DGtal  1.5.beta
Functions
curvature-measures-nc-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/NormalCycleComputer.h"
#include "DGtal/io/writers/SurfaceMeshWriter.h"
#include "DGtal/io/colormaps/GradientColorMap.h"
#include "DGtal/io/colormaps/QuantifiedColorMap.h"
Include dependency graph for curvature-measures-nc-3d.cpp:

Go to the source code of this file.

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-nc-3d.

This file is part of the DGtal library.

Definition in file curvature-measures-nc-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 120 of file curvature-measures-nc-3d.cpp.

121 {
122  if ( argc <= 1 )
123  {
124  usage( argc, argv );
125  return 0;
126  }
128  using namespace DGtal;
129  using namespace DGtal::Z3i;
130  typedef SurfaceMesh< RealPoint, RealVector > SM;
131  typedef NormalCycleComputer< RealPoint, RealVector > NC;
132  typedef SurfaceMeshHelper< RealPoint, RealVector > SMH;
134  std::string input = argv[ 1 ];
135  int m = argc > 2 ? atoi( argv[ 2 ] ) : 20; // nb latitude points
136  int n = argc > 3 ? atoi( argv[ 3 ] ) : 20; // nb longitude points
137  double R = argc > 4 ? atof( argv[ 4 ] ) : 0.5; // radius of measuring ball
138 
140  SM smesh;
141  double exp_H_min = 0.0;
142  double exp_H_max = 0.0;
143  double exp_G_min = 0.0;
144  double exp_G_max = 0.0;
145  if ( input == "torus" )
146  {
147  const double big_radius = 3.0;
148  const double small_radius = 1.0;
149  smesh = SMH::makeTorus( big_radius, small_radius,
150  RealPoint { 0.0, 0.0, 0.0 }, m, n, 0,
151  SMH::NormalsType::VERTEX_NORMALS );
152  exp_H_min = ( 0.5 / ( small_radius - big_radius ) + 0.5 / small_radius );
153  exp_H_max = ( 0.5 / ( big_radius + small_radius ) + 0.5 / small_radius );
154  exp_G_min = ( 1.0 / ( small_radius - big_radius ) * 1.0 / small_radius );
155  exp_G_max = ( 1.0 / ( big_radius + small_radius ) * 1.0 / small_radius );
156  }
157  else if ( input == "sphere" )
158  {
159  const double radius = 2.0;
160  smesh = SMH::makeSphere( radius, RealPoint { 0.0, 0.0, 0.0 }, m, n,
161  SMH::NormalsType::VERTEX_NORMALS );
162  exp_H_min = 1.0 / radius;
163  exp_H_max = 1.0 / radius;
164  exp_G_min = 1.0 / ( radius * radius );
165  exp_G_max = 1.0 / ( radius * radius );
166  }
167  else if ( input == "lantern" )
168  {
169  const double radius = 2.0;
170  smesh = SMH::makeLantern( radius, 1.0, RealPoint { 0.0, 0.0, 0.0 }, m, n,
171  SMH::NormalsType::VERTEX_NORMALS );
172  exp_H_min = 0.5 / radius;
173  exp_H_max = 0.5 / radius;
174  exp_G_min = 0.0;
175  exp_G_max = 0.0;
176  }
178 
180  // builds a NormalCycleComputer object onto the mesh
181  NC nc( smesh );
182  // computes area, mean and Gaussian curvature measures
183  auto mu0 = nc.computeMu0();
184  auto mu1 = nc.computeMu1();
185  auto mu2 = nc.computeMu2();
187 
189  // estimates mean (H) and Gaussian (G) curvatures by measure normalization.
190  std::vector< double > H( smesh.nbFaces() );
191  std::vector< double > G( smesh.nbFaces() );
192  for ( auto f = 0; f < smesh.nbFaces(); ++f )
193  {
194  const auto b = smesh.faceCentroid( f );
195  const auto area = mu0.measure( b, R, f );
196  H[ f ] = nc.meanCurvature ( area, mu1.measure( b, R, f ) );
197  G[ f ] = nc.GaussianCurvature( area, mu2.measure( b, R, f ) );
198  }
200 
202  auto H_min_max = std::minmax_element( H.cbegin(), H.cend() );
203  auto G_min_max = std::minmax_element( G.cbegin(), G.cend() );
204  std::cout << "Expected mean curvatures:"
205  << " min=" << exp_H_min << " max=" << exp_H_max
206  << std::endl;
207  std::cout << "Computed mean curvatures:"
208  << " min=" << *H_min_max.first << " max=" << *H_min_max.second
209  << std::endl;
210  std::cout << "Expected Gaussian curvatures:"
211  << " min=" << exp_G_min << " max=" << exp_G_max
212  << std::endl;
213  std::cout << "Computed Gaussian curvatures:"
214  << " min=" << *G_min_max.first << " max=" << *G_min_max.second
215  << std::endl;
217 
219  typedef SurfaceMeshWriter< RealPoint, RealVector > SMW;
220  const auto colormapH = makeQuantifiedColorMap( makeColorMap( -0.625, 0.625 ) );
221  const auto colormapG = makeQuantifiedColorMap( makeColorMap( -0.625, 0.625 ) );
222  auto colorsH = SMW::Colors( smesh.nbFaces() );
223  auto colorsG = SMW::Colors( smesh.nbFaces() );
224  for ( auto i = 0; i < smesh.nbFaces(); i++ )
225  {
226  colorsH[ i ] = colormapH( H[ i ] );
227  colorsG[ i ] = colormapG( G[ i ] );
228  }
229  SMW::writeOBJ( "example-nc-H", smesh, colorsH );
230  SMW::writeOBJ( "example-nc-G", smesh, colorsG );
232  return 0;
233 }
DGtal::PointVector
Aim: Implements basic operations that will be used in Point and Vector classes.
Definition: PointVector.h:593
makeColorMap
DGtal::GradientColorMap< double > makeColorMap(double min_value, double max_value)
[curvature-measures-Includes]
Definition: curvature-measures-nc-3d.cpp:93
usage
void usage(int argc, char *argv[])
Definition: curvature-measures-nc-3d.cpp:104
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::NormalCycleComputer
Aim: Utility class to compute curvatures measures induced by (1) the normal cycle induced by a Surfac...
Definition: NormalCycleComputer.h:68
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 DGtal::H, 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 93 of file curvature-measures-nc-3d.cpp.

