DGtal  1.2.0
testConvexityHelper.cpp
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1
31 #include <iostream>
32 #include <vector>
33 #include <algorithm>
34 #include "DGtal/base/Common.h"
35 #include "DGtal/kernel/SpaceND.h"
36 #include "DGtal/geometry/volumes/ConvexityHelper.h"
37 #include "DGtal/shapes/SurfaceMesh.h"
38 #include "DGtalCatch.h"
40
41 using namespace std;
42 using namespace DGtal;
43
44
46 // Functions for testing class ConvexityHelper in 2D.
48
49 SCENARIO( "ConvexityHelper< 2 > unit tests",
50  "[convexity_helper][lattice_polytope][2d]" )
51 {
52  typedef ConvexityHelper< 2 > Helper;
53  typedef Helper::Point Point;
54  typedef ConvexCellComplex< Point > CvxCellComplex;
55  GIVEN( "Given a star { (0,0), (-4,-1), (-3,5), (7,3), (5, -2) } " ) {
56  std::vector<Point> V
57  = { Point(0,0), Point(-4,-1), Point(-3,5), Point(7,3), Point(5, -2) };
58  WHEN( "Computing its lattice polytope" ){
59  const auto P = Helper::computeLatticePolytope( V, false, true );
60  CAPTURE( P );
61  THEN( "The polytope is valid and has 4 non trivial facets" ) {
62  REQUIRE( P.nbHalfSpaces() - 4 == 4 );
63  }
64  THEN( "The polytope is Minkowski summable" ) {
65  REQUIRE( P.canBeSummed() );
66  }
67  THEN( "The polytope contains the input points" ) {
68  REQUIRE( P.isInside( V[ 0 ] ) );
69  REQUIRE( P.isInside( V[ 1 ] ) );
70  REQUIRE( P.isInside( V[ 2 ] ) );
71  REQUIRE( P.isInside( V[ 3 ] ) );
72  REQUIRE( P.isInside( V[ 4 ] ) );
73  }
74  THEN( "The polytope contains 58 points" ) {
75  REQUIRE( P.count() == 58 );
76  }
77  THEN( "The interior of the polytope contains 53 points" ) {
78  REQUIRE( P.countInterior() == 53 );
79  }
80  THEN( "The boundary of the polytope contains 5 points" ) {
81  REQUIRE( P.countBoundary() == 5 );
82  }
83  }
84  }
85  GIVEN( "Given a square with an additional outside vertex " ) {
86  std::vector<Point> V
87  = { Point(-10,-10), Point(10,-10), Point(-10,10), Point(10,10),
88  Point(0,18) };
89  WHEN( "Computing its Delaunay cell complex" ){
90  CvxCellComplex complex;
91  bool ok = Helper::computeDelaunayCellComplex( complex, V, false );
92  CAPTURE( complex );
93  THEN( "The complex has 2 cells, 6 faces, 5 vertices" ) {
94  REQUIRE( ok );
95  REQUIRE( complex.nbCells() == 2 );
96  REQUIRE( complex.nbFaces() == 6 );
97  REQUIRE( complex.nbVertices() == 5 );
98  }
99  THEN( "The faces of cells are finite" ) {
100  bool ok_finite = true;
101  for ( auto c = 0; c < complex.nbCells(); ++c ) {
102  const auto faces = complex.cellFaces( c );
103  for ( auto f : faces )
104  ok_finite = ok_finite && ! complex.isInfinite( complex.faceCell( f ) );
105  }
106  REQUIRE( ok_finite );
107  }
108  THEN( "The opposite of faces of cells are infinite except two" ) {
109  int nb_finite = 0;
110  for ( auto c = 0; c < complex.nbCells(); ++c ) {
111  const auto faces = complex.cellFaces( c );
112  for ( auto f : faces ) {
113  const auto opp_f = complex.opposite( f );
114  nb_finite += complex.isInfinite( complex.faceCell( opp_f ) ) ? 0 : 1;
115  }
116  }
117  REQUIRE( nb_finite == 2 );
118  }
119  }
120  }
121 }
122
124 // Functions for testing class ConvexityHelper in 3D.
