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tdeedu/kig/objects/polygon_imp.cpp

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