DGtal 2.2.0
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testLatticePolytope2D.cpp File Reference
DGtal Test Files
#include <iostream>
#include "DGtal/base/Common.h"
#include "DGtal/arithmetic/LatticePolytope2D.h"
#include "DGtal/shapes/Shapes.h"
#include "DGtal/io/boards/Board2D.h"
Include dependency graph for testLatticePolytope2D.cpp:

Go to the source code of this file.

Functions

template<typename LatticePolytope2D>
bool checkCut (LatticePolytope2D &cip, typename LatticePolytope2D::HalfSpace hs)
template<typename Space>
bool testLatticePolytope2D ()
int myRand (int nb)
template<typename Space>
bool exhaustiveTestLatticePolytope2D ()
template<typename Space>
bool specificTestLatticePolytope2D ()
template<typename Space>
bool checkOutputConvexHullBorder ()
int main (int, char **)

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
2012/04/19

Functions for testing class LatticePolytope2D.

This file is part of the DGtal library.

Definition in file testLatticePolytope2D.cpp.

Function Documentation

◆ checkCut()

template<typename LatticePolytope2D>
bool checkCut ( LatticePolytope2D & cip,
typename LatticePolytope2D::HalfSpace hs )

Definition at line 51 of file testLatticePolytope2D.cpp.

53{
54 trace.beginBlock ( "Check cut, see <cip.eps> and <cip2.eps>" );
55 typedef typename LatticePolytope2D::Domain Domain;
56 typedef typename DigitalSetSelector< Domain, BIG_DS+HIGH_BEL_DS >::Type DigitalSet;
57 typedef typename DigitalSet::ConstIterator ConstIterator;
58
59 Domain d = cip.boundingBoxDomain();
60#ifdef DEBUG_LatticePolytope2D
61 Board2D board;
62 board << SetMode( d.className(), "Grid" ) << d;
63 DigitalSet aSet( d );
64 Shapes<Domain>::makeSetFromPointPredicate( aSet, hs );
65 Color col1( 100, 100, 255 );
66 Color col2( 180, 180, 255 );
67 board << CustomStyle( aSet.className(), new CustomColors( col1, col2 ) )
68 << aSet;
69 board << SetMode( cip.className(), "Transparent" ) << cip;
70 board.saveEPS( "cip.eps" );
71 board.clear();
72#endif
73
74 DigitalSet cipSet( d );
75 DigitalSet cipSet2( d );
76 cip.getIncludedDigitalPoints( cipSet );
77 cip.cut( hs );
78 cip.getIncludedDigitalPoints( cipSet2 );
79#ifdef DEBUG_LatticePolytope2D
80 board << SetMode( d.className(), "Grid" ) << d;
81 board << CustomStyle( aSet.className(), new CustomColors( col1, col2 ) )
82 << cipSet;
83 board << CustomStyle( aSet.className(), new CustomColors( Color( 255, 180, 20 ), Color( 200, 170, 0 ) ) )
84 << cipSet2;
85 board << SetMode( cip.className(), "Transparent" ) << cip;
86 board.saveEPS( "cip2.eps" );
87#endif
88
89 unsigned int nbok = 0;
90 unsigned int nb = 0;
91 for ( ConstIterator it = cipSet2.begin(), it_end = cipSet2.end();
92 it != it_end; ++it )
93 {
94 nbok += ( cipSet.find( *it ) != cipSet.end() ) ? 1 : 0;
95 ++nb;
96 nbok += hs( *it );
97 ++nb;
98 }
99 for ( ConstIterator it = cipSet.begin(), it_end = cipSet.end();
100 it != it_end; ++it )
101 {
102 if ( cipSet2.find( *it ) == cipSet2.end() )
103 nbok += ! hs( *it );
104 else
105 nbok += hs( *it );
106 ++nb;
107 }
108 trace.info() << "(" << nbok << "/" << nb << ")"
109 << " cip.size()=" << cip.size()
110 << " #before=" << cipSet.size()
111 << " #after=" << cipSet2.size()
112 << std::endl;
113 trace.endBlock();
114 return nbok == nb;
115}
DGtal::Board2D
Aim: This class specializes a 'Board' class so as to display DGtal objects more naturally (with <<)....
Definition Board2D.h:71
DGtal::Color
Structure representing an RGB triple with alpha component.
Definition Color.h:77
DGtal::LatticePolytope2D::boundingBoxDomain
Domain boundingBoxDomain() const
DGtal::LatticePolytope2D::className
std::string className() const
DGtal::LatticePolytope2D::Domain
HyperRectDomain< Space > Domain
Definition LatticePolytope2D.h:97
DGtal::Shapes::makeSetFromPointPredicate
static void makeSetFromPointPredicate(DigitalSet &aSet, const PointPredicate &aPP)
DGtal::Trace::beginBlock
void beginBlock(const std::string &keyword="")
DGtal::Trace::info
std::ostream & info()
DGtal::Trace::endBlock
double endBlock()
LibBoard::Board::clear
void clear(const DGtal::Color &color=DGtal::Color::None)
Definition Board.cpp:151
LibBoard::Board::saveEPS
void saveEPS(const char *filename, PageSize size=Board::BoundingBox, double margin=10.0) const
Definition Board.cpp:804
DGtal::trace
Trace trace
DGtal::CustomColors
Custom style class redefining the pen color and the fill color. You may use Board2D::Color::None for ...
Definition Board2D.h:279
DGtal::CustomStyle::CustomStyle
CustomStyle(std::string classname, DrawableWithBoard2D *style)
Definition Board2D.h:224
DGtal::DigitalSetSelector::Type
DigitalSetByAssociativeContainer< Domain, std::unordered_set< typename Domain::Point > > Type
Definition DigitalSetSelector.h:102
DGtal::SetMode::SetMode
SetMode(std::string classname, std::string mode)
Definition Board2D.h:254
DigitalSet
Z2i::DigitalSet DigitalSet
Definition testVoronoiMapComplete.cpp:40

References DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::begin(), DGtal::Trace::beginBlock(), DGtal::LatticePolytope2D< TSpace, TSequence >::boundingBoxDomain(), checkCut(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::className(), DGtal::LatticePolytope2D< TSpace, TSequence >::className(), LibBoard::Board::clear(), DGtal::Color::Color(), DGtal::CustomStyle::CustomStyle(), DGtal::LatticePolytope2D< TSpace, TSequence >::cut(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::end(), DGtal::Trace::endBlock(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::find(), DGtal::LatticePolytope2D< TSpace, TSequence >::getIncludedDigitalPoints(), DGtal::Trace::info(), DGtal::Shapes< TDomain >::makeSetFromPointPredicate(), LibBoard::Board::saveEPS(), DGtal::SetMode::SetMode(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::size(), DGtal::LatticePolytope2D< TSpace, TSequence >::size(), and DGtal::trace.

Referenced by checkCut(), exhaustiveTestLatticePolytope2D(), specificTestLatticePolytope2D(), and testLatticePolytope2D().

◆ checkOutputConvexHullBorder()

template<typename Space>
bool checkOutputConvexHullBorder ( )

Definition at line 334 of file testLatticePolytope2D.cpp.

335{
336 typedef typename Space::Point Point;
337 typedef typename Space::Vector Vector;
338 typedef typename Space::Integer Integer;
339 typedef LatticePolytope2D<Space> CIP;
340 typedef typename CIP::Domain Domain;
341 typedef typename CIP::HalfSpace HalfSpace;
342 typedef typename DigitalSetSelector< Domain, BIG_DS+HIGH_BEL_DS >::Type DigitalSet;
343 IntegerComputer<Integer> ic;
344
345 BOOST_CONCEPT_ASSERT(( boost::Container< CIP > ));
346
347 Point c1( 0, 0 );
348 Point c3( 30, 0 );
349 Point A( -10, -2 );
350 Point B( 40, 27 );
351 Point In( 1, 0 );
352 HalfSpace hs1( c1, c1 + Vector( 0, 1 ), In, ic );
353 HalfSpace hs2( A, B, In, ic );
354 HalfSpace hs3( c3, c3 + Vector( 0, 1 ), In, ic );
355 CIP cip;
356 cip.pushBack( c1 );
357 cip.computeConvexHullBorder( std::back_inserter( cip ), c1, c3, hs1, hs2, hs3 );
358 cip.pushBack( c3 );
359
360 Domain d = cip.boundingBoxDomain();
361 Board2D board;
362 board << SetMode( d.className(), "Grid" ) << d;
363 DigitalSet aSet( d );
364 Shapes<Domain>::makeSetFromPointPredicate( aSet, hs2 );
365 Color col1( 100, 180, 100 );
366 Color col2( 220, 250, 220 );
367 board << CustomStyle( aSet.className(), new CustomColors( col1, col2 ) )
368 << aSet;
369 board << SetMode( cip.className(), "Transparent" ) << cip;
370 // Point p( 0, 0 );
371 // board << CustomStyle( p.className(), new CustomColors( Color::Red, Color::Red ) )
372 // << p;
373 board.saveEPS( "cip4.eps" );
374 board.clear();
375 return true;
376}
DGtal::IntegerComputer
Aim: This class gathers several types and methods to make computation with integers.
Definition IntegerComputer.h:83
DGtal::LatticePolytope2D
Aim: Represents a 2D polytope, i.e. a convex polygon, in the two-dimensional digital plane....
Definition LatticePolytope2D.h:83
DGtal::SpaceND< 3, Integer >::Point
PointVector< dim, Integer > Point
