/usr/include/vtk-5.8/vtkDelaunay3D.h is in libvtk5-dev 5.8.0-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 | /*=========================================================================
Program: Visualization Toolkit
Module: vtkDelaunay3D.h
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.
=========================================================================*/
// .NAME vtkDelaunay3D - create 3D Delaunay triangulation of input points
// .SECTION Description
// vtkDelaunay3D is a filter that constructs a 3D Delaunay
// triangulation from a list of input points. These points may be
// represented by any dataset of type vtkPointSet and subclasses. The
// output of the filter is an unstructured grid dataset. Usually the
// output is a tetrahedral mesh, but if a non-zero alpha distance
// value is specified (called the "alpha" value), then only tetrahedra,
// triangles, edges, and vertices lying within the alpha radius are
// output. In other words, non-zero alpha values may result in arbitrary
// combinations of tetrahedra, triangles, lines, and vertices. (The notion
// of alpha value is derived from Edelsbrunner's work on "alpha shapes".)
//
// The 3D Delaunay triangulation is defined as the triangulation that
// satisfies the Delaunay criterion for n-dimensional simplexes (in
// this case n=3 and the simplexes are tetrahedra). This criterion
// states that a circumsphere of each simplex in a triangulation
// contains only the n+1 defining points of the simplex. (See text for
// more information.) While in two dimensions this translates into an
// "optimal" triangulation, this is not true in 3D, since a measurement
// for optimality in 3D is not agreed on.
//
// Delaunay triangulations are used to build topological structures
// from unorganized (or unstructured) points. The input to this filter
// is a list of points specified in 3D. (If you wish to create 2D
// triangulations see vtkDelaunay2D.) The output is an unstructured grid.
//
// The Delaunay triangulation can be numerically sensitive. To prevent
// problems, try to avoid injecting points that will result in
// triangles with bad aspect ratios (1000:1 or greater). In practice
// this means inserting points that are "widely dispersed", and
// enables smooth transition of triangle sizes throughout the
// mesh. (You may even want to add extra points to create a better
// point distribution.) If numerical problems are present, you will
// see a warning message to this effect at the end of the
// triangulation process.
// .SECTION Caveats
// Points arranged on a regular lattice (termed degenerate cases) can be
// triangulated in more than one way (at least according to the Delaunay
// criterion). The choice of triangulation (as implemented by
// this algorithm) depends on the order of the input points. The first four
// points will form a tetrahedron; other degenerate points (relative to this
// initial tetrahedron) will not break it.
//
// Points that are coincident (or nearly so) may be discarded by the
// algorithm. This is because the Delaunay triangulation requires
// unique input points. You can control the definition of coincidence
// with the "Tolerance" instance variable.
//
// The output of the Delaunay triangulation is supposedly a convex hull. In
// certain cases this implementation may not generate the convex hull. This
// behavior can be controlled by the Offset instance variable. Offset is a
// multiplier used to control the size of the initial triangulation. The
// larger the offset value, the more likely you will generate a convex hull;
// and the more likely you are to see numerical problems.
//
// The implementation of this algorithm varies from the 2D Delaunay
// algorithm (i.e., vtkDelaunay2D) in an important way. When points are
// injected into the triangulation, the search for the enclosing tetrahedron
// is quite different. In the 3D case, the closest previously inserted point
// point is found, and then the connected tetrahedra are searched to find
// the containing one. (In 2D, a "walk" towards the enclosing triangle is
// performed.) If the triangulation is Delaunay, then an enclosing tetrahedron
// will be found. However, in degenerate cases an enclosing tetrahedron may
// not be found and the point will be rejected.
// .SECTION See Also
// vtkDelaunay2D vtkGaussianSplatter vtkUnstructuredGrid
#ifndef __vtkDelaunay3D_h
#define __vtkDelaunay3D_h
#include "vtkUnstructuredGridAlgorithm.h"
class vtkIdList;
class vtkPointLocator;
class vtkPointSet;
class vtkPoints;
class vtkTetraArray;
class vtkIncrementalPointLocator;
class VTK_GRAPHICS_EXPORT vtkDelaunay3D : public vtkUnstructuredGridAlgorithm
{
public:
vtkTypeMacro(vtkDelaunay3D,vtkUnstructuredGridAlgorithm);
void PrintSelf(ostream& os, vtkIndent indent);
// Description:
// Construct object with Alpha = 0.0; Tolerance = 0.001; Offset = 2.5;
// BoundingTriangulation turned off.
static vtkDelaunay3D *New();
// Description:
// Specify alpha (or distance) value to control output of this filter.
