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/*=========================================================================
Program: Visualization Toolkit
Module: vtkPentagonalPrism.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.
=========================================================================*/
//.SECTION Thanks
// Thanks to Philippe Guerville who developed this class. <br>
// Thanks to Charles Pignerol (CEA-DAM, France) who ported this class under
// VTK 4.
// Thanks to Jean Favre (CSCS, Switzerland) who contributed to integrate this
// class in VTK. <br>
// Please address all comments to Jean Favre (jfavre at cscs.ch).
#include "vtkPentagonalPrism.h"
#include "vtkObjectFactory.h"
#include "vtkLine.h"
#include "vtkQuad.h"
#include "vtkPolygon.h"
#include "vtkTriangle.h"
#include "vtkMath.h"
#include "vtkPoints.h"
vtkStandardNewMacro(vtkPentagonalPrism);
static const double VTK_DIVERGED = 1.e6;
//----------------------------------------------------------------------------
// Construct the prism with ten points.
vtkPentagonalPrism::vtkPentagonalPrism()
{
int i;
this->Points->SetNumberOfPoints(10);
this->PointIds->SetNumberOfIds(10);
for (i = 0; i < 10; i++)
{
this->Points->SetPoint(i, 0.0, 0.0, 0.0);
this->PointIds->SetId(i,0);
}
this->Line = vtkLine::New();
this->Quad = vtkQuad::New();
this->Triangle = vtkTriangle::New();
this->Polygon = vtkPolygon::New();
this->Polygon->PointIds->SetNumberOfIds(5);
this->Polygon->Points->SetNumberOfPoints(5);
for (i = 0; i < 5; i++)
{
this->Polygon->Points->SetPoint(i, 0.0, 0.0, 0.0);
this->Polygon->PointIds->SetId(i,0);
}
}
//----------------------------------------------------------------------------
vtkPentagonalPrism::~vtkPentagonalPrism()
{
this->Line->Delete();
this->Quad->Delete();
this->Triangle->Delete();
this->Polygon->Delete();
}
//
// Method to calculate parametric coordinates in an ten noded
// linear prism element from global coordinates.
//
static const int VTK_PENTA_MAX_ITERATION=10;
static const double VTK_PENTA_CONVERGED=1.e-03;
//----------------------------------------------------------------------------
int vtkPentagonalPrism::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[30];
// 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_PENTA_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<10; 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+10];
tcol[j] += pt[j] * derivs[i+20];
}
}
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_PENTA_CONVERGED) &&
((fabs(pcoords[1]-params[1])) < VTK_PENTA_CONVERGED) &&
((fabs(pcoords[2]-params[2])) < VTK_PENTA_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[10];
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
//
// see vtkPentagonalPrismCellPCoords for V#i values:
