DGtal  1.4.beta
Functions
curvature-measures-icnc-XY-3d.cpp File Reference
DGtal Examples
#include <iostream>
#include <algorithm>
#include "DGtal/base/Common.h"
#include "DGtal/shapes/SurfaceMesh.h"
#include "DGtal/shapes/SurfaceMeshHelper.h"
#include "DGtal/geometry/meshes/CorrectedNormalCurrentComputer.h"
#include "DGtal/io/writers/SurfaceMeshWriter.h"
#include "DGtal/io/colormaps/GradientColorMap.h"
#include "DGtal/io/colormaps/QuantifiedColorMap.h"
#include "DGtal/helpers/Shortcuts.h"
Include dependency graph for curvature-measures-icnc-XY-3d.cpp:

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Functions

DGtal::GradientColorMap< double > makeColorMap (double min_value, double max_value)
 [curvature-measures-Includes] More...
 
void usage (int argc, char *argv[])
 
int main (int argc, char *argv[])
 

Detailed Description

This program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.

Author
Jacques-Olivier Lachaud (jacqu.nosp@m.es-o.nosp@m.livie.nosp@m.r.la.nosp@m.chaud.nosp@m.@uni.nosp@m.v-sav.nosp@m.oie..nosp@m.fr ) Laboratory of Mathematics (CNRS, UMR 5127), University of Savoie, France
Date
2021/10/25

An example file named curvature-measures-icnc-XY-3d.

This file is part of the DGtal library.

Definition in file curvature-measures-icnc-XY-3d.cpp.

Function Documentation

◆ main()

int main ( int  argc,
char *  argv[] 
)

[curvature-measures-Typedefs]

[curvature-measures-Typedefs]

[curvature-measures-SurfaceMesh]

[curvature-measures-SurfaceMesh]

[curvature-measures-CNC]

[curvature-measures-CNC]

[curvature-measures-estimations]

[curvature-measures-estimations]

[curvature-measures-check]

[curvature-measures-check]

[curvature-measures-output]

[curvature-measures-output]

Definition at line 139 of file curvature-measures-icnc-XY-3d.cpp.