// For a non-zero alpha value, only edges, faces, or tetra contained
// within the circumsphere (of radius alpha) will be output. Otherwise,
// only tetrahedra will be output.
vtkSetClampMacro(Alpha,double,0.0,VTK_DOUBLE_MAX);
vtkGetMacro(Alpha,double);
// Description:
// Specify a tolerance to control discarding of closely spaced points.
// This tolerance is specified as a fraction of the diagonal length of
// the bounding box of the points.
vtkSetClampMacro(Tolerance,double,0.0,1.0);
vtkGetMacro(Tolerance,double);
// Description:
// Specify a multiplier to control the size of the initial, bounding
// Delaunay triangulation.
vtkSetClampMacro(Offset,double,2.5,VTK_DOUBLE_MAX);
vtkGetMacro(Offset,double);
// Description:
// Boolean controls whether bounding triangulation points (and associated
// triangles) are included in the output. (These are introduced as an
// initial triangulation to begin the triangulation process. This feature
// is nice for debugging output.)
vtkSetMacro(BoundingTriangulation,int);
vtkGetMacro(BoundingTriangulation,int);
vtkBooleanMacro(BoundingTriangulation,int);
// Description:
// Set / get a spatial locator for merging points. By default,
// an instance of vtkPointLocator is used.
void SetLocator(vtkIncrementalPointLocator *locator);
vtkGetObjectMacro(Locator,vtkIncrementalPointLocator);
// Description:
// Create default locator. Used to create one when none is specified. The
// locator is used to eliminate "coincident" points.
void CreateDefaultLocator();
// Description:
// This is a helper method used with InsertPoint() to create
// tetrahedronalizations of points. Its purpose is construct an initial
// Delaunay triangulation into which to inject other points. You must
// specify the center of a cubical bounding box and its length, as well
// as the number of points to insert. The method returns a pointer to
// an unstructured grid. Use this pointer to manipulate the mesh as
// necessary. You must delete (with Delete()) the mesh when done.
// Note: This initialization method places points forming bounding octahedron
// at the end of the Mesh's point list. That is, InsertPoint() assumes that
// you will be inserting points between (0,numPtsToInsert-1).
vtkUnstructuredGrid *InitPointInsertion(double center[3], double length,
vtkIdType numPts, vtkPoints* &pts);
// Description:
// This is a helper method used with InitPointInsertion() to create
// tetrahedronalizations of points. Its purpose is to inject point at
// coordinates specified into tetrahedronalization. The point id is an index
// into the list of points in the mesh structure. (See
// vtkDelaunay3D::InitPointInsertion() for more information.) When you have
// completed inserting points, traverse the mesh structure to extract desired
// tetrahedra (or tetra faces and edges).The holeTetras id list lists all the
// tetrahedra that are deleted (invalid) in the mesh structure.
void InsertPoint(vtkUnstructuredGrid *Mesh, vtkPoints *points,
vtkIdType id, double x[3], vtkIdList *holeTetras);
// Description:
// Invoke this method after all points have been inserted. The purpose of
// the method is to clean up internal data structures. Note that the
// (vtkUnstructuredGrid *)Mesh returned from InitPointInsertion() is NOT
// deleted, you still are responsible for cleaning that up.
void EndPointInsertion();
// Description:
// Return the MTime also considering the locator.
unsigned long GetMTime();
protected:
vtkDelaunay3D();
~vtkDelaunay3D();
int RequestData(vtkInformation *, vtkInformationVector **, vtkInformationVector *);
double Alpha;
double Tolerance;
int BoundingTriangulation;
double Offset;
vtkIncrementalPointLocator *Locator; //help locate points faster
vtkTetraArray *TetraArray; //used to keep track of circumspheres/neighbors
int FindTetra(vtkUnstructuredGrid *Mesh, double x[3], vtkIdType tetId,
int depth);
int InSphere(double x[3], vtkIdType tetraId);
void InsertTetra(vtkUnstructuredGrid *Mesh, vtkPoints *pts,
vtkIdType tetraId);
int NumberOfDuplicatePoints; //keep track of bad data
int NumberOfDegeneracies;
// Keep track of number of references to points to avoid new/delete calls
int *References;
vtkIdType FindEnclosingFaces(double x[3], vtkUnstructuredGrid *Mesh,
vtkIdList *tetras, vtkIdList *faces,
vtkIncrementalPointLocator *Locator);
virtual int FillInputPortInformation(int, vtkInformation*);
private: //members added for performance
vtkIdList *Tetras; //used in InsertPoint
vtkIdList *Faces; //used in InsertPoint
vtkIdList *BoundaryPts; //used by InsertPoint
vtkIdList *CheckedTetras; //used by InsertPoint
vtkIdList *NeiTetras; //used by InsertPoint
private:
vtkDelaunay3D(const vtkDelaunay3D&); // Not implemented.
void operator=(const vtkDelaunay3D&); // Not implemented.
};
#endif
|