// The general idea is that for Point #0 (V1,V1,0) the shape function should be
// 0 on the 4 other node. So expr of the line passing through points
// (x1,y1) and (x2,y2) is as follow:
// (x1-x2)*y - (y1-y2)*x - (x1*y2 - x2*y1) = 0
// x(i):=1/2+1/2*Cos( Pi + Pi/4 + i*2*Pi/5)
// y(i):=1/2+1/2*Sin( Pi + Pi/4 + i*2*Pi/5)
// For instance EXPRA is x(2)-x(1)
// EXPRB is y(2)-y(1) (== x(4)-x(3))
// EXPRC is x(1)*y(2)-x(2)*y(1)
// EXPRD is x(2)-x(3) (because of sign)
// EXPRE is x(2)*y(3)-x(3)*y(2)
// EXPRF is x(0)-x(4)
// EXPRG is y(4)-y(0)
// EXPRH is x(0)*y(4)-x(4)*y(0)
// EXPRN was deducted to normalize the function
#define EXPRA 0.26684892042779546;
#define EXPRB 0.52372049461429937;
#define EXPRC 0.36619991616704034;
#define EXPRD 0.41562693777745341;
#define EXPRE 0.65339106685124182;
#define EXPRF 0.091949871500910163;
#define EXPRG 0.58054864046304711;
#define EXPRH 0.098485126908190265;
#define EXPRN 9.2621670111997307;
void vtkPentagonalPrism::InterpolationFunctions(double pcoords[3], double sf[10])
{
double r, s, t;
r = pcoords[0];
s = pcoords[1];
t = pcoords[2];
const double a = EXPRA;
const double b = EXPRB;
const double c = EXPRC;
const double d = EXPRD;
const double e = EXPRE;
const double f = EXPRF;
const double g = EXPRG;
const double h = EXPRH;
const double n = EXPRN;
//First pentagon
sf[0] = -n*(-a*s + b*r - c)*( b*s - a*r - c)*(t - 1.0);
sf[1] = n*( d*s + d*r - e)*( f*s + g*r - h)*(t - 1.0);
sf[2] = -n*( b*s - a*r - c)*(-g*s - f*r + h)*(t - 1.0);
sf[3] = n*(-a*s + b*r - c)*( f*s + g*r - h)*(t - 1.0);
sf[4] = -n*(-g*s - f*r + h)*( d*s + d*r - e)*(t - 1.0);
//Second pentagon
sf[5] = n*(-a*s + b*r - c)*( b*s - a*r - c)*(t - 0.0);
sf[6] = -n*( d*s + d*r - e)*( f*s + g*r - h)*(t - 0.0);
sf[7] = n*( b*s - a*r - c)*(-g*s - f*r + h)*(t - 0.0);
sf[8] = -n*(-a*s + b*r - c)*( f*s + g*r - h)*(t - 0.0);
//sf[9] = n*(-g*s - f*r + h)*( d*s + d*r - e)*(t - 0.0);
sf[9] = 1. - (sf[0]+sf[1]+sf[2]+sf[3]+sf[4]+sf[5]+sf[6]+sf[7]+sf[8]);
}
//----------------------------------------------------------------------------
//
// Compute iso-parametric interpolation derivatives
//
void vtkPentagonalPrism::InterpolationDerivs(double pcoords[3], double derivs[30])
{
double r, s, t;
r = pcoords[0];
s = pcoords[1];
t = pcoords[2];
const double a = EXPRA;
const double b = EXPRB;
const double c = EXPRC;
const double d = EXPRD;
const double e = EXPRE;
const double f = EXPRF;
const double g = EXPRG;
const double h = EXPRH;
const double n = EXPRN;
// r-derivatives
//First pentagon
derivs[0] = -n*(-2*a*b*r + (a*a + b*b)*s + a*c - b*c)*(t - 1.0);
derivs[1] = n*( 2*d*g*r + d*(f + g)*s - d*h - e*g)*(t - 1.0);
derivs[2] = -n*( 2*a*f*r + (a*g - b*f)*s - a*h + c*f)*(t - 1.0);
derivs[3] = n*( 2*b*g*r + (b*f - a*g)*s - b*h - c*g)*(t - 1.0);
