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/*=========================================================================
Program: Visualization Toolkit
Module: vtkPixel.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 "vtkPixel.h"
#include "vtkObjectFactory.h"
#include "vtkQuad.h"
#include "vtkTriangle.h"
#include "vtkPlane.h"
#include "vtkMath.h"
#include "vtkCellArray.h"
#include "vtkLine.h"
#include "vtkIncrementalPointLocator.h"
#include "vtkPointData.h"
#include "vtkCellData.h"
#include "vtkPoints.h"
vtkStandardNewMacro(vtkPixel);
//----------------------------------------------------------------------------
// Construct the pixel with four points.
vtkPixel::vtkPixel()
{
int i;
this->Points->SetNumberOfPoints(4);
this->PointIds->SetNumberOfIds(4);
for (i = 0; i < 4; i++)
{
this->Points->SetPoint(i, 0.0, 0.0, 0.0);
}
for (i = 0; i < 4; i++)
{
this->PointIds->SetId(i,0);
}
this->Line = vtkLine::New();
}
//----------------------------------------------------------------------------
vtkPixel::~vtkPixel()
{
this->Line->Delete();
}
//----------------------------------------------------------------------------
int vtkPixel::EvaluatePosition(double x[3], double* closestPoint,
int& subId, double pcoords[3],
double& dist2, double *weights)
{
double pt1[3], pt2[3], pt3[3];
int i;
double p[3], p21[3], p31[3], cp[3];
double l21, l31, n[3];
subId = 0;
pcoords[2] = 0.0;
// Get normal for pixel
//
this->Points->GetPoint(0, pt1);
this->Points->GetPoint(1, pt2);
this->Points->GetPoint(2, pt3);
vtkTriangle::ComputeNormal (pt1, pt2, pt3, n);
// Project point to plane
//
vtkPlane::ProjectPoint(x,pt1,n,cp);
for (i=0; i<3; i++)
{
p21[i] = pt2[i] - pt1[i];
p31[i] = pt3[i] - pt1[i];
p[i] = x[i] - pt1[i];
}
if ( (l21=vtkMath::Norm(p21)) == 0.0 )
{
l21 = 1.0;
}
if ( (l31=vtkMath::Norm(p31)) == 0.0 )
{
l31 = 1.0;
}
pcoords[0] = vtkMath::Dot(p21,p) / (l21*l21);
pcoords[1] = vtkMath::Dot(p31,p) / (l31*l31);
this->InterpolationFunctions(pcoords, weights);
if ( pcoords[0] >= 0.0 && pcoords[0] <= 1.0 &&
pcoords[1] >= 0.0 && pcoords[1] <= 1.0 )
{
if (closestPoint)
{
closestPoint[0] = cp[0];
closestPoint[1] = cp[1];
closestPoint[2] = cp[2];
dist2 =
vtkMath::Distance2BetweenPoints(closestPoint,x); //projection distance
}
return 1;
}
else
{
double pc[3], w[4];
if (closestPoint)
{
for (i=0; i<2; i++)
{
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 vtkPixel::EvaluateLocation(int& subId, double pcoords[3], double x[3],
double *weights)
{
double pt1[3], pt2[3], pt3[3];
int i;
subId = 0;
this->Points->GetPoint(0, pt1);
this->Points->GetPoint(1, pt2);
this->Points->GetPoint(2, pt3);
for (i=0; i<3; i++)
{
x[i] = pt1[i] + pcoords[0]*(pt2[i] - pt1[i]) +
pcoords[1]*(pt3[i] - pt1[i]);
}
this->InterpolationFunctions(pcoords, weights);
}
//----------------------------------------------------------------------------
int vtkPixel::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(3));
}
else if ( t1 < 0.0 && t2 < 0.0 )
{
pts->SetId(0,this->PointIds->GetId(3));
pts->SetId(1,this->PointIds->GetId(2));
}
else //( t1 < 0.0 && t2 >= 0.0 )
{
pts->SetId(0,this->PointIds->GetId(2));
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 squares
//
#include "vtkMarchingSquaresCases.h"
static int edges[4][2] = { {0,1}, {1,3}, {2,3}, {0,2} };
void vtkPixel::Contour(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator,
vtkCellArray *vtkNotUsed(verts),
vtkCellArray *lines,
vtkCellArray *vtkNotUsed(polys),
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd)
{
static int CASE_MASK[4] = {1,2,8,4}; //note differenceom quad!
