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/*=========================================================================
Program: Visualization Toolkit
Module: vtkQuad.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 "vtkQuad.h"
#include "vtkObjectFactory.h"
#include "vtkCellArray.h"
#include "vtkCellData.h"
#include "vtkLine.h"
#include "vtkTriangle.h"
#include "vtkMath.h"
#include "vtkPlane.h"
#include "vtkPointData.h"
#include "vtkIncrementalPointLocator.h"
#include "vtkPoints.h"
vtkStandardNewMacro(vtkQuad);
static const double VTK_DIVERGED = 1.e6;
//----------------------------------------------------------------------------
// Construct the quad with four points.
vtkQuad::vtkQuad()
{
this->Points->SetNumberOfPoints(4);
this->PointIds->SetNumberOfIds(4);
for (int i = 0; i < 4; i++)
{
this->Points->SetPoint(i, 0.0, 0.0, 0.0);
this->PointIds->SetId(i,0);
}
this->Line = vtkLine::New();
this->Triangle = vtkTriangle::New();
}
//----------------------------------------------------------------------------
vtkQuad::~vtkQuad()
{
this->Line->Delete();
this->Triangle->Delete();
}
//----------------------------------------------------------------------------
static const int VTK_QUAD_MAX_ITERATION=20;
static const double VTK_QUAD_CONVERGED=1.e-04;
inline static void ComputeNormal(vtkQuad *self, double pt1[3], double pt2[3],
double pt3[3], double n[3])
{
vtkTriangle::ComputeNormal (pt1, pt2, pt3, n);
// If first three points are co-linear, then use fourth point
//
double pt4[3];
if ( n[0] == 0.0 && n[1] == 0.0 && n[2] == 0.0 )
{
self->Points->GetPoint(3,pt4);
vtkTriangle::ComputeNormal (pt2, pt3, pt4, n);
}
}
//----------------------------------------------------------------------------
int vtkQuad::EvaluatePosition(double x[3], double* closestPoint,
int& subId, double pcoords[3],
double& dist2, double *weights)
{
int i, j;
double pt1[3], pt2[3], pt3[3], pt[3], n[3];
double det;
double maxComponent;
int idx=0, indices[2];
int iteration, converged;
double params[2];
double fcol[2], rcol[2], scol[2], cp[3];
double derivs[8];
subId = 0;
pcoords[0] = pcoords[1] = params[0] = params[1] = 0.5;
// Get normal for quadrilateral
//
this->Points->GetPoint(0, pt1);
this->Points->GetPoint(1, pt2);
this->Points->GetPoint(2, pt3);
ComputeNormal (this, pt1, pt2, pt3, n);
// Project point to plane
//
vtkPlane::ProjectPoint(x,pt1,n,cp);
// Construct matrices. Since we have over determined system, need to find
// which 2 out of 3 equations to use to develop equations. (Any 2 should
// work since we've projected point to plane.)
