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551 lines
15 KiB
551 lines
15 KiB
// Copyright (C) 2004 Pino Toscano <toscano.pino@tiscali.it>
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// This program is free software; you can redistribute it and/or
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// modify it under the terms of the GNU General Public License
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// as published by the Free Software Foundation; either version 2
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// of the License, or (at your option) any later version.
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// This program is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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// You should have received a copy of the GNU General Public License
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// along with this program; if not, write to the Free Software
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// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
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// 02110-1301, USA.
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#include "polygon_imp.h"
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#include "bogus_imp.h"
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#include "line_imp.h"
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#include "point_imp.h"
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#include "../misc/common.h"
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#include "../misc/coordinate.h"
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#include "../misc/kigpainter.h"
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#include "../misc/kigtransform.h"
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#include "../kig/kig_document.h"
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#include "../kig/kig_view.h"
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#include <klocale.h>
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#include <cmath>
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PolygonImp::PolygonImp( uint npoints, const std::vector<Coordinate>& points,
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const Coordinate& centerofmass )
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: mnpoints( npoints ), mpoints( points ), mcenterofmass( centerofmass )
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{
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// mpoints = points;
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}
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PolygonImp::PolygonImp( const std::vector<Coordinate>& points )
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{
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uint npoints = points.size();
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Coordinate centerofmassn = Coordinate( 0, 0 );
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for ( uint i = 0; i < npoints; ++i )
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{
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centerofmassn += points[i];
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}
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mpoints = points;
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mcenterofmass = centerofmassn/npoints;
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mnpoints = npoints;
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}
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PolygonImp::~PolygonImp()
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{
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}
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Coordinate PolygonImp::attachPoint() const
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{
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return mcenterofmass;
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}
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ObjectImp* PolygonImp::transform( const Transformation& t ) const
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{
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/*mp:
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* any projective transformation makes sense for a polygon,
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* since segments transform into segments (but see below...)
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* of course regular polygons will no longer be
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* regular if t is not homothetic.
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* for projective transformations the polygon could transform to
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* an unbounded nonconnected polygon; this happens if some side
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* of the polygon crosses the critical line that maps to infinity
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* this can be easily checked using the getProjectiveIndicator
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* function
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*/
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// if ( ! t.isHomothetic() )
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// return new InvalidImp();
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if ( ! t.isAffine() ) /* in this case we need a more extensive test */
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{
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double maxp = -1.0;
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double minp = 1.0;
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for ( uint i = 0; i < mpoints.size(); ++i )
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{
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double p = t.getProjectiveIndicator( mpoints[i] );
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if ( p > maxp ) maxp = p;
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if ( p < minp ) minp = p;
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}
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if ( maxp > 0 && minp < 0 ) return new InvalidImp;
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}
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std::vector<Coordinate> np;
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for ( uint i = 0; i < mpoints.size(); ++i )
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{
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Coordinate nc = t.apply( mpoints[i] );
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if ( !nc.valid() )
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return new InvalidImp;
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np.push_back( nc );
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}
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return new PolygonImp( np );
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}
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void PolygonImp::draw( KigPainter& p ) const
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{
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p.drawPolygon( mpoints );
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}
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bool PolygonImp::isInPolygon( const Coordinate& p ) const
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{
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// (algorithm sent to me by domi)
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// We intersect with the horizontal ray from point to the right and
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// count the number of intersections. That, along with some
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// minor optimalisations of the intersection test..
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bool inside_flag = false;
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double cx = p.x;
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double cy = p.y;
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Coordinate prevpoint = mpoints.back();
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bool prevpointbelow = mpoints.back().y >= cy;
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for ( uint i = 0; i < mpoints.size(); ++i )
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{
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Coordinate point = mpoints[i];
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bool pointbelow = point.y >= cy;
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if ( prevpointbelow != pointbelow )
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{
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// possibility of intersection: points on different side from
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// the X axis
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//bool rightofpt = point.x >= cx;
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// mp: we need to be a little bit more conservative here, in
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// order to treat properly the case when the point is on the
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// boundary
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//if ( rightofpt == ( prevpoint.x >= cx ) )
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if ( ( point.x - cx )*(prevpoint.x - cx ) > 0 )
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{
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// points on same side of Y axis -> easy to test intersection
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// intersection iff one point to the right of c
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if ( point.x >= cx )
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inside_flag = !inside_flag;
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}
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else
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{
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// points on different sides of Y axis -> we need to calculate
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// the intersection.