derivs[4] = -n*(-2*d*f*r - d*(f + g)*s + d*h + e*f)*(t - 1.0);
//Second pentagon
derivs[5] = n*(-2*a*b*r + (a*a + b*b)*s + a*c - b*c)*(t - 0.0);
derivs[6] = -n*( 2*d*g*r + d*(f + g)*s - d*h - e*g)*(t - 0.0);
derivs[7] = n*( 2*a*f*r + (a*g - b*f)*s - a*h + c*f)*(t - 0.0);
derivs[8] = -n*( 2*b*g*r + (b*f - a*g)*s - b*h - c*g)*(t - 0.0);
//derivs[9] = n*(-2*d*f*r - d*(f + g)*s + d*h + e*f)*(t - 0.0);
derivs[9] = -(derivs[0]+derivs[1]+derivs[2]+derivs[3]+derivs[4]+derivs[5]
+derivs[6]+derivs[7]+derivs[8]);
// s-derivatives
//First pentagon
derivs[10] = -n*(-2*a*b*s + (a*a + b*b)*r + a*c - b*c)*(t - 1.0);
derivs[11] = n*( 2*d*f*s + d*(f + g)*r - d*h - e*f)*(t - 1.0);
derivs[12] = -n*(-2*b*g*s + (a*g - b*f)*r + b*h + c*g)*(t - 1.0);
derivs[13] = n*(-2*a*f*s + (b*f - a*g)*r + a*h - c*f)*(t - 1.0);
derivs[14] = -n*(-2*d*g*s - d*(f + g)*r + d*h + e*g)*(t - 1.0);
//Second pentagon
derivs[15] = n*(-2*a*b*s + (a*a + b*b)*r + a*c - b*c)*(t - 0.0);
derivs[16] = -n*( 2*d*f*s + d*(f + g)*r - d*h - e*f)*(t - 0.0);
derivs[17] = n*(-2*b*g*s + (a*g - b*f)*r + b*h + c*g)*(t - 0.0);
derivs[18] = -n*(-2*a*f*s + (b*f - a*g)*r + a*h - c*f)*(t - 0.0);
//derivs[19] = n*(-2*d*g*s - d*(f + g)*r + d*h + e*g)*(t - 0.0);
derivs[19] = -(derivs[10]+derivs[11]+derivs[12]+derivs[13]+derivs[14]+derivs[15]
+derivs[16]+derivs[17]+derivs[18]);
// t-derivatives
//First pentagon
derivs[20] = -n*(-a*s + b*r - c)*( b*s - a*r - c);
derivs[21] = n*( d*s + d*r - e)*( f*s + g*r - h);
derivs[22] = -n*( b*s - a*r - c)*(-g*s - f*r + h);
derivs[23] = n*(-a*s + b*r - c)*( f*s + g*r - h);
derivs[24] = -n*(-g*s - f*r + h)*( d*s + d*r - e);
//Second pentagon
derivs[25] = n*(-a*s + b*r - c)*( b*s - a*r - c);
derivs[26] = -n*( d*s + d*r - e)*( f*s + g*r - h);
derivs[27] = n*( b*s - a*r - c)*(-g*s - f*r + h);
derivs[28] = -n*(-a*s + b*r - c)*( f*s + g*r - h);
//derivs[29] = n*(-g*s - f*r + h)*( d*s + d*r - e);
derivs[29] = -(derivs[20]+derivs[21]+derivs[22]+derivs[23]+derivs[24]+derivs[25]
+derivs[26]+derivs[27]+derivs[28]);
}
//----------------------------------------------------------------------------
void vtkPentagonalPrism::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 < 10; i++)
{
this->Points->GetPoint(i, pt);
for (j = 0; j < 3; j++)
{
x[j] += pt [j] * weights [i];
}
}
}
static int edges[15][2] = { {0,1}, {1,2}, {2,3},
{3,4}, {4,0}, {5,6},
{6,7}, {7,8}, {8,9},
{9,5}, {0,5}, {1,6},
{2,7}, {3,8}, {4,9} };
static int faces[7][5] = { {0,4,3,2,1}, {5,6,7,8,9},
{0,1,6,5,-1}, {1,2,7,6,-1},
{2,3,8,7,-1}, {3,4,9,8,-1},
{4,0,5,9,-1} };
#define VTK_MAX(a,b) (((a)>(b))?(a):(b))
#define VTK_MIN(a,b) (((a)<(b))?(a):(b))
//----------------------------------------------------------------------------
// Returns the closest face to the point specified. Closeness is measured
// parametrically.