//
for (maxComponent=0.0, i=0; i<3; i++)
{
if (fabs(n[i]) > maxComponent)
{
maxComponent = fabs(n[i]);
idx = i;
}
}
for (j=0, i=0; i<3; i++)
{
if ( i != idx )
{
indices[j++] = i;
}
}
// Use Newton's method to solve for parametric coordinates
//
for (iteration=converged=0; !converged
&& (iteration < VTK_QUAD_MAX_ITERATION);
iteration++)
{
// calculate element interpolation functions and derivatives
//
this->InterpolationFunctions(pcoords, weights);
this->InterpolationDerivs(pcoords, derivs);
// calculate newton functions
//
for (i=0; i<2; i++)
{
fcol[i] = rcol[i] = scol[i] = 0.0;
}
for (i=0; i<4; i++)
{
this->Points->GetPoint(i, pt);
for (j=0; j<2; j++)
{
fcol[j] += pt[indices[j]] * weights[i];
rcol[j] += pt[indices[j]] * derivs[i];
scol[j] += pt[indices[j]] * derivs[i+4];
}
}
for (j=0; j<2; j++)
{
fcol[j] -= cp[indices[j]];
}
// compute determinants and generate improvements
//
if ( (det=vtkMath::Determinant2x2(rcol,scol)) == 0.0 )
{
return -1;
}
pcoords[0] = params[0] - vtkMath::Determinant2x2 (fcol,scol) / det;
pcoords[1] = params[1] - vtkMath::Determinant2x2 (rcol,fcol) / det;
// check for convergence
//
if ( ((fabs(pcoords[0]-params[0])) < VTK_QUAD_CONVERGED) &&
((fabs(pcoords[1]-params[1])) < VTK_QUAD_CONVERGED) )
{
converged = 1;
}
// Test for bad divergence (S.Hirschberg 11.12.2001)
else if ((fabs(pcoords[0]) > VTK_DIVERGED) ||
(fabs(pcoords[1]) > VTK_DIVERGED))
{
return -1;
}
// if not converged, repeat
//
else
{
params[0] = pcoords[0];
params[1] = pcoords[1];
}
}
// 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 )
{
if (closestPoint)
{
dist2 =
vtkMath::Distance2BetweenPoints(cp,x); //projection distance
closestPoint[0] = cp[0];
closestPoint[1] = cp[1];
closestPoint[2] = cp[2];
}
return 1;
}
else
{
double t;
double pt4[3];
if (closestPoint)
{
this->Points->GetPoint(3, pt4);
if ( pcoords[0] < 0.0 && pcoords[1] < 0.0 )
{
dist2 = vtkMath::Distance2BetweenPoints(x,pt1);
for (i=0; i<3; i++)
{
closestPoint[i] = pt1[i];
}
}
else if ( pcoords[0] > 1.0 && pcoords[1] < 0.0 )
{
dist2 = vtkMath::Distance2BetweenPoints(x,pt2);
for (i=0; i<3; i++)
{
closestPoint[i] = pt2[i];
}
}
else if ( pcoords[0] > 1.0 && pcoords[1] > 1.0 )
{
dist2 = vtkMath::Distance2BetweenPoints(x,pt3);
for (i=0; i<3; i++)
{
closestPoint[i] = pt3[i];
}
}
else if ( pcoords[0] < 0.0 && pcoords[1] > 1.0 )
{
dist2 = vtkMath::Distance2BetweenPoints(x,pt4);
for (i=0; i<3; i++)
{
closestPoint[i] = pt4[i];
}
}
else if ( pcoords[0] < 0.0 )
{
dist2 = vtkLine::DistanceToLine(x,pt1,pt4,t,closestPoint);
}
else if ( pcoords[0] > 1.0 )
{
dist2 = vtkLine::DistanceToLine(x,pt2,pt3,t,closestPoint);
}
else if ( pcoords[1] < 0.0 )
{
dist2 = vtkLine::DistanceToLine(x,pt1,pt2,t,closestPoint);
}
else if ( pcoords[1] > 1.0 )
{
dist2 = vtkLine::DistanceToLine(x,pt3,pt4,t,closestPoint);
}
}
return 0;
}
}
//----------------------------------------------------------------------------
void vtkQuad::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<4; i++)
{
this->Points->GetPoint(i, pt);
for (j=0; j<3; j++)
{
x[j] += pt[j] * weights[i];
}
}
}
//----------------------------------------------------------------------------
// Compute iso-parametric interpolation functions
//
void vtkQuad::InterpolationFunctions(double pcoords[3], double sf[4])
{
double rm, sm;
rm = 1. - pcoords[0];
sm = 1. - pcoords[1];
sf[0] = rm * sm;
sf[1] = pcoords[0] * sm;
sf[2] = pcoords[0] * pcoords[1];
sf[3] = rm * pcoords[1];
}
//----------------------------------------------------------------------------
void vtkQuad::InterpolationDerivs(double pcoords[3], double derivs[8])
{
double rm, sm;
rm = 1. - pcoords[0];
sm = 1. - pcoords[1];
derivs[0] = -sm;
derivs[1] = sm;
derivs[2] = pcoords[1];
derivs[3] = -pcoords[1];
derivs[4] = -rm;
derivs[5] = -pcoords[0];
derivs[6] = pcoords[0];
derivs[7] = rm;
}
//----------------------------------------------------------------------------
int vtkQuad::CellBoundary(int vtkNotUsed(subId), double pcoords[3],
vtkIdList *pts)
{
double t1=pcoords[0]-pcoords[1];
double t2=1.0-pcoords[0]-pcoords[1];
pts->SetNumberOfIds(2);
// compare against two lines in parametric space that divide element
// into four pieces.
