DGtal 1.3.0
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testBoundedRationalPolytope.cpp File Reference
DGtal Test Files
#include <iostream>
#include <vector>
#include <algorithm>
#include "DGtal/base/Common.h"
#include "DGtal/kernel/SpaceND.h"
#include "DGtal/geometry/volumes/BoundedRationalPolytope.h"
#include "DGtalCatch.h"

Go to the source code of this file.

Functions

 SCENARIO ("BoundedRationalPolytope< Z2 > unit tests", "[rational_polytope][2d]")
 
 SCENARIO ("BoundedRationalPolytope< Z3 > unit tests", "[rational_polytope][3d]")
 

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
2020/04/28

Functions for testing class BoundedRationalPolytope.

This file is part of the DGtal library.

Definition in file testBoundedRationalPolytope.cpp.

Function Documentation

◆ SCENARIO() [1/2]

SCENARIO ( "BoundedRationalPolytope< Z2 > unit tests"  ,
""  [rational_polytope][2d] 
)

Definition at line 48 of file testBoundedRationalPolytope.cpp.

49{
50 typedef SpaceND<2,int> Space;
51 typedef Space::Point Point;
52 typedef Space::Vector Vector;
53 typedef BoundedRationalPolytope< Space > Polytope;
54
55 GIVEN( "A triangle P at (0,0), (5/2,0), (0,7/2)" ) {
56 Point a( 0, 0 );
57 Point b( 5, 0 );
58 Point c( 0, 7 );
59 Polytope P { Point(2,2), a, b, c };
60 THEN( "It contains more than 3 integer points" ) {
61 REQUIRE( P.count() > 3 );
62 }
63 THEN( "It contains more points than its area" ) {
64 REQUIRE( P.count() > (5*7/8) );
65 }
66 THEN( "It satisfies #In(P) <= #Int(P) + #Bd(P)" ) {
67 auto nb = P.count();
68 auto nb_int = P.countInterior();
69 auto nb_bd = P.countBoundary();
70 CAPTURE( nb );
71 CAPTURE( nb_int );
72 CAPTURE( nb_bd );
73 REQUIRE( nb <= nb_int + nb_bd );
74 }
75 WHEN( "Cut by some half-space" ) {
76 Polytope Q = P;
77 Q.cut( Vector( -1, 1 ), 3 );
78 THEN( "It contains less points" ) {
79 REQUIRE( Q.count() < P.count() );
80 }
81 }
82 WHEN( "Multiplied by 4 as Q = 4 * P, it becomes a lattice polytope" ) {
83 Polytope Q = 4 * P;
84 THEN( "It satisfies Pick's formula, ie 2*Area(P) = 2*#Int(P) + #Bd(P) - 2" ) {
85 Polytope IntQ = Q.interiorPolytope();
86 auto nb_int = IntQ.count();
87 auto nb_bd = Q.count() - IntQ.count();
88 auto area2 = (5*2)*(7*2);
89 CAPTURE( Q );
90 CAPTURE( nb_int );
91 CAPTURE( nb_bd );
92 CAPTURE( area2 );
93 REQUIRE( area2 == 2*nb_int + nb_bd - 2 );
94 }
95 }
96 }
97 GIVEN( "A closed segment S at (4/2,0/2), (-8/2,-4/2)" ) {
98 Point a( 4, 0 );
99 Point b( -8, -4 );
100 Polytope P { Point(2,2), a, b };
101 THEN( "Its interior is empty #Int(P) == 0" ) {
102 auto nb_int = P.countInterior();
103 REQUIRE( nb_int == 0 );
104 }
105 THEN( "It satisfies #In(P) == #Int(P) + #Bd(P) == #Bd(P) == 3" ) {
106 auto nb = P.count();
107 auto nb_int = P.countInterior();
108 auto nb_bd = P.countBoundary();
109 CAPTURE( nb );
110 CAPTURE( nb_int );
111 CAPTURE( nb_bd );
112 std::vector<Point> Ppts;
113 P.getPoints( Ppts );
114 CAPTURE( P );
115 CAPTURE( Ppts );
116 REQUIRE( nb_bd == 3 );
117 REQUIRE( nb == nb_int + nb_bd );
118 }
119 }
120 GIVEN( "A thin triangle P at (4/4,2/4), (2/4,4/4), (9/4,9/4)" ) {
121 Point a( 4, 2 );
122 Point b( 2, 4 );
123 Point c( 9, 9 );
124 Polytope P { Point(4,4), a, b, c };
125 THEN( "It contains 2 integer points" ) {
126 REQUIRE( P.count() == 2 );
127 }
128 THEN( "Its boundary is empty" ) {
129 REQUIRE( P.countBoundary() == 0 );
130 }
131 WHEN( "Multiplied by 4 as Q = 4 * P, it becomes a lattice polytope" ) {
132 Polytope Q = 4 * P;
133 THEN( "It satisfies Pick's formula, ie 2*Area(P) = 2*#Int(P) + #Bd(P) - 2" ) {
134 Polytope IntQ = Q.interiorPolytope();
135 auto nb_int = IntQ.count();
136 auto nb_bd = Q.count() - IntQ.count();
137 auto area2 = 24;
138 CAPTURE( Q );
139 CAPTURE( nb_int );
140 CAPTURE( nb_bd );
141 CAPTURE( area2 );
142 REQUIRE( area2 == 2*nb_int + nb_bd - 2 );
143 }
144 }
145 WHEN( "Multiplied by 10/3 as Q = 10/3 * P, it is a rational polytope" ) {
146 Polytope Q = Polytope::Rational( 10, 3 ) * P;
147 THEN( "It has a denominator 3 * gcd(4,10) == 6" ) {
148 REQUIRE( Q.denominator() == 6 );
149 }
150 THEN( "#( 3P Cap Z2 ) <= #( Q Cap Z2 ) < #( 4P Cap Z2 )" ) {
151 Polytope R = 3 * P;
152 Polytope S = 4 * P;
153 auto nbQ = Q.count();
154 auto nbR = R.count();
155 auto nbS = S.count();
156 CAPTURE( nbR );
157 CAPTURE( nbQ );
158 CAPTURE( nbS );
159 REQUIRE( nbR <= nbQ );
160 REQUIRE( nbQ <= nbS );
161 }
162 THEN( "6/5*Q is a polytope equal to 4*P." ) {
163 Polytope R = Polytope::Rational( 6, 5 ) * Q;
164 Polytope S = 4 * P;
165 std::vector<Point> Rpts, Spts;
166 R.getPoints( Rpts );
167 S.getPoints( Spts );
168 CAPTURE( Rpts );
169 CAPTURE( Spts );
170 REQUIRE( std::equal( Rpts.cbegin(), Rpts.cend(), Spts.cbegin() ) );
171 }
172 }
173 }
174} // SCENARIO( "BoundedRationalPolytope< Z2 > unit tests", "[rational_polytope][2d]" )
DGtal::BoundedRationalPolytope
Aim: Represents an nD rational polytope, i.e. a convex polyhedron bounded by vertices with rational c...
Definition: BoundedRationalPolytope.h:75
Point
MyPointD Point
Definition: testClone2.cpp:383
Vector
FreemanChain< int >::Vector Vector
Definition: testCombinDSS.cpp:60
CAPTURE
CAPTURE(thicknessHV)
GIVEN
GIVEN("A cubical complex with random 3-cells")
Definition: testCubicalComplex.cpp:70
REQUIRE
REQUIRE(domain.isInside(aPoint))