126
127 SCENARIO( "ConvexityHelper< 3 > unit tests",
128  "[convexity_helper][3d]" )
129 {
130  typedef ConvexityHelper< 3 > Helper;
131  typedef Helper::Point Point;
135  typedef PolygonalSurface< Point > LatticePolySurf;
136  typedef ConvexCellComplex< Point > CvxCellComplex;
137  GIVEN( "Given an octahedron star { (0,0,0), (-2,0,0), (2,0,0), (0,-2,0), (0,2,0), (0,0,-2), (0,0,2) } " ) {
138  std::vector<Point> V
139  = { Point(0,0,0), Point(-2,0,0), Point(2,0,0), Point(0,-2,0), Point(0,2,0),
140  Point(0,0,-2), Point(0,0,2) };
141  WHEN( "Computing its lattice polytope" ){
142  const auto P = Helper::computeLatticePolytope( V, false, true );
143  CAPTURE( P );
144  THEN( "The polytope is valid and has 8 non trivial facets plus 12 edge constraints" ) {
145  REQUIRE( P.nbHalfSpaces() - 6 == 20 );
146  }
147  THEN( "The polytope is Minkowski summable" ) {
148  REQUIRE( P.canBeSummed() );
149  }
150  THEN( "The polytope contains the input points" ) {
151  REQUIRE( P.isInside( V[ 0 ] ) );
152  REQUIRE( P.isInside( V[ 1 ] ) );
153  REQUIRE( P.isInside( V[ 2 ] ) );
154  REQUIRE( P.isInside( V[ 3 ] ) );
155  REQUIRE( P.isInside( V[ 4 ] ) );
156  REQUIRE( P.isInside( V[ 5 ] ) );
157  REQUIRE( P.isInside( V[ 6 ] ) );
158  }
159  THEN( "The polytope contains 25 points" ) {
160  REQUIRE( P.count() == 25 );
161  }
162  THEN( "The interior of the polytope contains 7 points" ) {
163  REQUIRE( P.countInterior() == 7 );
164  }
165  THEN( "The boundary of the polytope contains 18 points" ) {
166  REQUIRE( P.countBoundary() == 18 );
167  }
168  }
169  WHEN( "Computing the boundary of its convex hull as a SurfaceMesh" ){
170  SMesh smesh;
171  bool ok = Helper::computeConvexHullBoundary( smesh, V, false );
172  CAPTURE( smesh );
173  THEN( "The surface mesh is valid and has 6 vertices, 12 edges and 8 faces" ) {
174  REQUIRE( ok );
175  REQUIRE( smesh.nbVertices() == 6 );
176  REQUIRE( smesh.nbEdges() == 12 );
177  REQUIRE( smesh.nbFaces() == 8 );
178  }
179  THEN( "The surface mesh has the topology of a sphere" ) {
180  REQUIRE( smesh.Euler() == 2 );
181  REQUIRE( smesh.computeManifoldBoundaryEdges().size() == 0 );
182  REQUIRE( smesh.computeNonManifoldEdges().size() == 0 );
183  }
184  }
185  WHEN( "Computing the boundary of its convex hull as a lattice PolygonalSurface" ){
186  LatticePolySurf lpsurf;
187  bool ok = Helper::computeConvexHullBoundary( lpsurf, V, false );
188  CAPTURE( lpsurf );
189  THEN( "The polygonal surface is valid and has 6 vertices, 12 edges and 8 faces" ) {
190  REQUIRE( ok );
191  REQUIRE( lpsurf.nbVertices() == 6 );
192  REQUIRE( lpsurf.nbEdges() == 12 );
193  REQUIRE( lpsurf.nbFaces() == 8 );
194  REQUIRE( lpsurf.nbArcs() == 24 );
195  }
196  THEN( "The polygonal surface has the topology of a sphere and no boundary" ) {
197  REQUIRE( lpsurf.Euler() == 2 );
198  REQUIRE( lpsurf.allBoundaryArcs().size() == 0 );
199  REQUIRE( lpsurf.allBoundaryVertices().size() == 0 );
200  }
201  }
202  WHEN( "Computing its convex hull as a ConvexCellComplex" ){
203  CvxCellComplex complex;
204  bool ok = Helper::computeConvexHullCellComplex( complex, V, false );
205  CAPTURE( complex );
206  THEN( "The convex cell complex is valid and has 6 vertices, 8 faces and 1 finite cell" ) {
207  REQUIRE( ok );
208  REQUIRE( complex.nbVertices() == 6 );
209  REQUIRE( complex.nbFaces() == 8 );
210  REQUIRE( complex.nbCells() == 1 );
211  }
212  }
213  }
214  GIVEN( "Given a cube with an additional outside vertex " ) {
215  std::vector<Point> V
216  = { Point(-10,-10,-10), Point(10,-10,-10), Point(-10,10,-10), Point(10,10,-10),
217  Point(-10,-10,10), Point(10,-10,10), Point(-10,10,10), Point(10,10,10),
218  Point(0,0,18) };
219  WHEN( "Computing its Delaunay cell complex" ){
220  CvxCellComplex complex;
221  bool ok = Helper::computeDelaunayCellComplex( complex, V, false );
222  CAPTURE( complex );
223  THEN( "The complex has 2 cells, 10 faces, 9 vertices" ) {
224  REQUIRE( ok );
225  REQUIRE( complex.nbCells() == 2 );
226  REQUIRE( complex.nbFaces() == 10 );
227  REQUIRE( complex.nbVertices() == 9 );
228  }
229  THEN( "The faces of cells are finite" ) {
230  bool ok_finite = true;
231  for ( auto c = 0; c < complex.nbCells(); ++c ) {
232  const auto faces = complex.cellFaces( c );
233  for ( auto f : faces )
234  ok_finite = ok_finite && ! complex.isInfinite( complex.faceCell( f ) );
235  }
236  REQUIRE( ok_finite );
237  }
238  THEN( "The opposite of faces of cells are infinite except two" ) {
239  int nb_finite = 0;
240  for ( auto c = 0; c < complex.nbCells(); ++c ) {
241  const auto faces = complex.cellFaces( c );
242  for ( auto f : faces ) {
243  const auto opp_f = complex.opposite( f );
244  nb_finite += complex.isInfinite( complex.faceCell( opp_f ) ) ? 0 : 1;
245  }
246  }
247  REQUIRE( nb_finite == 2 );
248  }
249  }
250  }
251 }
Aim: Represents a polygon mesh, i.e. a 2-dimensional combinatorial surface whose faces are (topologic...
DGtal is the top-level namespace which contains all DGtal functions and types.
Z3i::RealVector RealVector
Aim: represents a d-dimensional complex in a d-dimensional space with the following properties and re...
Aim: Provides a set of functions to facilitate the computation of convex hulls and polytopes,...
Aim: Represents an embedded mesh as faces and a list of vertices. Vertices may be shared among faces ...
Definition: SurfaceMesh.h:92
Z2i::RealPoint RealPoint
MyPointD Point
Definition: testClone2.cpp:383
CAPTURE(thicknessHV)
SCENARIO("ConvexityHelper< 2 > unit tests", "[convexity_helper][lattice_polytope][2d]")
GIVEN("A cubical complex with random 3-cells")
REQUIRE(domain.isInside(aPoint))