if ( t1 >= 0.0 && t2 >= 0.0 )
{
pts->SetId(0,this->PointIds->GetId(0));
pts->SetId(1,this->PointIds->GetId(1));
}
else if ( t1 >= 0.0 && t2 < 0.0 )
{
pts->SetId(0,this->PointIds->GetId(1));
pts->SetId(1,this->PointIds->GetId(2));
}
else if ( t1 < 0.0 && t2 < 0.0 )
{
pts->SetId(0,this->PointIds->GetId(2));
pts->SetId(1,this->PointIds->GetId(3));
}
else //( t1 < 0.0 && t2 >= 0.0 )
{
pts->SetId(0,this->PointIds->GetId(3));
pts->SetId(1,this->PointIds->GetId(0));
}
if ( pcoords[0] < 0.0 || pcoords[0] > 1.0 ||
pcoords[1] < 0.0 || pcoords[1] > 1.0 )
{
return 0;
}
else
{
return 1;
}
}
//----------------------------------------------------------------------------
// Marching (convex) quadrilaterals
//
static int edges[4][2] = { {0,1}, {1,2}, {3,2}, {0,3} };
typedef int EDGE_LIST;
typedef struct {
EDGE_LIST edges[5];
} LINE_CASES;
static LINE_CASES lineCases[] = {
{{-1, -1, -1, -1, -1}},
{{0, 3, -1, -1, -1}},
{{1, 0, -1, -1, -1}},
{{1, 3, -1, -1, -1}},
{{2, 1, -1, -1, -1}},
{{0, 3, 2, 1, -1}},
{{2, 0, -1, -1, -1}},
{{2, 3, -1, -1, -1}},
{{3, 2, -1, -1, -1}},
{{0, 2, -1, -1, -1}},
{{1, 0, 3, 2, -1}},
{{1, 2, -1, -1, -1}},
{{3, 1, -1, -1, -1}},
{{0, 1, -1, -1, -1}},
{{3, 0, -1, -1, -1}},
{{-1, -1, -1, -1, -1}}
};
//----------------------------------------------------------------------------
int *vtkQuad::GetEdgeArray(int edgeId)
{
return edges[edgeId];
}
//----------------------------------------------------------------------------
void vtkQuad::Contour(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator,
vtkCellArray *verts,
vtkCellArray *lines,
vtkCellArray *vtkNotUsed(polys),
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd)
{
static int CASE_MASK[4] = {1,2,4,8};
LINE_CASES *lineCase;
EDGE_LIST *edge;
int i, j, index, *vert;
int newCellId;
vtkIdType pts[2];
int e1, e2;
double t, x1[3], x2[3], x[3], deltaScalar;
vtkIdType offset = verts->GetNumberOfCells();
// Build the case table
for ( i=0, index = 0; i < 4; i++)
{
if (cellScalars->GetComponent(i,0) >= value)
{
index |= CASE_MASK[i];
}
}
lineCase = lineCases + index;
edge = lineCase->edges;
for ( ; edge[0] > -1; edge += 2 )
{
for (i=0; i<2; i++) // insert line
{
vert = edges[edge[i]];
// calculate a preferred interpolation direction
deltaScalar = (cellScalars->GetComponent(vert[1],0)
- cellScalars->GetComponent(vert[0],0));
if (deltaScalar > 0)
{
e1 = vert[0]; e2 = vert[1];
}
else
{
e1 = vert[1]; e2 = vert[0];
deltaScalar = -deltaScalar;
}
// linear interpolation
if (deltaScalar == 0.0)
{
t = 0.0;
}
else
{
t = (value - cellScalars->GetComponent(e1,0)) / deltaScalar;
}
this->Points->GetPoint(e1, x1);
this->Points->GetPoint(e2, 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(e1);
vtkIdType p2 = this->PointIds->GetId(e2);
outPd->InterpolateEdge(inPd,pts[i],p1,p2,t);
}
}
}
// check for degenerate line
if ( pts[0] != pts[1] )
{
newCellId = offset + lines->InsertNextCell(2,pts);
outCd->CopyData(inCd,cellId,newCellId);
}
}
}
//----------------------------------------------------------------------------
vtkCell *vtkQuad::GetEdge(int edgeId)
{
int edgeIdPlus1 = edgeId + 1;
if (edgeIdPlus1 > 3)
{
edgeIdPlus1 = 0;
}
// load point id's
this->Line->PointIds->SetId(0,this->PointIds->GetId(edgeId));
this->Line->PointIds->SetId(1,this->PointIds->GetId(edgeIdPlus1));