vtkMarchingSquaresLineCases *lineCase;
EDGE_LIST *edge;
int i, j, index, *vert;
int newCellId;
vtkIdType pts[2];
double t, x1[3], x2[3], x[3];
// Build the case table
for ( i=0, index = 0; i < 4; i++)
{
if (cellScalars->GetComponent(i,0) >= value)
{
index |= CASE_MASK[i];
}
}
lineCase = vtkMarchingSquaresLineCases::GetCases() + index;
edge = lineCase->edges;
for ( ; edge[0] > -1; edge += 2 )
{
for (i=0; i<2; i++) // insert line
{
vert = edges[edge[i]];
t = (value - cellScalars->GetComponent(vert[0],0)) /
(cellScalars->GetComponent(vert[1],0) -
cellScalars->GetComponent(vert[0],0));
this->Points->GetPoint(vert[0], x1);
this->Points->GetPoint(vert[1], x2);
for (j=0; j<3; j++)
{
x[j] = x1[j] + t * (x2[j] - x1[j]);
}
if ( locator->InsertUniquePoint(x, pts[i]) )
{
if ( outPd )
{
int p1 = this->PointIds->GetId(vert[0]);
int p2 = this->PointIds->GetId(vert[1]);
outPd->InterpolateEdge(inPd,pts[i],p1,p2,t);
}
}
}
// check for degenerate line
if ( pts[0] != pts[1] )
{
newCellId = lines->InsertNextCell(2,pts);
outCd->CopyData(inCd,cellId,newCellId);
}
}
}
//----------------------------------------------------------------------------
vtkCell *vtkPixel::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;
}
//----------------------------------------------------------------------------
//
// Compute interpolation functions (similar but different than Quad interpolation
// functions)
//
void vtkPixel::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] = rm * pcoords[1];
sf[3] = pcoords[0] * pcoords[1];
}
//----------------------------------------------------------------------------
//
// Compute derivatives of interpolation functions.
//
void vtkPixel::InterpolationDerivs(double pcoords[3], double derivs[8])
{
double rm, sm;
rm = 1. - pcoords[0];
sm = 1. - pcoords[1];
// r derivatives
derivs[0] = -sm;
derivs[1] = sm;
derivs[2] = -pcoords[1];
derivs[3] = pcoords[1];
// s derivatives
derivs[4] = -rm;
derivs[5] = -pcoords[0];
derivs[6] = rm;
derivs[7] = pcoords[0];
}
//----------------------------------------------------------------------------
//
// Intersect plane; see whether point is inside.
//
int vtkPixel::IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
double x[3], double pcoords[3], int& subId)
{
double pt1[3], pt4[3], n[3];
double tol2 = tol*tol;
double closestPoint[3];
double dist2, weights[4];
int i;
subId = 0;
pcoords[0] = pcoords[1] = pcoords[2] = 0.0;
//
// Get normal for triangle
//
this->Points->GetPoint(0, pt1);
this->Points->GetPoint(3, pt4);
n[0] = n[1] = n[2] = 0.0;
for (i=0; i<3; i++)
{
if ( (pt4[i] - pt1[i]) <= 0.0 )
{
n[i] = 1.0;
break;
}
}
//
// Intersect plane of pixel with line
//
if ( ! vtkPlane::IntersectWithLine(p1,p2,n,pt1,t,x) )
{
return 0;
}
//
// Use evaluate position
//
if (this->EvaluatePosition(x, closestPoint, subId, pcoords, dist2, weights))
{
if ( dist2 <= tol2 )
{
return 1;
}
}
return 0;
}
//----------------------------------------------------------------------------
int vtkPixel::Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts)
{
pts->Reset();
ptIds->Reset();
if ( (index % 2) )
{
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(1));
pts->InsertPoint(3,this->Points->GetPoint(1));
ptIds->InsertId(4,this->PointIds->GetId(3));
pts->InsertPoint(4,this->Points->GetPoint(3));
ptIds->InsertId(5,this->PointIds->GetId(2));
pts->InsertPoint(5,this->Points->GetPoint(2));
}
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(0));
pts->InsertPoint(3,this->Points->GetPoint(0));
ptIds->InsertId(4,this->PointIds->GetId(3));
pts->InsertPoint(4,this->Points->GetPoint(3));
ptIds->InsertId(5,this->PointIds->GetId(2));
pts->InsertPoint(5,this->Points->GetPoint(2));
}
return 1;
}
//----------------------------------------------------------------------------
void vtkPixel::Derivatives(int vtkNotUsed(subId),
double pcoords[3],
double *values,
int dim, double *derivs)
{
double functionDerivs[8], sum;
int i, j, k, plane, idx[2], jj;
double x0[3], x1[3], x2[3], x3[3], spacing[3];
this->Points->GetPoint(0, x0);
this->Points->GetPoint(1, x1);
this->Points->GetPoint(2, x2);
this->Points->GetPoint(3, x3);
//figure which plane this pixel is in
for (i=0; i < 3; i++)
{
spacing[i] = x3[i] - x0[i];
}
if ( spacing[0] > spacing[2] && spacing[1] > spacing[2] ) // z-plane
{
plane = 2;
idx[0] = 0; idx[1] = 1;
}
else if ( spacing[0] > spacing[1] && spacing[2] > spacing[1] ) // y-plane
{
plane = 1;
idx[0] = 0; idx[1] = 2;
}
else // x-plane
{
plane = 0;
idx[0] = 1; idx[1] = 2;
}
spacing[0] = x1[idx[0]] - x0[idx[0]];
spacing[1] = x2[idx[1]] - x0[idx[1]];
// get derivatives in r-s directions
this->InterpolationDerivs(pcoords, functionDerivs);
// since two of the x-y-z axes are aligned with r-s axes, only need to scale
// the derivative values by the data spacing.