References CAPTURE(), GIVEN(), and REQUIRE().

◆ SCENARIO() [2/2]

SCENARIO ( "BoundedRationalPolytope< Z3 > unit tests"  ,
""  [rational_polytope][3d] 
)

Definition at line 176 of file testBoundedRationalPolytope.cpp.

177{
178 typedef SpaceND<3,int> Space;
179 typedef Space::Point Point;
180 typedef Space::Vector Vector;
181 typedef BoundedRationalPolytope< Space > Polytope;
182
183 GIVEN( "A tetrahedron P at (0,0,0), (5/2,0,0), (0,7/2,0), (0,0,3/2)" ) {
184 Point a( 0, 0, 0 );
185 Point b( 5, 0, 0 );
186 Point c( 0, 7, 0 );
187 Point d( 0, 0, 3 );
188 Polytope P { Point(2,2), a, b, c, d };
189 THEN( "It contains more than 3 integer points" ) {
190 REQUIRE( P.count() > 3 );
191 }
192 THEN( "It contains more points than its volume" ) {
193 REQUIRE( P.count() > (5*7*3/8/6) );
194 }
195 THEN( "It satisfies #In(P) <= #Int(P) + #Bd(P)" ) {
196 auto nb = P.count();
197 auto nb_int = P.countInterior();
198 auto nb_bd = P.countBoundary();
199 CAPTURE( nb );
200 CAPTURE( nb_int );
201 CAPTURE( nb_bd );
202 REQUIRE( nb <= nb_int + nb_bd );
203 }
204 WHEN( "Multiplied by 4 as Q = 2 * P, it becomes a lattice polytope" ) {
205 Polytope Q = 2 * P;
206 THEN( "Its denominator is 1" ) {
207 REQUIRE( Q.denominator() == 1 );
208 }
209 THEN( "It has more interior and boundary points than P" ) {
210 auto nb = P.count();
211 auto nb_int = P.countInterior();
212 auto nb_bd = P.countBoundary();
213 Polytope IntQ = Q.interiorPolytope();
214 auto nb_intQ = IntQ.count();
215 auto nbQ = Q.count();
216 auto nb_bdQ = nbQ - nb_intQ;
217 CAPTURE( Q );
218 REQUIRE( nb_int < nb_intQ );
219 REQUIRE( nb_bd < nb_bdQ );
220 REQUIRE( nb < nbQ );
221 }
222 }
223 WHEN( "Considering an increasing series f_i = 3/2, 2, 9/4, 3, 11/3, the number of inside points of f_i * P is increasing" ) {
224 Polytope Q1 = Polytope::Rational( 3 , 2 ) * P;
225 Polytope Q2 = Polytope::Rational( 2 , 1 ) * P;
226 Polytope Q3 = Polytope::Rational( 9 , 4 ) * P;
227 Polytope Q4 = Polytope::Rational( 3 , 1 ) * P;
228 Polytope Q5 = Polytope::Rational( 11, 3 ) * P;
229 auto nb = P .count();
230 auto nb1 = Q1.count();
231 auto nb2 = Q2.count();
232 auto nb3 = Q3.count();
233 auto nb4 = Q4.count();
234 auto nb5 = Q5.count();
235 REQUIRE( nb < nb1 );
236 REQUIRE( nb1 < nb2 );
237 REQUIRE( nb2 < nb3 );
238 REQUIRE( nb3 < nb4 );
239 REQUIRE( nb4 < nb5 );
240 }
241 }
242}

References CAPTURE(), GIVEN(), and REQUIRE().

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