// load coordinates
this->Line->Points->SetPoint(0,this->Points->GetPoint(edgeId));
this->Line->Points->SetPoint(1,this->Points->GetPoint(edgeIdPlus1));
return this->Line;
}
//----------------------------------------------------------------------------
// Intersect plane; see whether point is in quadrilateral. This code
// splits the quad into two triangles and intersects them (because the
// quad may be non-planar).
//
int vtkQuad::IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
double x[3], double pcoords[3], int& subId)
{
int diagonalCase;
double d1 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(0),
this->Points->GetPoint(2));
double d2 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(1),
this->Points->GetPoint(3));
subId = 0;
// Figure out how to uniquely tessellate the quad. Watch out for
// equivalent triangulations (i.e., the triangulation is equivalent
// no matter where the diagonal). In this case use the point ids as
// a tie breaker to insure unique triangulation across the quad.
//
if ( d1 == d2 ) //rare case; discriminate based on point id
{
int i, id, maxId=0, maxIdx=0;
for (i=0; i<4; i++) //find the maximum id
{
if ( (id=this->PointIds->GetId(i)) > maxId )
{
maxId = id;
maxIdx = i;
}
}
if ( maxIdx == 0 || maxIdx == 2) diagonalCase = 0;
else diagonalCase = 1;
}
else if ( d1 < d2 )
{
diagonalCase = 0;
}
else //d2 < d1
{
diagonalCase = 1;
}
// Note: in the following code the parametric coords must be adjusted to
// reflect the use of the triangle parametric coordinate system.
switch (diagonalCase)
{
case 0:
this->Triangle->Points->SetPoint(0,this->Points->GetPoint(0));
this->Triangle->Points->SetPoint(1,this->Points->GetPoint(1));
this->Triangle->Points->SetPoint(2,this->Points->GetPoint(2));
if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
{
pcoords[0] = pcoords[0] + pcoords[1];
return 1;
}
this->Triangle->Points->SetPoint(0,this->Points->GetPoint(2));
this->Triangle->Points->SetPoint(1,this->Points->GetPoint(3));
this->Triangle->Points->SetPoint(2,this->Points->GetPoint(0));
if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
{
pcoords[0] = 1.0 - (pcoords[0]+pcoords[1]);
pcoords[1] = 1.0 - pcoords[1];
return 1;
}
return 0;
case 1:
this->Triangle->Points->SetPoint(0,this->Points->GetPoint(0));
this->Triangle->Points->SetPoint(1,this->Points->GetPoint(1));
this->Triangle->Points->SetPoint(2,this->Points->GetPoint(3));
if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
{
return 1;
}
this->Triangle->Points->SetPoint(0,this->Points->GetPoint(2));
this->Triangle->Points->SetPoint(1,this->Points->GetPoint(3));
this->Triangle->Points->SetPoint(2,this->Points->GetPoint(1));
if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
{
pcoords[0] = 1.0 - pcoords[0];
pcoords[1] = 1.0 - pcoords[1];
return 1;
}
return 0;
}
return 0;
}
//----------------------------------------------------------------------------
int vtkQuad::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds,
vtkPoints *pts)
{
double d1, d2;
pts->Reset();
ptIds->Reset();
// use minimum diagonal (Delaunay triangles) - assumed convex
d1 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(0),
this->Points->GetPoint(2));
d2 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(1),