Definition SpaceND.h:110
DGtal::SpaceND< 3, Integer >::Vector
PointVector< dim, Integer > Vector
Definition SpaceND.h:113
boost::Container
Go to http://www.sgi.com/tech/stl/Container.html.
Definition Boost.dox:104

References A< TC, TD >::A(), B< TC >::B(), checkOutputConvexHullBorder(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::className(), LibBoard::Board::clear(), DGtal::CustomStyle::CustomStyle(), DGtal::Shapes< TDomain >::makeSetFromPointPredicate(), LibBoard::Board::saveEPS(), and DGtal::SetMode::SetMode().

Referenced by checkOutputConvexHullBorder(), and main().

◆ exhaustiveTestLatticePolytope2D()

template<typename Space>
bool exhaustiveTestLatticePolytope2D ( )

Example of a test. To be completed.

Definition at line 218 of file testLatticePolytope2D.cpp.

219{
220 unsigned int nbok = 0;
221 unsigned int nb = 0;
222
223 trace.beginBlock ( "Testing block LatticePolytope2D area and centroid" );
224 typedef typename Space::Point Point;
225 typedef typename Space::Vector Vector;
226 typedef typename Space::Integer Integer;
227 typedef LatticePolytope2D<Space> CIP;
228 typedef typename CIP::Point3I Point3I;
229 typedef typename CIP::Domain Domain;
230 typedef typename CIP::HalfSpace HalfSpace;
231
232 CIP cip;
233 cip.pushBack( Point( 0, 0 ) );
234 cip.pushBack( Point( 8, -3 ) );
235 cip.pushBack( Point( 17, 2 ) );
236 cip.pushBack( Point( 21, 13 ) );
237 cip.pushBack( Point( 13, 19 ) );
238 cip.pushBack( Point( 6, 17 ) );
239 cip.pushBack( Point( -3, 6 ) );
240 Integer area2 = cip.twiceArea();
241 trace.info() << "- 2*area = " << area2 << std::endl;
242 Point3I c = cip.centroid( area2 );
243 trace.info() << "- centroid = " << c << std::endl;
244 Domain d = cip.boundingBoxDomain();
245 trace.info() << "- domain = " << d << std::endl;
246 trace.endBlock();
247
248 trace.beginBlock ( "Check cuts..." );
249 for ( unsigned int j = 0; j < 100; ++j )
250 {
251 CIP cip2 = cip;
252 int x = 0;
253 int y = 0;
254 while ( ( x == 0 ) && ( y == 0 ) )
255 {
256 x = myRand( 63 ) - 31;
257 y = myRand( 63 ) - 31;
258 }
259 int g = IntegerComputer<int>::staticGcd( x , y );
260 x /= g; y /= g;
261 int cc = myRand( 4 ) *x + myRand( 4 ) * y + myRand( 40 ) + 40;
262 for ( unsigned int i = 0; i < 10; ++i, cc -= myRand( 40 ) )
263 {
264 HalfSpace h( Vector( x, y ), cc );
265 trace.info() << "[" << j << " size=" << cip2.size() << "]"
266 << " cut by (" << x << "," << y << ")," << c << std::endl;
267 ++nb; nbok += checkCut( cip2, h ) ? 1 : 0;
268 trace.info() << "(" << nbok << "/" << nb << ") cuts" << std::endl;
269 //std::cerr << " " << cip2.size() << flush;
270 if ( nb != nbok ) break;
271 }
272 std::cerr << std::endl;
273 if ( nb != nbok ) break;
274 }
275 trace.endBlock();
276 return nbok == nb;
277}
DGtal::IntegerComputer::staticGcd
static Integer staticGcd(IntegerParamType a, IntegerParamType b)
g
std::mt19937 g(rd())
checkCut
bool checkCut(LatticePolytope2D &cip, typename LatticePolytope2D::HalfSpace hs)
Definition testLatticePolytope2D.cpp:51
myRand
int myRand(int nb)
Definition testLatticePolytope2D.cpp:208

