, 3, 2, 6, -1}}, //26
{{ 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, //27
{{ 1, 4, 3, 1, 5, 4, -1, -1, -1, -1, -1, -1, -1}}, //28
{{ 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, //29
{{ 4, 3, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, //30
{{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}} //31
};
//----------------------------------------------------------------------------
void vtkPyramid::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[5] = {1,2,4,8,16};
TRIANGLE_CASES *triCase;
EDGE_LIST *edge;
int i, j, index, *vert, 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 < 5; i++)
{
if (cellScalars->GetComponent(i,0) >= value)
{
index |= CASE_MASK[i];
}
}
triCase = triCases + 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 *vtkPyramid::GetEdgeArray(int edgeId)
{
return edges[edgeId];
}
//----------------------------------------------------------------------------
vtkCell *vtkPyramid::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 *vtkPyramid::GetFaceArray(int faceId)
{
return faces[faceId];
}
//----------------------------------------------------------------------------
vtkCell *vtkPyramid::GetFace(int faceId)
{
int *verts;
verts = faces[faceId];
if ( verts[3] != -1 ) // quad cell
{
// load point id's
this->Quad->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
this->Quad->PointIds->SetId(1,this->PointIds->GetId(verts[1]));
this->Quad->PointIds->SetId(2,this->PointIds->GetId(verts[2]));
this->Quad->PointIds->SetId(3,this->PointIds->GetId(verts[3]));
// load coordinates
this->Quad->Points->SetPoint(0,this->Points->GetPoint(verts[0]));
this->Quad->Points->SetPoint(1,this->Points->GetPoint(verts[1]));
this->Quad->Points->SetPoint(2,this->Points->GetPoint(verts[2]));
this->Quad->Points->SetPoint(3,this->Points->GetPoint(verts[3]));
return this->Quad;
}
else
{
// load point id's
this->Triangle->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
this->Triangle->PointIds->SetId(1,this->PointIds->GetId(verts[1]));
this->Triangle->PointIds->SetId(2,this->PointIds->GetId(verts[2]));
// load coordinates
this->Triangle->Points->SetPoint(0,this->Points->GetPoint(verts[0]));
this->Triangle->Points->SetPoint(1,this->Points->GetPoint(verts[1]));
this->Triangle->Points->SetPoint(2,this->Points->GetPoint(verts[2]));
return this->Triangle;
}
}
//----------------------------------------------------------------------------
// Intersect faces against line.
//
int vtkPyramid::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], dist2, weights[5];
int faceNum;
t = VTK_DOUBLE_MAX;
//first intersect the triangle faces
for (faceNum=1; faceNum<5; faceNum++)
{
this->Points->GetPoint(faces[faceNum][0], pt1);
this->Points->GetPoint(faces[faceNum][1], pt2);
this->Points->GetPoint(faces[faceNum][2], pt3);
this->Triangle->Points->SetPoint(0,pt1);
this->Triangle->Points->SetPoint(1,pt2);
this->Triangle->Points->SetPoint(2,pt3);
if ( this->Triangle->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];
this->EvaluatePosition(x, xTemp, subId, pcoords, dist2, weights);
}
}
}
//now intersect the quad face
this->Points->GetPoint(faces[0][0], pt1);
this->Points->GetPoint(faces[0][1], pt2);
this->Points->GetPoint(faces[0][2], pt3);
this->Points->GetPoint(faces[0][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];
pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 0.0;
}
}
return intersection;
}
//----------------------------------------------------------------------------
int vtkPyramid::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds, vtkPoints *pts)
{
int p[4], i;
ptIds->Reset();
pts->Reset();
// The base of the pyramid must be split into two triangles. There are two
// ways to do this (across either diagonal). Pick the shorter diagonal.