this->Points->GetPoint(3));
if ( d1 <= d2 )
{
ptIds->InsertId(0,this->PointIds->GetId(0));
pts->InsertPoint(0,this->Points->GetPoint(0));
ptIds->InsertId(1,this->PointIds->GetId(1));
pts->InsertPoint(1,this->Points->GetPoint(1));
ptIds->InsertId(2,this->PointIds->GetId(2));
pts->InsertPoint(2,this->Points->GetPoint(2));
ptIds->InsertId(3,this->PointIds->GetId(0));
pts->InsertPoint(3,this->Points->GetPoint(0));
ptIds->InsertId(4,this->PointIds->GetId(2));
pts->InsertPoint(4,this->Points->GetPoint(2));
ptIds->InsertId(5,this->PointIds->GetId(3));
pts->InsertPoint(5,this->Points->GetPoint(3));
}
else
{
ptIds->InsertId(0,this->PointIds->GetId(0));
pts->InsertPoint(0,this->Points->GetPoint(0));
ptIds->InsertId(1,this->PointIds->GetId(1));
pts->InsertPoint(1,this->Points->GetPoint(1));
ptIds->InsertId(2,this->PointIds->GetId(3));
pts->InsertPoint(2,this->Points->GetPoint(3));
ptIds->InsertId(3,this->PointIds->GetId(1));
pts->InsertPoint(3,this->Points->GetPoint(1));
ptIds->InsertId(4,this->PointIds->GetId(2));
pts->InsertPoint(4,this->Points->GetPoint(2));
ptIds->InsertId(5,this->PointIds->GetId(3));
pts->InsertPoint(5,this->Points->GetPoint(3));
}
return 1;
}
//----------------------------------------------------------------------------
void vtkQuad::Derivatives(int vtkNotUsed(subId), double pcoords[3],
double *values, int dim, double *derivs)
{
double v0[2], v1[2], v2[2], v3[2], v10[3], v20[3], lenX;
double x0[3], x1[3], x2[3], x3[3], n[3], vec20[3], vec30[3];
double *J[2], J0[2], J1[2];
double *JI[2], JI0[2], JI1[2];
double funcDerivs[8], sum[2], dBydx, dBydy;
int i, j;
// Project points of quad into 2D system
this->Points->GetPoint(0, x0);
this->Points->GetPoint(1, x1);
this->Points->GetPoint(2, x2);
ComputeNormal (this,x0, x1, x2, n);
this->Points->GetPoint(3, x3);
for (i=0; i < 3; i++)
{
v10[i] = x1[i] - x0[i];
vec20[i] = x2[i] - x0[i];
vec30[i] = x3[i] - x0[i];
}
vtkMath::Cross(n,v10,v20); //creates local y' axis
if ( (lenX=vtkMath::Normalize(v10)) <= 0.0
|| vtkMath::Normalize(v20) <= 0.0 ) //degenerate
{
for ( j=0; j < dim; j++ )
{
for ( i=0; i < 3; i++ )
{
derivs[j*dim + i] = 0.0;
}
}
return;
}
v0[0] = v0[1] = 0.0; //convert points to 2D (i.e., local system)
v1[0] = lenX; v1[1] = 0.0;
v2[0] = vtkMath::Dot(vec20,v10);
v2[1] = vtkMath::Dot(vec20,v20);
v3[0] = vtkMath::Dot(vec30,v10);
v3[1] = vtkMath::Dot(vec30,v20);
this->InterpolationDerivs(pcoords, funcDerivs);
// Compute Jacobian and inverse Jacobian
J[0] = J0; J[1] = J1;
JI[0] = JI0; JI[1] = JI1;
J[0][0] = v0[0]*funcDerivs[0] + v1[0]*funcDerivs[1] +
v2[0]*funcDerivs[2] + v3[0]*funcDerivs[3];
J[0][1] = v0[1]*funcDerivs[0] + v1[1]*funcDerivs[1] +
v2[1]*funcDerivs[2] + v3[1]*funcDerivs[3];
J[1][0] = v0[0]*funcDerivs[4] + v1[0]*funcDerivs[5] +
v2[0]*funcDerivs[6] + v3[0]*funcDerivs[7];
J[1][1] = v0[1]*funcDerivs[4] + v1[1]*funcDerivs[5] +
v2[1]*funcDerivs[6] + v3[1]*funcDerivs[7];
// Compute inverse Jacobian, return if Jacobian is singular
if (!vtkMath::InvertMatrix(J,JI,2))
{
for ( j=0; j < dim; j++ )
{
for ( i=0; i < 3; i++ )
{
derivs[j*dim + i] = 0.0;
}
}
return;
}
// Loop over "dim" derivative values. For each set of values,
// compute derivatives
// in local system and then transform into modelling system.