References DGtal::Trace::beginBlock(), checkCut(), DGtal::Trace::endBlock(), exhaustiveTestLatticePolytope2D(), g(), DGtal::Trace::info(), myRand(), DGtal::IntegerComputer< TInteger >::staticGcd(), and DGtal::trace.

Referenced by exhaustiveTestLatticePolytope2D(), and main().

◆ main()

int main ( int ,
char **  )

Definition at line 381 of file testLatticePolytope2D.cpp.

382{
383 trace.beginBlock ( "Testing class LatticePolytope2D" );
384
385 typedef SpaceND<2, DGtal::int64_t> Z2;
386 typedef SpaceND<2, DGtal::BigInteger> Z2I;
387 bool res = testLatticePolytope2D<Z2>()
388 && testLatticePolytope2D<Z2I>()
389 && exhaustiveTestLatticePolytope2D<Z2>()
390 && checkOutputConvexHullBorder<Z2>();
391 //&& specificTestLatticePolytope2D<Z2>();
392 //&& exhaustiveTestLatticePolytope2D<Z2I>();
393 trace.emphase() << ( res ? "Passed." : "Error." ) << endl;
394 trace.endBlock();
395 return res ? 0 : 1;
396}
DGtal::Trace::emphase
std::ostream & emphase()
DGtal::Z2i::Z2
Space Z2
Definition StdDefs.h:76
checkOutputConvexHullBorder
bool checkOutputConvexHullBorder()
Definition testLatticePolytope2D.cpp:334
testLatticePolytope2D
bool testLatticePolytope2D()
Definition testLatticePolytope2D.cpp:122
exhaustiveTestLatticePolytope2D
bool exhaustiveTestLatticePolytope2D()
Definition testLatticePolytope2D.cpp:218

References DGtal::Trace::beginBlock(), checkOutputConvexHullBorder(), DGtal::Trace::emphase(), DGtal::Trace::endBlock(), exhaustiveTestLatticePolytope2D(), main(), testLatticePolytope2D(), and DGtal::trace.

◆ myRand()

int myRand ( int nb)

Definition at line 208 of file testLatticePolytope2D.cpp.

209{
210 return rand() % nb;
211}

References myRand().

Referenced by exhaustiveTestLatticePolytope2D(), and myRand().

◆ specificTestLatticePolytope2D()

template<typename Space>
bool specificTestLatticePolytope2D ( )

Example of a test. To be completed.

Definition at line 284 of file testLatticePolytope2D.cpp.

