DGtal  0.9.4beta
trackImplicitPolynomialSurfaceToOFF.cpp
1 
55 #include <iostream>
58 #include "DGtal/helpers/StdDefs.h"
59 #include "DGtal/topology/helpers/Surfaces.h"
60 #include "DGtal/topology/DigitalSurface.h"
61 #include "DGtal/topology/SetOfSurfels.h"
62 #include "DGtal/math/MPolynomial.h"
63 #include "DGtal/shapes/GaussDigitizer.h"
64 #include "DGtal/shapes/implicit/ImplicitPolynomial3Shape.h"
65 #include "DGtal/shapes/implicit/ImplicitFunctionDiff1LinearCellEmbedder.h"
66 #include "DGtal/io/readers/MPolynomialReader.h"
68 
70 
71 using namespace std;
72 using namespace DGtal;
73 using namespace Z3i;
74 
76 
77 
78 void usage( int /*argc*/, char** argv )
79 {
80  std::cerr << "Usage: " << argv[ 0 ] << " <Polynomial> <Px> <Py> <Pz> <Qx> <Qy> <Qz> <step>" << std::endl;
81  std::cerr << "\t - displays the boundary of a shape defined implicitly by a 3-polynomial <Polynomial>." << std::endl;
82  std::cerr << "\t - P and Q defines the bounding box." << std::endl;
83  std::cerr << "\t - step is the grid step." << std::endl;
84  std::cerr << "\t - You may try x^3y+xz^3+y^3z+z^3+5z or (y^2+z^2-1)^2 +(x^2+y^2-1)^3 " << std::endl;
85  std::cerr << "\t - See http://www.freigeist.cc/gallery.html" << std::endl;
86 }
87 
88 int main( int argc, char** argv )
89 {
90  if ( argc < 9 )
91  {
92  usage( argc, argv );
93  return 1;
94  }
95  double p1[ 3 ];
96  double p2[ 3 ];
97  for ( unsigned int i = 0; i < 3; ++i )
98  {
99  p1[ i ] = atof( argv[ 2+i ] );
100  p2[ i ] = atof( argv[ 5+i ] );
101  }
102  double step = atof( argv[ 8 ] );
103 
105  trace.beginBlock( "Making polynomial surface." );
106  typedef Space::RealPoint RealPoint;
107  typedef RealPoint::Coordinate Ring;
113 
114  // See http://www.freigeist.cc/gallery.html
115  Polynomial3 P;
116  Polynomial3Reader reader;
117  std::string poly_str = argv[ 1 ];
118  std::string::const_iterator iter
119  = reader.read( P, poly_str.begin(), poly_str.end() );
120  if ( iter != poly_str.end() )
121  {
122  std::cerr << "ERROR: I read only <"
123  << poly_str.substr( 0, iter - poly_str.begin() )
124  << ">, and I built P=" << P << std::endl;
125  return 1;
126  }
127  // Durchblick x3y+xz3+y3z+z3+5z = 0
128 
129  // MPolynomial<3, double> P = mmonomial<double>( 3, 1, 0 )
130  // + mmonomial<double>( 1, 0, 3 )
131  // + mmonomial<double>( 0, 3, 1 )
132  // + mmonomial<double>( 0, 0, 3 )
133  // + 5 * mmonomial<double>( 0, 0, 1 );
134  // Crixxi (y2+z2-1)2 +(x2+y2-1)3 = 0
135  // developed = y4 +2y2z2+z4-2z2 -y2 + x6+3x4y2+3x2y4+y6-3x4-6x2y2-3y4+3x2
136  // MPolynomial<3, double> P = mmonomial<double>(0,4,0)
137  // + 2 * mmonomial<double>(0,2,2)
138  // + mmonomial<double>(0,2,0)
139  // + mmonomial<double>(0,0,4)
140  // - 2 * mmonomial<double>(0,0,2)
141  // + mmonomial<double>(6,0,0)
142  // + 3 * mmonomial<double>(4,2,0)
143  // + 3 * mmonomial<double>(2,4,0)
144  // + mmonomial<double>(0,6,0)
145  // - 3 * mmonomial<double>(4,0,0)
146  // - 6 * mmonomial<double>(2,2,0)
147  // - 3 * mmonomial<double>(0,4,0)
148  // + 3 * mmonomial<double>(2,0,0);
149 
150  trace.info() << "P( X_0, X_1, X_2 ) = " << P << std::endl;
151  ImplicitShape ishape( P );
152  DigitalShape dshape;
153  dshape.attach( ishape );
154  dshape.init( RealPoint( p1 ), RealPoint( p2 ), step );
155  Domain domain = dshape.getDomain();
156  trace.endBlock();
158 
160  // Construct the Khalimsky space from the image domain
161  KSpace K;
162  // NB: it is \b necessary to work with a \b closed cellular space
163  // since umbrellas use separators and pivots, which must exist for
164  // arbitrary surfels.