// First compute derivatives in local x'-y' coordinate system
for ( j=0; j < dim; j++ )
{
sum[0] = sum[1] = 0.0;
for ( i=0; i < 4; i++) //loop over interp. function derivatives
{
sum[0] += funcDerivs[i] * values[dim*i + j];
sum[1] += funcDerivs[4 + i] * values[dim*i + j];
}
dBydx = sum[0]*JI[0][0] + sum[1]*JI[0][1];
dBydy = sum[0]*JI[1][0] + sum[1]*JI[1][1];
// Transform into global system (dot product with global axes)
derivs[3*j] = dBydx * v10[0] + dBydy * v20[0];
derivs[3*j + 1] = dBydx * v10[1] + dBydy * v20[1];
derivs[3*j + 2] = dBydx * v10[2] + dBydy * v20[2];
}
}
//----------------------------------------------------------------------------
// support quad clipping
typedef int QUAD_EDGE_LIST;
typedef struct {
QUAD_EDGE_LIST edges[14];
} QUAD_CASES;
static QUAD_CASES quadCases[] = {
{{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 0
{{ 3, 100, 0, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 1
{{ 3, 101, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 2
{{ 4, 100, 101, 1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 3
{{ 3, 102, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 4
{{ 3, 100, 0, 3, 3, 102, 2, 1, 4, 0, 1, 2, 3, -1}}, // 5
{{ 4, 101, 102, 2, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 6
{{ 3, 100, 101, 3, 3, 101, 2, 3, 3, 101, 102, 2, -1, -1}}, // 7
{{ 3, 103, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 8
{{ 4, 100, 0, 2, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 9
{{ 3, 101, 1, 0, 3, 103, 3, 2, 4, 0, 1, 2, 3, -1}}, // 10
{{ 3, 100, 101, 1, 3, 100, 1, 2, 3, 100, 2, 103, -1, -1}}, // 11
{{ 4, 102, 103, 3, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 12
{{ 3, 100, 0, 103, 3, 0, 1, 103, 3, 1, 102, 103, -1, -1}}, // 13
{{ 3, 0, 101, 102, 3, 0, 102, 3, 3, 102, 103, 3, -1, -1}}, // 14
{{ 4, 100, 101, 102, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 15
};
static QUAD_CASES quadCasesComplement[] = {
{{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 0
{{ 3, 100, 0, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 1
{{ 3, 101, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 2
{{ 4, 100, 101, 1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 3
{{ 3, 102, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 4
{{ 3, 100, 0, 3, 3, 102, 2, 1, -1, -1, -1, -1, -1, -1}}, // 5
{{ 4, 101, 102, 2, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 6
{{ 3, 100, 101, 3, 3, 101, 2, 3, 3, 101, 102, 2, -1, -1}}, // 7
{{ 3, 103, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 8
{{ 4, 100, 0, 2, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 9
{{ 3, 101, 1, 0, 3, 103, 3, 2, -1, -1, -1, -1, -1, -1}}, // 10
{{ 3, 100, 101, 1, 3, 100, 1, 2, 3, 100, 2, 103, -1, -1}}, // 11
{{ 4, 102, 103, 3, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 12
{{ 3, 100, 0, 103, 3, 0, 1, 103, 3, 1, 102, 103, -1, -1}}, // 13
{{ 3, 0, 101, 102, 3, 0, 102, 3, 3, 102, 103, 3, -1, -1}}, // 14
{{ 4, 100, 101, 102, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 15
};
//----------------------------------------------------------------------------
// Clip this quad using scalar value provided. Like contouring, except
// that it cuts the quad to produce other quads and/or triangles.