285{
286 unsigned int nbok = 0;
287 unsigned int nb = 0;
288
289 typedef typename Space::Point Point;
290 typedef typename Space::Vector Vector;
291 typedef LatticePolytope2D<Space> CIP;
292 typedef typename CIP::Domain Domain;
293 typedef typename CIP::HalfSpace HalfSpace;
294 typedef typename CIP::ConstIterator ConstIterator;
295 typedef typename DigitalSetSelector< Domain, BIG_DS+HIGH_BEL_DS >::Type DigitalSet;
296
297 CIP cip;
298 cip.pushBack( Point( 0, 0 ) );
299 cip.pushBack( Point( 8, -3 ) );
300 cip.pushBack( Point( 17, 2 ) );
301 cip.pushBack( Point( 21, 13 ) );
302 cip.pushBack( Point( 13, 19 ) );
303 cip.pushBack( Point( 6, 17 ) );
304 cip.pushBack( Point( -3, 6 ) );
305 HalfSpace hs1( Vector( -5, 11 ), 8 ); //12
306 HalfSpace hs2( Vector( -3, -11 ), 8 ); //-37
307 ++nb; nbok += checkCut( cip, hs1 ) ? 1 : 0;
308
309 Domain d = cip.boundingBoxDomain();
310 Board2D board;
311 board << SetMode( d.className(), "Grid" ) << d;
312 DigitalSet aSet( d );
313 ConstIterator itv = cip.begin();
314 ++itv; ++itv; ++itv; ++itv; ++itv; ++itv; ++itv;
315 HalfSpace hs( cip.halfSpace( itv ) );
316 Shapes<Domain>::makeSetFromPointPredicate( aSet, hs );
317 Color col1( 100, 180, 100 );
318 Color col2( 130, 200, 130 );
319 board << CustomStyle( aSet.className(), new CustomColors( col1, col2 ) )
320 << aSet;
321 board << SetMode( cip.className(), "Transparent" ) << cip;
322 Point p( 0, 0 );
323 board << CustomStyle( p.className(), new CustomColors( Color::Red, Color::Red ) )
324 << p;
325 board.saveEPS( "cip3.eps" );
326 board.clear();
327
328 ++nb; nbok += checkCut( cip, hs2 ) ? 1 : 0;
329 return nbok == nb;
330}
DGtal::Color::Red
static const Color Red
Definition Color.h:425

References checkCut(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::className(), LibBoard::Board::clear(), DGtal::CustomStyle::CustomStyle(), DGtal::Shapes< TDomain >::makeSetFromPointPredicate(), DGtal::Color::Red, LibBoard::Board::saveEPS(), DGtal::SetMode::SetMode(), and specificTestLatticePolytope2D().

Referenced by specificTestLatticePolytope2D().

◆ testLatticePolytope2D()

template<typename Space>
bool testLatticePolytope2D ( )

Example of a test. To be completed.

Definition at line 122 of file testLatticePolytope2D.cpp.