140 {
141  if ( argc <= 1 )
142  {
143  usage( argc, argv );
144  return 0;
145  }
147  using namespace DGtal;
148  using namespace DGtal::Z3i;
149  typedef SurfaceMesh< RealPoint, RealVector > SM;
150  typedef CorrectedNormalCurrentComputer< RealPoint, RealVector > CNC;
151  typedef SurfaceMeshHelper< RealPoint, RealVector > SMH;
153  // a shape in "torus|lantern|sphere"
154  std::string input = argv[ 1 ];
155  int m = argc > 2 ? atoi( argv[ 2 ] ) : 20; // nb latitude points
156  int n = argc > 3 ? atoi( argv[ 3 ] ) : 20; // nb longitude points
157  double R = argc > 4 ? atof( argv[ 4 ] ) : 0.5; // radius of measuring ball
158 
160  SM smesh;
161  double exp_K1_min = 0.0;
162  double exp_K1_max = 0.0;
163  double exp_K2_min = 0.0;
164  double exp_K2_max = 0.0;
165  if ( input == "torus" )
166  {
167  const double big_radius = 3.0;
168  const double small_radius = 1.00001; // avoid codacy warnings
169  smesh = SMH::makeTorus( big_radius, small_radius,
170  RealPoint { 0.0, 0.0, 0.0 }, m, n, 0,
171  SMH::NormalsType::VERTEX_NORMALS );
172  exp_K1_min = ( 1.0 / ( small_radius - big_radius ) );
173  exp_K1_max = ( 1.0 / ( big_radius + small_radius ) );
174  exp_K2_min = 1.0 / small_radius;
175  exp_K2_max = 1.0 / small_radius;
176  }
177  else if ( input == "sphere" )
178  {
179  const double radius = 2.0;
180  smesh = SMH::makeSphere( radius, RealPoint { 0.0, 0.0, 0.0 }, m, n,
181  SMH::NormalsType::VERTEX_NORMALS );
182  exp_K1_min = 1.0 / radius;
183  exp_K1_max = 1.0 / radius;
184  exp_K2_min = 1.0 / radius;
185  exp_K2_max = 1.0 / radius;
186  }
187  else if ( input == "lantern" )
188  {
189  const double radius = 2.0;
190  smesh = SMH::makeLantern( radius, 1.0, RealPoint { 0.0, 0.0, 0.0 }, m, n,
191  SMH::NormalsType::VERTEX_NORMALS );
192  exp_K1_min = 0.0;
193  exp_K1_max = 0.0;
194  exp_K2_min = 1.0 / radius;
195  exp_K2_max = 1.0 / radius;
196  }
198 
200  // builds a CorrectedNormalCurrentComputer object onto the mesh
201  CNC cnc( smesh );
202  // computes area, anisotropic XY curvature measures
203  auto mu0 = cnc.computeMu0();
204  auto muXY = cnc.computeMuXY();
206 
208  // Estimates principal curvatures (K1,K2) and directions (D1,D2) by
209  // measure normalization and eigen decomposition.
210  std::vector< double > K1( smesh.nbFaces() );
211  std::vector< double > K2( smesh.nbFaces() );
212  std::vector< RealVector > D1( smesh.nbFaces() );
213  std::vector< RealVector > D2( smesh.nbFaces() );
214  // Principal directions computation requires a local face normal
215  smesh.computeFaceNormalsFromPositions();
216  for ( auto f = 0; f < smesh.nbFaces(); ++f )
217  {
218  const auto b = smesh.faceCentroid( f );
219  const auto N = smesh.faceNormals()[ f ];
220  const auto area = mu0 .measure( b, R, f );
221  const auto M = muXY.measure( b, R, f );
222  std::tie( K1[ f ], K2[ f ], D1[ f ], D2[ f ] )
223  = cnc.principalCurvatures( area, M, N );
224  }
226 
228  auto K1_min_max = std::minmax_element( K1.cbegin(), K1.cend() );
229  auto K2_min_max = std::minmax_element( K2.cbegin(), K2.cend() );
230  std::cout << "Expected k1 curvatures:"
231  << " min=" << exp_K1_min << " max=" << exp_K1_max
232  << std::endl;
233  std::cout << "Computed k1 curvatures:"
234  << " min=" << *K1_min_max.first << " max=" << *K1_min_max.second
235  << std::endl;
236  std::cout << "Expected k2 curvatures:"
237  << " min=" << exp_K2_min << " max=" << exp_K2_max
238  << std::endl;
239  std::cout << "Computed k2 curvatures:"
240  << " min=" << *K2_min_max.first << " max=" << *K2_min_max.second
241  << std::endl;
243 
245  typedef SurfaceMeshWriter< RealPoint, RealVector > SMW;
246  typedef Shortcuts< KSpace > SH;
247  const auto colormapK1 = makeQuantifiedColorMap( makeColorMap( -0.625, 0.625 ) );
248  const auto colormapK2 = makeQuantifiedColorMap( makeColorMap( -0.625, 0.625 ) );
249  auto colorsK1 = SMW::Colors( smesh.nbFaces() );
250  auto colorsK2 = SMW::Colors( smesh.nbFaces() );
251  for ( auto i = 0; i < smesh.nbFaces(); i++ )
252  {
253  colorsK1[ i ] = colormapK1( K1[ i ] );
254  colorsK2[ i ] = colormapK2( K2[ i ] );
255  }
256  SMW::writeOBJ( "example-cnc-K1", smesh, colorsK1 );
257  SMW::writeOBJ( "example-cnc-K2", smesh, colorsK2 );
258  const auto avg_e = smesh.averageEdgeLength();
259  SH::RealPoints positions( smesh.nbFaces() );
260  for ( auto f = 0; f < positions.size(); ++f )
261  {
262  D1[ f ] *= smesh.localWindow( f );
263  positions[ f ] = smesh.faceCentroid( f ) - 0.5 * D1[ f ];
264  }
265  SH::saveVectorFieldOBJ( positions, D1, 0.05 * avg_e, SH::Colors(),
266  "example-cnc-D1",
267  SH::Color::Black, SH::Color( 0, 128, 0 ) );
268  for ( auto f = 0; f < positions.size(); ++f )
269  {
270  D2[ f ] *= smesh.localWindow( f );
271  positions[ f ] = smesh.faceCentroid( f ) - 0.5 * D2[ f ];
272  }
273  SH::saveVectorFieldOBJ( positions, D2, 0.05 * avg_e, SH::Colors(),
274  "example-cnc-D2",
275  SH::Color::Black, SH::Color(128, 0,128 ) );
276 
278  return 0;
279 }
DGtal::PointVector
Aim: Implements basic operations that will be used in Point and Vector classes.
Definition: PointVector.h:593
DGtal::Shortcuts
Aim: This class is used to simplify shape and surface creation. With it, you can create new shapes an...
Definition: Shortcuts.h:105
makeColorMap
DGtal::GradientColorMap< double > makeColorMap(double min_value, double max_value)
[curvature-measures-Includes]
Definition: curvature-measures-icnc-XY-3d.cpp:111
usage
void usage(int argc, char *argv[])
Definition: curvature-measures-icnc-XY-3d.cpp:122
DGtal::Z2i::K2
KSpace K2
Definition: StdDefs.h:78
DGtal::Z3i
Z3i this namespace gathers the standard of types for 3D imagery.
DGtal
DGtal is the top-level namespace which contains all DGtal functions and types.
DGtal::makeQuantifiedColorMap
QuantifiedColorMap< TColorMap > makeQuantifiedColorMap(TColorMap colormap, int nb=50)
Definition: QuantifiedColorMap.h:113
DGtal::CorrectedNormalCurrentComputer
Aim: Utility class to compute curvature measures induced by (1) a corrected normal current defined by...
Definition: CorrectedNormalCurrentComputer.h:70
DGtal::SurfaceMeshHelper
Aim: An helper class for building classical meshes.
Definition: SurfaceMeshHelper.h:64
DGtal::SurfaceMeshWriter
Aim: An helper class for writing mesh file formats (Waverfront OBJ at this point) and creating a Surf...
Definition: SurfaceMeshWriter.h:65
DGtal::SurfaceMesh
Aim: Represents an embedded mesh as faces and a list of vertices. Vertices may be shared among faces ...
Definition: SurfaceMesh.h:92