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// mp: we want to check if the point is on the boundary, and
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// return false in such case
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double num = ( point.y - cy )*( prevpoint.x - point.x );
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double den = prevpoint.y - point.y;
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if ( num == den*( point.x - cx ) ) return false;
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if ( num/den <= point.x - cx )
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inside_flag = !inside_flag;
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}
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}
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prevpoint = point;
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prevpointbelow = pointbelow;
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}
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return inside_flag;
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}
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#define selectpolygonwithinside 1
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#ifdef selectpolygonwithinside
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bool PolygonImp::contains( const Coordinate& p, int, const KigWidget& ) const
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{
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return isInPolygon( p );
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}
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#else
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bool PolygonImp::contains( const Coordinate& p, int width, const KigWidget& w ) const
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{
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bool ret = false;
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uint reduceddim = mpoints.size() - 1;
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for ( uint i = 0; i < reduceddim; ++i )
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{
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ret |= isOnSegment( p, mpoints[i], mpoints[i+1], w.screenInfo().normalMiss( width ) );
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}
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ret |= isOnSegment( p, mpoints[reduceddim], mpoints[0], w.screenInfo().normalMiss( width ) );
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return ret;
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}
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#endif
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bool PolygonImp::inRect( const Rect& r, int width, const KigWidget& w ) const
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{
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bool ret = false;
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uint reduceddim = mpoints.size() - 1;
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for ( uint i = 0; i < reduceddim; ++i )
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{
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SegmentImp* s = new SegmentImp( mpoints[i], mpoints[i+1] );
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ret |= lineInRect( r, mpoints[i], mpoints[i+1], width, s, w );
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delete s;
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s = 0;
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}
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SegmentImp* t = new SegmentImp( mpoints[reduceddim], mpoints[0] );
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ret |= lineInRect( r, mpoints[reduceddim], mpoints[0], width, t, w );
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delete t;
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t = 0;
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return ret;
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}
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bool PolygonImp::valid() const
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{
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return true;
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}
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const uint PolygonImp::numberOfProperties() const
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{
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return Parent::numberOfProperties() + 5;
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}
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const QCStringList PolygonImp::propertiesInternalNames() const
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{
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QCStringList l = Parent::propertiesInternalNames();
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l += "polygon-number-of-sides";
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l += "polygon-perimeter";
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l += "polygon-surface";
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l += "polygon-center-of-mass";
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l += "polygon-winding-number";
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assert( l.size() == PolygonImp::numberOfProperties() );
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return l;
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}
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const QCStringList PolygonImp::properties() const
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{
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QCStringList l = Parent::properties();
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l += I18N_NOOP( "Number of sides" );
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l += I18N_NOOP( "Perimeter" );
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l += I18N_NOOP( "Surface" );
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l += I18N_NOOP( "Center of Mass of the Vertices" );
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l += I18N_NOOP( "Winding Number" );
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assert( l.size() == PolygonImp::numberOfProperties() );
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return l;
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}
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const ObjectImpType* PolygonImp::impRequirementForProperty( uint which ) const
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{
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if ( which < Parent::numberOfProperties() )
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return Parent::impRequirementForProperty( which );
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else return PolygonImp::stype();
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}
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const char* PolygonImp::iconForProperty( uint which ) const
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{
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assert( which < PolygonImp::numberOfProperties() );
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if ( which < Parent::numberOfProperties() )
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return Parent::iconForProperty( which );
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else if ( which == Parent::numberOfProperties() )
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return "en"; // number of sides
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else if ( which == Parent::numberOfProperties() + 1 )
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return "circumference"; // perimeter
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else if ( which == Parent::numberOfProperties() + 2 )
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return "areaCircle"; // surface
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else if ( which == Parent::numberOfProperties() + 3 )
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return "point"; // center of mass
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else if ( which == Parent::numberOfProperties() + 4 )
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return "w"; // winding number
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else assert( false );
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return "";
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}
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ObjectImp* PolygonImp::property( uint which, const KigDocument& w ) const
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{
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assert( which < PolygonImp::numberOfProperties() );
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if ( which < Parent::numberOfProperties() )
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return Parent::property( which, w );
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else if ( which == Parent::numberOfProperties() )
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{
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// number of points
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return new IntImp( mnpoints );
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}
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else if ( which == Parent::numberOfProperties() + 1)
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{
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double circumference = 0.;
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// circumference
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for ( uint i = 0; i < mpoints.size(); ++i )
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{
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uint prev = ( i + mpoints.size() - 1 ) % mpoints.size();
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circumference += ( mpoints[i] - mpoints[prev] ).length();
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}
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return new DoubleImp( circumference );
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}
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else if ( which == Parent::numberOfProperties() + 2)
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{
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int wn = windingNumber (); // not able to compute area for such polygons...