123{
124 unsigned int nbok = 0;
125 unsigned int nb = 0;
126
127 trace.beginBlock ( "Testing block LatticePolytope2D area and centroid" );
128 typedef typename Space::Point Point;
129 typedef typename Space::Vector Vector;
130 typedef typename Space::Integer Integer;
131 typedef LatticePolytope2D<Space> CIP;
132 typedef typename CIP::Point3I Point3I;
133 typedef typename CIP::Domain Domain;
134 typedef typename CIP::HalfSpace HalfSpace;
135 typedef typename CIP::Iterator Iterator;
136 typedef typename DigitalSetSelector< Domain, BIG_DS+HIGH_BEL_DS >::Type DigitalSet;
137
138 CIP cip;
139 cip.pushBack( Point( 0, 0 ) );
140 cip.pushBack( Point( 5, 0 ) );
141 cip.pushBack( Point( 0, 3 ) );
142 Integer area2 = cip.twiceArea();
143 trace.info() << "- 2*area = " << area2 << std::endl;
144 ++nb; nbok += ( area2 == 15 ) ? 1 : 0;
145 trace.info() << "(" << nbok << "/" << nb << ") "
146 << "2*area == 15" << std::endl;
147 Point3I c = cip.centroid( area2 );
148 trace.info() << "- centroid = " << c << std::endl;
149 ++nb; nbok += ( c == Point3I( 75, 45, 45 ) ) ? 1 : 0;
150 trace.info() << "(" << nbok << "/" << nb << ") "
151 << "centroid == [75,45,45]" << std::endl;
152 Domain d = cip.boundingBoxDomain();
153 trace.info() << "- domain = " << d << std::endl;
154 trace.endBlock();
155
156 trace.beginBlock ( "Output LatticePolytope2D in <cip.eps>" );
157 cip.pushBack( Point( -4, 4 ) );
158 cip.pushBack( Point( -7, 2 ) );
159 cip.pushBack( Point( -5, 1 ) );
160 Board2D board;
161 d = cip.boundingBoxDomain();
162 board << SetMode( d.className(), "Grid" ) << d;
163 DigitalSet aSet( d );
164 HalfSpace h( Vector( 1, 3 ), 8 );
165 //HalfSpace h = cip.halfSpace( ++cip.begin() );
166 Shapes<Domain>::makeSetFromPointPredicate( aSet, h );
167 Color col1( 100, 100, 255 );
168 Color col2( 180, 180, 255 );
169 board << CustomStyle( aSet.className(), new CustomColors( col1, col2 ) )
170 << aSet;
171 cip.getIncludedDigitalPoints( aSet );
172 board << CustomStyle( aSet.className(), new CustomColors( Color( 255, 180, 20 ), Color( 200, 130, 0 ) ) )
173 << aSet;
174 board << SetMode( cip.className(), "Transparent" ) << cip;
175 Iterator itA1, itB2;
176 //SizeCouple nbs =
177 cip.findCut( itA1, itB2, h );
178 Iterator itB1 = itA1; ++itB1;
179 if ( itB1 == cip.end() ) itB1 = cip.begin();
180 Iterator itA2 = itB2; ++itA2;
181 if ( itA2 == cip.end() ) itA2 = cip.begin();
182 Color col3( 0, 255, 0 );
183 Color col4( 255, 0, 0 );
184 board << CustomStyle( Point().className(), new CustomColors( col3, col3 ) )
185 << *itA1 << *itA2;
186 board << CustomStyle( Point().className(), new CustomColors( col4, col4 ) )
187 << *itB1 << *itB2;
188 board.saveEPS( "cip.eps" );
189 board.saveSVG( "cip.svg" );
190 trace.endBlock();
191
192 trace.beginBlock ( "Output cut LatticePolytope2D in <cip2.eps>" );
193 board.clear();
194 board << SetMode( d.className(), "Grid" ) << d;
195 board << SetMode( cip.className(), "Transparent" ) << cip;
196 bool wasCut = cip.cut( h );
197 FATAL_ERROR(wasCut);
198 board << SetMode( cip.className(), "Filled" ) << cip;
199 board.saveEPS( "cip2.eps" );
200 board.saveSVG( "cip2.svg" );
201 trace.endBlock();
202
203 checkCut( cip, HalfSpace( Vector( -2, 3 ), 4 ) );
204
205 return nbok == nb;
206}
LibBoard::Board::saveSVG
void saveSVG(const char *filename, PageSize size=Board::BoundingBox, double margin=10.0) const
Definition Board.cpp:1011
DGtal::CustomColors::CustomColors
CustomColors(const Color &penColor, const Color &fillColor)
Definition Board2D.h:289

References DGtal::Trace::beginBlock(), checkCut(), DGtal::DigitalSetByAssociativeContainer< TDomain, TContainer >::className(), LibBoard::Board::clear(), DGtal::Color::Color(), DGtal::CustomColors::CustomColors(), DGtal::CustomStyle::CustomStyle(), DGtal::Trace::endBlock(), DGtal::Trace::info(), DGtal::Shapes< TDomain >::makeSetFromPointPredicate(), LibBoard::Board::saveEPS(), LibBoard::Board::saveSVG(), DGtal::SetMode::SetMode(), testLatticePolytope2D(), and DGtal::trace.

Referenced by main(), and testLatticePolytope2D().