double base_points[4][3];
for (i = 0; i < 4; i++)
{
this->Points->GetPoint(i, base_points[i]);
}
double diagonal1, diagonal2;
diagonal1 = vtkMath::Distance2BetweenPoints(base_points[0], base_points[2]);
diagonal2 = vtkMath::Distance2BetweenPoints(base_points[1], base_points[3]);
if (diagonal1 < diagonal2)
{
for (i=0; i < 4; i++)
{
p[0] = 0; p[1] = 1; p[2] = 2; p[3] = 4;
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
for (i=0; i < 4; i++)
{
p[0] = 0; p[1] = 2; p[2] = 3; p[3] = 4;
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
}
else
{
for (i=0; i < 4; i++)
{
p[0] = 0; p[1] = 1; p[2] = 3; p[3] = 4;
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
for (i=0; i < 4; i++)
{
p[0] = 1; p[1] = 2; p[2] = 3; p[3] = 4;
ptIds->InsertNextId(this->PointIds->GetId(p[i]));
pts->InsertNextPoint(this->Points->GetPoint(p[i]));
}
}
return !(diagonal1 == diagonal2);
}
//----------------------------------------------------------------------------
void vtkPyramid::Derivatives(int vtkNotUsed(subId), double pcoords[3],
double *values, int dim, double *derivs)
{
double *jI[3], j0[3], j1[3], j2[3];
double functionDerivs[15], sum[3], value;
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 < 5; i++) //loop over interp. function derivatives
{
value = values[dim*i + k];
sum[0] += functionDerivs[i] * value;
sum[1] += functionDerivs[5 + i] * value;
sum[2] += functionDerivs[10 + i] * value;
}
for (j=0; j < 3; j++) //loop over derivative directions
{
derivs[3*k + j] = sum[0]*jI[0][j] + sum[1]*jI[1][j] + sum[2]*jI[2][j];
}
}
}
//----------------------------------------------------------------------------
// Compute iso-parametric interpolation functions for pyramid
//
void vtkPyramid::InterpolationFunctions(double pcoords[3], double sf[5])
{
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] = pcoords[2];
}
//----------------------------------------------------------------------------
void vtkPyramid::InterpolationDerivs(double pcoords[3], double derivs[15])
{
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] = 0.0;
// s-derivatives
derivs[5] = -rm*tm;
derivs[6] = -pcoords[0]*tm;
derivs[7] = pcoords[0]*tm;
derivs[8] = rm*tm;
derivs[9] = 0.0;
// t-derivatives
derivs[10] = -rm*sm;
derivs[11] = -pcoords[0]*sm;
derivs[12] = -pcoords[0]*pcoords[1];
derivs[13] = -rm*pcoords[1];
derivs[14] = 1.0;
}
//----------------------------------------------------------------------------
// Given parametric coordinates compute inverse Jacobian transformation
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
// function derivatives. Returns 0 if no inverse exists.
// Note for pyramid: the inverse Jacobian is undefined at the apex.
int vtkPyramid::JacobianInverse(double pcoords[3], double **inverse, double derivs[15])
{
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 < 5; j++ )
{
this->Points->GetPoint(j, x);
for ( i=0; i < 3; i++ )
{
m0[i] += x[i] * derivs[j];
m1[i] += x[i] * derivs[5 + j];
m2[i] += x[i] * derivs[10 + j];
}
}
// now find the inverse
if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
{
#define VTK_MAX_WARNS 3
static int numWarns=0;
if ( numWarns++ < VTK_MAX_WARNS )
{
vtkErrorMacro(<<"Jacobian inverse not found");
vtkErrorMacro(<<"Matrix:" << m[0][0] << " " << m[0][1] << " " << m[0][2]
<< m[1][0] << " " << m[1][1] << " " << m[1][2]
<< m[2][0] << " " << m[2][1] << " " << m[2][2] );
return 0;
}
}
return 1;
}
//----------------------------------------------------------------------------
void vtkPyramid::GetEdgePoints(int edgeId, int* &pts)
{
pts = this->GetEdgeArray(edgeId);
}
//----------------------------------------------------------------------------
void vtkPyramid::GetFacePoints(int faceId, int* &pts)
{
pts = this->GetFaceArray(faceId);
}
static double vtkPyramidCellPCoords[15] = {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};
//----------------------------------------------------------------------------
double *vtkPyramid::GetParametricCoords()
{
return vtkPyramidCellPCoords;
}
//----------------------------------------------------------------------------
void vtkPyramid::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os,indent);
os << indent << "Line:\n";
this->Line->PrintSelf(os,indent.GetNextIndent());
os << indent << "Triangle:\n";
this->Triangle->PrintSelf(os,indent.GetNextIndent());
os << indent << "Quad:\n";
this->Quad->PrintSelf(os,indent.GetNextIndent());
}
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