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if ( wn < 0 ) wn = -wn;
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if ( wn != 1 ) return new InvalidImp;
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double surface2 = 0.0;
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Coordinate prevpoint = mpoints.back();
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for ( uint i = 0; i < mpoints.size(); ++i )
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{
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Coordinate point = mpoints[i];
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surface2 += ( point.x - prevpoint.x ) * ( point.y + prevpoint.y );
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prevpoint = point;
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}
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return new DoubleImp( fabs( surface2 / 2 ) );
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}
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else if ( which == Parent::numberOfProperties() + 3 )
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{
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return new PointImp( mcenterofmass );
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}
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else if ( which == Parent::numberOfProperties() + 4 )
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{
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// winding number
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return new IntImp( windingNumber() );
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}
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else assert( false );
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return new InvalidImp;
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}
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const std::vector<Coordinate> PolygonImp::points() const
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{
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std::vector<Coordinate> np;
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np.reserve( mpoints.size() );
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std::copy( mpoints.begin(), mpoints.end(), std::back_inserter( np ) );
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return np;
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}
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const uint PolygonImp::npoints() const
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{
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return mnpoints;
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}
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PolygonImp* PolygonImp::copy() const
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{
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return new PolygonImp( mpoints );
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}
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void PolygonImp::visit( ObjectImpVisitor* vtor ) const
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{
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vtor->visit( this );
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}
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bool PolygonImp::equals( const ObjectImp& rhs ) const
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{
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return rhs.inherits( PolygonImp::stype() ) &&
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static_cast<const PolygonImp&>( rhs ).points() == mpoints;
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}
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const ObjectImpType* PolygonImp::stype()
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{
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static const ObjectImpType t(
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Parent::stype(), "polygon",
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I18N_NOOP( "polygon" ),
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I18N_NOOP( "Select this polygon" ),
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I18N_NOOP( "Select polygon %1" ),
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I18N_NOOP( "Remove a Polygon" ),
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I18N_NOOP( "Add a Polygon" ),
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I18N_NOOP( "Move a Polygon" ),
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I18N_NOOP( "Attach to this polygon" ),
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I18N_NOOP( "Show a Polygon" ),
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I18N_NOOP( "Hide a Polygon" )
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);
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return &t;
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}
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const ObjectImpType* PolygonImp::stype3()
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{
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static const ObjectImpType t3(
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PolygonImp::stype(), "triangle",
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I18N_NOOP( "triangle" ),
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I18N_NOOP( "Select this triangle" ),
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I18N_NOOP( "Select triangle %1" ),
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I18N_NOOP( "Remove a Triangle" ),
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I18N_NOOP( "Add a Triangle" ),
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I18N_NOOP( "Move a Triangle" ),
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I18N_NOOP( "Attach to this triangle" ),
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I18N_NOOP( "Show a Triangle" ),
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I18N_NOOP( "Hide a Triangle" )
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);
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return &t3;
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}
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const ObjectImpType* PolygonImp::stype4()
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{
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static const ObjectImpType t4(
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PolygonImp::stype(), "quadrilateral",
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I18N_NOOP( "quadrilateral" ),
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I18N_NOOP( "Select this quadrilateral" ),
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I18N_NOOP( "Select quadrilateral %1" ),
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I18N_NOOP( "Remove a Quadrilateral" ),
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I18N_NOOP( "Add a Quadrilateral" ),
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I18N_NOOP( "Move a Quadrilateral" ),
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I18N_NOOP( "Attach to this quadrilateral" ),
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I18N_NOOP( "Show a Quadrilateral" ),
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I18N_NOOP( "Hide a Quadrilateral" )
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);
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return &t4;
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}
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const ObjectImpType* PolygonImp::type() const
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{
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uint n = mpoints.size();
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if ( n == 3 ) return PolygonImp::stype3();
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if ( n == 4 ) return PolygonImp::stype4();
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return PolygonImp::stype();
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}
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bool PolygonImp::isPropertyDefinedOnOrThroughThisImp( uint which ) const
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{
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assert( which < PolygonImp::numberOfProperties() );
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if ( which < Parent::numberOfProperties() )
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return Parent::isPropertyDefinedOnOrThroughThisImp( which );
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return false;
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}
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Rect PolygonImp::surroundingRect() const
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{
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Rect r( 0., 0., 0., 0. );
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for ( uint i = 0; i < mpoints.size(); ++i )
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{
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r.setContains( mpoints[i] );
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}
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return r;
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}
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int PolygonImp::windingNumber() const
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{
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/*
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* this is defined as the sum of the external angles while at
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* all vertices, then normalized by 2pi. The external angle
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* is the angle we steer at each vertex while we walk along the
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* boundary of the polygon.