int vtkPentagonalPrism::CellBoundary(int subId, double pcoords[3],
vtkIdList *pts)
{
// load coordinates
double *points = this->GetParametricCoords();
for(int i=0;i<5;i++)
{
this->Polygon->PointIds->SetId(i, i);
this->Polygon->Points->SetPoint(i, &points[3*i]);
}
this->Polygon->CellBoundary( subId, pcoords, pts);
int min = VTK_MIN(pts->GetId( 0 ), pts->GetId( 1 ));
int max = VTK_MAX(pts->GetId( 0 ), pts->GetId( 1 ));
//Base on the edge find the quad that correspond:
int index;
if( (index = (max - min)) > 1)
{
index = 6;
}
else
{
index += min + 1;
}
double a[3], b[3], u[3], v[3];
this->Polygon->Points->GetPoint(pts->GetId( 0 ), a);
this->Polygon->Points->GetPoint(pts->GetId( 1 ), b);
u[0] = b[0] - a[0];
u[1] = b[1] - a[1];
v[0] = pcoords[0] - a[0];
v[1] = pcoords[1] - a[1];
double dot = vtkMath::Dot2D(v, u);
double uNorm = vtkMath::Norm2D( u );
if (uNorm)
{
dot /= uNorm;
}
dot = (v[0]*v[0] + v[1]*v[1]) - dot*dot;
// mathematically dot must be >= zero but, suprise suprise, it can actually
// be negative
if (dot > 0)
{
dot = sqrt( dot );
}
else
{
dot = 0;
}
int *verts;
if(pcoords[2] < 0.5)
{
//could be closer to face 1
//compare that distance to the distance to the quad.
if(dot < pcoords[2])
{
//We are closer to the quad face
verts = faces[index];
for(int i=0; i<4; i++)
{
pts->InsertId(i, verts[i]);
}
}
else
{
//we are closer to the penta face 1
for(int i=0; i<5; i++)
{
pts->InsertId(i, faces[0][i]);
}
}
}
else
{
//could be closer to face 2
//compare that distance to the distance to the quad.
if(dot < (1. - pcoords[2]) )
{
//We are closer to the quad face
verts = faces[index];
for(int i=0; i<4; i++)
{
pts->InsertId(i, verts[i]);
}
}
else
{
//we are closer to the penta face 2
for(int i=0; i<5; i++)
{
pts->InsertId(i, faces[1][i]);
}
}
}
// determine whether point is inside of hexagon
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;
}
}
//----------------------------------------------------------------------------
int *vtkPentagonalPrism::GetEdgeArray(int edgeId)
{
return edges[edgeId];
}
//----------------------------------------------------------------------------
vtkCell *vtkPentagonalPrism::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 *vtkPentagonalPrism::GetFaceArray(int faceId)
{
return faces[faceId];
}
//----------------------------------------------------------------------------
vtkCell *vtkPentagonalPrism::GetFace(int faceId)
{
int *verts;
verts = faces[faceId];
if ( verts[4] != -1 ) // polys cell
{
// load point id's
this->Polygon->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
this->Polygon->PointIds->SetId(1,this->PointIds->GetId(verts[1]));
this->Polygon->PointIds->SetId(2,this->PointIds->GetId(verts[2]));
this->Polygon->PointIds->SetId(3,this->PointIds->GetId(verts[3]));
this->Polygon->PointIds->SetId(4,this->PointIds->GetId(verts[4]));
// load coordinates
this->Polygon->Points->SetPoint(0,this->Points->GetPoint(verts[0]));
this->Polygon->Points->SetPoint(1,this->Points->GetPoint(verts[1]));
this->Polygon->Points->SetPoint(2,this->Points->GetPoint(verts[2]));
this->Polygon->Points->SetPoint(3,this->Points->GetPoint(verts[3]));
this->Polygon->Points->SetPoint(4,this->Points->GetPoint(verts[4]));
return this->Polygon;
}
else
{
// 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;
}
}
//----------------------------------------------------------------------------
//
// Intersect prism faces against line. Each prism face is a quadrilateral.