94 {
95  DGtal::GradientColorMap< double > gradcmap( min_value, max_value );
96  gradcmap.addColor( DGtal::Color( 0, 0, 255 ) );
97  gradcmap.addColor( DGtal::Color( 0, 255, 255 ) );
98  gradcmap.addColor( DGtal::Color( 255, 255, 255 ) );
99  gradcmap.addColor( DGtal::Color( 255, 255, 0 ) );
100  gradcmap.addColor( DGtal::Color( 255, 0, 0 ) );
101  return gradcmap;
102 }
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 104 of file curvature-measures-nc-3d.cpp.

105 {
106  std::cout << "Usage: " << std::endl
107  << "\t" << argv[ 0 ] << " <shape> <m> <n> <R>" << std::endl
108  << std::endl
109  << "Computation of mean and Gaussian curvatures on a shape, " << std::endl
110  << "using Normal cycle curvature measures (based on the" << std::endl
111  << "theory of Normal cycle)" << std::endl
112  << "- builds a <shape> in {torus,lantern,sphere}, with " << std::endl
113  << " <m> latitude points and <n> longitude points." << std::endl
114  << "- <R> is the radius of the measuring balls." << std::endl
115  << "It produces several OBJ files to display mean and" << std::endl
116  << "Gaussian curvature estimation results: `example-cnc-H.obj`" << std::endl
117  << "and `example-cnc-G.obj` as well as the associated MTL file." << std::endl;
118 }

Referenced by main().