References makeColorMap(), DGtal::makeQuantifiedColorMap(), and usage().

◆ makeColorMap()

DGtal::GradientColorMap< double > makeColorMap ( double  min_value,
double  max_value 
)

[curvature-measures-Includes]

[curvature-measures-Includes]

Definition at line 111 of file curvature-measures-icnc-XY-3d.cpp.

112 {
113  DGtal::GradientColorMap< double > gradcmap( min_value, max_value );
114  gradcmap.addColor( DGtal::Color( 0, 0, 255 ) );
115  gradcmap.addColor( DGtal::Color( 0, 255, 255 ) );
116  gradcmap.addColor( DGtal::Color( 255, 255, 255 ) );
117  gradcmap.addColor( DGtal::Color( 255, 255, 0 ) );
118  gradcmap.addColor( DGtal::Color( 255, 0, 0 ) );
119  return gradcmap;
120 }
DGtal::Color
Structure representing an RGB triple with alpha component.
Definition: Color.h:68
DGtal::GradientColorMap
Aim: This class template may be used to (linearly) convert scalar values in a given range into a colo...
Definition: GradientColorMap.h:120

References DGtal::GradientColorMap< PValue, PDefaultPreset, PDefaultFirstColor, PDefaultLastColor >::addColor().

Referenced by main().

◆ usage()

void usage ( int  argc,
char *  argv[] 
)

Definition at line 122 of file curvature-measures-icnc-XY-3d.cpp.

123 {
124  std::cout << "Usage: " << std::endl
125  << "\t" << argv[ 0 ] << " <shape> <m> <n> <R>" << std::endl
126  << std::endl
127  << "Computation of principal curvatures and directions on a shape, " << std::endl
128  << "using interpolated corrected curvature measures (based " << std::endl
129  << "on the theory of corrected normal currents)." << std::endl
130  << "- builds a <shape> in {torus,lantern,sphere}, with " << std::endl
131  << " <m> latitude points and <n> longitude points." << std::endl
132  << "- <R> is the radius of the measuring balls." << std::endl
133  << "It produces several OBJ files to display principal " << std::endl
134  << "curvatures and directions estimations: `example-cnc-K1.obj`" << std::endl
135  << "`example-cnc-K2.obj`, `example-cnc-D1.obj`, and" << std::endl
136  << "`example-cnc-D2.obj` as well as associated MTL files." << std::endl;
137 }

Referenced by main().