165  bool space_ok = K.init( domain.lowerBound(),
166  domain.upperBound(), true // necessary
167  );
168  if (!space_ok)
169  {
170  trace.error() << "Error in the Khamisky space construction."<<std::endl;
171  return 2;
172  }
174 
176  typedef SurfelAdjacency<KSpace::dimension> MySurfelAdjacency;
177  MySurfelAdjacency surfAdj( true ); // interior in all directions.
179 
181  trace.beginBlock( "Extracting boundary by tracking the space. " );
182  typedef KSpace::Surfel Surfel;
183  typedef KSpace::SurfelSet SurfelSet;
184  typedef SetOfSurfels< KSpace, SurfelSet > MySetOfSurfels;
186 
187  // The surfels are tracked from an initial surfel, which is found by
188  // try/error.
189  MySetOfSurfels theSetOfSurfels( K, surfAdj );
190  Surfel bel = Surfaces<KSpace>::findABel( K, dshape, 100000 );
191  Surfaces<KSpace>::trackBoundary( theSetOfSurfels.surfelSet(),
192  K, surfAdj,
193  dshape, bel );
194  trace.endBlock();
196 
198  trace.beginBlock( "Making OFF surface <marching-cube.off>. " );
199  MyDigitalSurface digSurf( theSetOfSurfels );
200  trace.info() << "Digital surface has " << digSurf.size() << " surfels."
201  << std::endl;
202  // The cell embedder is used to place vertices closer to the set
203  // P(x,y,z)=0
204  typedef
206  ImplicitShape,
207  DigitalEmbedder >
208  CellEmbedder;
209  CellEmbedder cellEmbedder;
210  cellEmbedder.init( K, ishape, dshape.pointEmbedder() );
211  ofstream out( "marching-cube.off" );
212  if ( out.good() )
213  digSurf.exportEmbeddedSurfaceAs3DOFF( out, cellEmbedder );
214  out.close();
215  trace.endBlock();
217  trace.beginBlock( "Making NOFF surface <marching-cube.noff>. " );
218  ofstream out2( "marching-cube.noff" );
219  if ( out2.good() )
220  digSurf.exportEmbeddedSurfaceAs3DNOFF( out2, cellEmbedder );
221  out2.close();
222  trace.endBlock();
223 
224  return 0;
225 }
void beginBlock(const std::string &keyword="")
Iterator read(Polynomial &p, Iterator begin, Iterator end)
Aim: a cellular embedder for implicit functions, (default constructible, copy constructible, assignable). Model of CCellEmbedder and CWithGradientMap.
Trace trace
Definition: Common.h:137
Aim: A utility class for constructing surfaces (i.e. set of (n-1)-cells).
Definition: Surfaces.h:78
KhalimskySpaceND< 2, Integer > KSpace
Definition: StdDefs.h:77
Aim: This class converts a string polynomial expression in a multivariate polynomial.
STL namespace.
double endBlock()
Aim: Represents a set of n-1-cells in a nD space, together with adjacency relation between these cell...
Aim: Implements basic operations that will be used in Point and Vector classes.
Definition: PointVector.h:141
void attach(const EuclideanShape &shape)
void init(const RealPoint &xLow, const RealPoint &xUp, typename RealVector::Component gridStep)
Aim: A class for computing the Gauss digitization of some Euclidean shape, i.e. its intersection with...
Domain getDomain() const
Aim: model of CEuclideanOrientedShape concepts to create a shape from a polynomial.
const Point & upperBound() const
DGtal is the top-level namespace which contains all DGtal functions and types.
std::ostream & info()
Aim: A model of CDigitalSurfaceContainer which defines the digital surface as connected surfels...
Definition: SetOfSurfels.h:73
Space::RealPoint RealPoint
Definition: StdDefs.h:97
const Point & lowerBound() const
std::ostream & error()