//
int vtkPentagonalPrism::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], pt5[3];
double tTemp;
double pc[3], xTemp[3], dist2, weights[10];
int faceNum;
t = VTK_DOUBLE_MAX;
//first intersect the penta faces
for (faceNum=0; faceNum<2; 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->Points->GetPoint(faces[faceNum][4], pt5);
this->Quad->Points->SetPoint(0,pt1);
this->Quad->Points->SetPoint(1,pt2);
this->Quad->Points->SetPoint(2,pt3);
this->Quad->Points->SetPoint(3,pt4);
this->Triangle->Points->SetPoint(0,pt4);
this->Triangle->Points->SetPoint(1,pt5);
this->Triangle->Points->SetPoint(2,pt1);
if ( this->Quad->IntersectWithLine(p1, p2, tol, tTemp, xTemp, pc, subId) ||
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];
switch (faceNum)
{
case 0:
pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 0.0;
break;
case 1:
pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 1.0;
break;
}
}
}
}
//now intersect the _5_ quad faces
for (faceNum=2; 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->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];
this->EvaluatePosition(x, xTemp, subId, pcoords, dist2, weights);
}
}
}
return intersection;
}
//----------------------------------------------------------------------------
int vtkPentagonalPrism::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds, vtkPoints *pts)
{
ptIds->Reset();
pts->Reset();
for ( int i=0; i < 4; i++ )
{
ptIds->InsertId(i,this->PointIds->GetId(i));
pts->InsertPoint(i,this->Points->GetPoint(i));
}
return 1;
}
//----------------------------------------------------------------------------
//
// Compute derivatives in x-y-z directions. Use chain rule in combination
// with interpolation function derivatives.
//
void vtkPentagonalPrism::Derivatives(int vtkNotUsed(subId), double pcoords[3],
double *values, int dim, double *derivs)
{
double *jI[3], j0[3], j1[3], j2[3];
double functionDerivs[30], 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 < 10; i++) //loop over interp. function derivatives
{
sum[0] += functionDerivs[i] * values[dim*i + k];
sum[1] += functionDerivs[10 + i] * values[dim*i + k];
sum[2] += functionDerivs[20 + 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 vtkPentagonalPrism::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 < 10; j++ )
{
this->Points->GetPoint(j, x);
for ( i=0; i < 3; i++ )
{
m0[i] += x[i] * derivs[j];
m1[i] += x[i] * derivs[10 + j];
m2[i] += x[i] * derivs[20 + j];
}
}
// now find the inverse
if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
{
vtkErrorMacro(<<"Jacobian inverse not found");
return;
}
}
//----------------------------------------------------------------------------
void vtkPentagonalPrism::GetEdgePoints (int edgeId, int *&pts)
{
pts = this->GetEdgeArray(edgeId);
}
//----------------------------------------------------------------------------
void vtkPentagonalPrism::GetFacePoints (int faceId, int *&pts)
{
pts = this->GetFaceArray(faceId);
}
// How to find the points for the pentagon:
// The points for the iso parametric pentagon have to be properly chosen so that
// the inverse Jacobian is defined.
// To be regular the points have to on the circle, center (1/2,1/2) with radius
// sqrt(2)/2
// Then since there is an odd number of points they have to be simmetric
// to the first bisector
// Thus I pick the first point to be on this dividing line.
// We can then express point i (0, 4) to be:
// Vi_x = CenterOfCircle + 1/2 ( cos( pi + pi/4 + i*2*pi/5) )
// Vi_y = CenterOfCircle + 1/2 ( sin( pi + pi/4 + i*2*pi/5) )
#define V1 0.14644660940672624
#define V2 0.72699524986977337
#define V3 0.054496737905816071
#define V4 0.99384417029756889
#define V5 0.57821723252011548
static double vtkPentagonalPrismCellPCoords[30] = {
V1 , V1 , 0.0,
V2 , V3 , 0.0,
V4 , V5 , 0.0,
V5 , V4 , 0.0,
V3 , V2 , 0.0,
V1 , V1 , 1.0,
V2 , V3 , 1.0,
V4 , V5 , 1.0,
V5 , V4 , 1.0,
V3 , V2 , 1.0};
//----------------------------------------------------------------------------
double *vtkPentagonalPrism::GetParametricCoords()
{
return vtkPentagonalPrismCellPCoords;
}
//----------------------------------------------------------------------------
void vtkPentagonalPrism::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());
os << indent << "Polygon:\n";
this->Polygon->PrintSelf(os,indent.GetNextIndent());
}