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* In the end we only need to count how many time we cross the (1,0)
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* direction (positive x-axis) with a positive sign if we cross while
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* steering left and a negative sign viceversa
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*/
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int winding = 0;
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uint npoints = mpoints.size();
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Coordinate prevside = mpoints[0] - mpoints[npoints-1];
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for ( uint i = 0; i < npoints; ++i )
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{
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uint nexti = i + 1;
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if ( nexti >= npoints ) nexti = 0;
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Coordinate side = mpoints[nexti] - mpoints[i];
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double vecprod = side.x*prevside.y - side.y*prevside.x;
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int steeringdir = ( vecprod > 0 ) ? 1 : -1;
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if ( vecprod == 0.0 || side.y*prevside.y > 0 )
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{
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prevside = side;
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continue; // cannot cross the (1,0) direction
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}
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if ( side.y*steeringdir < 0 && prevside.y*steeringdir >= 0 )
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winding -= steeringdir;
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prevside = side;
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}
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return winding;
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}
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bool PolygonImp::isMonotoneSteering() const
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{
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/*
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* returns true if while walking along the boundary,
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* steering is always in the same direction
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*/
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uint npoints = mpoints.size();
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Coordinate prevside = mpoints[0] - mpoints[npoints-1];
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int prevsteeringdir = 0;
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for ( uint i = 0; i < npoints; ++i )
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{
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uint nexti = i + 1;
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if ( nexti >= npoints ) nexti = 0;
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Coordinate side = mpoints[nexti] - mpoints[i];
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double vecprod = side.x*prevside.y - side.y*prevside.x;
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int steeringdir = ( vecprod > 0 ) ? 1 : -1;
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if ( vecprod == 0.0 )
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{
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prevside = side;
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continue; // going straight
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}
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if ( prevsteeringdir*steeringdir < 0 ) return false;
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prevside = side;
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prevsteeringdir = steeringdir;
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}
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return true;
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}
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bool PolygonImp::isConvex() const
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{
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if ( ! isMonotoneSteering() ) return false;
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int winding = windingNumber();
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if ( winding < 0 ) winding = -winding;
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assert ( winding > 0 );
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return winding == 1;
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}
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std::vector<Coordinate> computeConvexHull( const std::vector<Coordinate>& points )
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{
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/*
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* compute the convex hull of the set of points, the resulting list
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* is the vertices of the resulting polygon listed in a counter clockwise
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* order. This algorithm is on order n^2, probably suboptimal, but
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* we don't expect to have large values for n.
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*/
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if ( points.size() < 3 ) return points;
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std::vector<Coordinate> worklist = points;
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std::vector<Coordinate> result;
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double ymin = worklist[0].y;
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uint imin = 0;
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for ( uint i = 1; i < worklist.size(); ++i )
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{
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if ( worklist[i].y < ymin )
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{
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ymin = worklist[i].y;
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imin = i;
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}
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}
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// worklist[imin] is definitely on the convex hull, let's start from there
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result.push_back( worklist[imin] );
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Coordinate startpoint = worklist[imin];
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Coordinate apoint = worklist[imin];
|
|
double aangle = 0.0;
|
|
|
|
while ( ! worklist.empty() )
|
|
{
|
|
int besti = -1;
|
|
double anglemin = 10000.0;
|
|
for ( uint i = 0; i < worklist.size(); ++i )
|
|
{
|
|
if ( worklist[i] == apoint ) continue;
|
|
Coordinate v = worklist[i] - apoint;
|
|
double angle = std::atan2( v.y, v.x );
|
|
while ( angle < aangle ) angle += 2*M_PI;
|
|
if ( angle < anglemin )
|
|
{ // found a better point
|
|
besti = i;
|
|
anglemin = angle;
|
|
}
|
|
}
|
|
|
|
if ( besti < 0 ) return result; // this happens, e.g. if all points coincide
|
|
apoint = worklist[besti];
|
|
aangle = anglemin;
|
|
if ( apoint == startpoint )
|
|
{
|
|
return result;
|
|
}
|
|
result.push_back( apoint );
|
|
worklist.erase( worklist.begin() + besti, worklist.begin() + besti + 1 );
|
|
}
|
|
assert( false );
|
|
return result;
|
|
}
|