for (k=0; k < dim; k++) //loop over values per vertex
{
for (jj=j=0; j < 3; j++) //loop over derivative directions
{
if ( j == plane ) // 0-derivate values in this direction
{
sum = 0.0;
}
else //compute derivatives
{
for (sum=0.0, i=0; i < 4; i++) //loop over interp. function derivatives
{
sum += functionDerivs[4*jj + i] * values[dim*i + k];
}
sum /= spacing[idx[jj++]];
}
derivs[3*k + j] = sum;
}
}
}
//----------------------------------------------------------------------------
// support pixel clipping
typedef int PIXEL_EDGE_LIST;
typedef struct {
PIXEL_EDGE_LIST edges[14];
} PIXEL_CASES;
static PIXEL_CASES pixelCases[] = {
{{ -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, 103, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 4
{{ 3, 100, 0, 3, 3, 103, 2, 1, 4, 0, 1, 2, 3, -1}}, // 5
{{ 4, 101, 103, 2, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 6
{{ 3, 100, 101, 3, 3, 101, 2, 3, 3, 101, 103, 2, -1, -1}}, // 7
{{ 3, 102, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 8
{{ 4, 100, 0, 2, 102, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 9
{{ 3, 101, 1, 0, 3, 102, 3, 2, 4, 0, 1, 2, 3, -1}}, // 10
{{ 3, 100, 101, 1, 3, 100, 1, 2, 3, 100, 2, 102, -1, -1}}, // 11
{{ 4, 103, 102, 3, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 12
{{ 3, 100, 0, 102, 3, 0, 1, 102, 3, 1, 103, 102, -1, -1}}, // 13
{{ 3, 0, 101, 103, 3, 0, 103, 3, 3, 103, 102, 3, -1, -1}}, // 14
{{ 4, 100, 101, 103, 102, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 15
};
static PIXEL_CASES pixelCasesComplement[] = {
{{ -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, 103, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 4
{{ 3, 100, 0, 3, 3, 103, 2, 1, -1, -1, -1, -1, -1, -1}}, // 5
{{ 4, 101, 103, 2, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 6
{{ 3, 100, 101, 3, 3, 101, 2, 3, 3, 101, 103, 2, -1, -1}}, // 7
{{ 3, 102, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 8
{{ 4, 100, 0, 2, 102, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 9
{{ 3, 101, 1, 0, 3, 102, 3, 2, -1, -1, -1, -1, -1, -1}}, // 10
{{ 3, 100, 101, 1, 3, 100, 1, 2, 3, 100, 2, 102, -1, -1}}, // 11
{{ 4, 103, 102, 3, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 12
{{ 3, 100, 0, 102, 3, 0, 1, 102, 3, 1, 103, 102, -1, -1}}, // 13
{{ 3, 0, 101, 103, 3, 0, 103, 3, 3, 103, 102, 3, -1, -1}}, // 14
{{ 4, 100, 101, 103, 102, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 15
};
//----------------------------------------------------------------------------
// Clip this pixel using scalar value provided. Like contouring, except
// that it cuts the pixel to produce quads and/or triangles.
void vtkPixel::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] = {1,2,8,4}; //note difference from quad!
PIXEL_CASES *pixelCase;
PIXEL_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
pixelCase = pixelCases + 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
pixelCase = pixelCasesComplement + index;
}
edge = pixelCase->edges;
// generate each pixel
for ( ; edge[0] > -1; edge += edge[0]+1 )
{
for (i=0; i < edge[0]; i++) // insert pixel 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]) )
{
int p1 = this->PointIds->GetId(e1);
int 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 pixel
{
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 vtkPixelCellPCoords[12] = {0.0,0.0,0.0, 1.0,0.0,0.0,
0.0,1.0,0.0, 1.0,1.0,0.0};
double *vtkPixel::GetParametricCoords()
{
return vtkPixelCellPCoords;
}
//----------------------------------------------------------------------------
void vtkPixel::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os,indent);
os << indent << "Line:\n";
this->Line->PrintSelf(os,indent.GetNextIndent());
}