void vtkQuad::Clip(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator, vtkCellArray *polys,
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
int insideOut)
{
static int CASE_MASK[4] = {1,2,4,8};
QUAD_CASES *quadCase;
QUAD_EDGE_LIST *edge;
int i, j, index, *vert;
int e1, e2;
int newCellId;
vtkIdType pts[4];
int vertexId;
double t, x1[3], x2[3], x[3], deltaScalar;
double scalar0, scalar1, e1Scalar;
// Build the index into the case table
if ( insideOut )
{
for ( i=0, index = 0; i < 4; i++)
{
if (cellScalars->GetComponent(i,0) <= value)
{
index |= CASE_MASK[i];
}
}
// Select case based on the index and get the list of edges for this case
quadCase = quadCases + index;
}
else
{
for ( i=0, index = 0; i < 4; i++)
{
if (cellScalars->GetComponent(i,0) > value)
{
index |= CASE_MASK[i];
}
}
// Select case based on the index and get the list of edges for this case
quadCase = quadCasesComplement + index;
}
edge = quadCase->edges;
// generate each quad
for ( ; edge[0] > -1; edge += edge[0]+1 )
{
for (i=0; i < edge[0]; i++) // insert quad or triangle
{
// vertex exists, and need not be interpolated
if (edge[i+1] >= 100)
{
vertexId = edge[i+1] - 100;
this->Points->GetPoint(vertexId, x);
if ( locator->InsertUniquePoint(x, pts[i]) )
{
outPd->CopyData(inPd,this->PointIds->GetId(vertexId),pts[i]);
}
}
else //new vertex, interpolate
{
vert = edges[edge[i+1]];
// calculate a preferred interpolation direction
scalar0 = cellScalars->GetComponent(vert[0],0);
scalar1 = cellScalars->GetComponent(vert[1],0);
deltaScalar = scalar1 - scalar0;
if (deltaScalar > 0)
{
e1 = vert[0]; e2 = vert[1];
e1Scalar = scalar0;
}
else
{
e1 = vert[1]; e2 = vert[0];
e1Scalar = scalar1;
deltaScalar = -deltaScalar;
}
// linear interpolation
if (deltaScalar == 0.0)
{
t = 0.0;
}
else
{
t = (value - e1Scalar) / deltaScalar;
}
this->Points->GetPoint(e1, x1);
this->Points->GetPoint(e2, x2);
for (j=0; j<3; j++)
{
x[j] = x1[j] + t * (x2[j] - x1[j]);
}
if ( locator->InsertUniquePoint(x, pts[i]) )
{
vtkIdType p1 = this->PointIds->GetId(e1);
vtkIdType p2 = this->PointIds->GetId(e2);
outPd->InterpolateEdge(inPd,pts[i],p1,p2,t);
}
}
}
// check for degenerate output
if ( edge[0] == 3 ) //i.e., a triangle
{
if (pts[0] == pts[1] || pts[0] == pts[2] || pts[1] == pts[2] )
{
continue;
}
}
else // a quad
{
if ((pts[0] == pts[3] && pts[1] == pts[2]) ||
(pts[0] == pts[1] && pts[3] == pts[2]) )
{
continue;
}
}
newCellId = polys->InsertNextCell(edge[0],pts);
outCd->CopyData(inCd,cellId,newCellId);
}
}
//----------------------------------------------------------------------------
static double vtkQuadCellPCoords[12] = {0.0,0.0,0.0, 1.0,0.0,0.0,
1.0,1.0,0.0, 0.0,1.0,0.0};
double *vtkQuad::GetParametricCoords()
{
return vtkQuadCellPCoords;
}
//----------------------------------------------------------------------------
void vtkQuad::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());
}
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