void minkowskiSum( const LineString& gA, const Polygon_2& gB, Polygon_set_2& polygonSet )
{
if ( gA.isEmpty() ) {
return ;
}
int npt = gA.numPoints() ;
for ( int i = 0; i < npt - 1 ; i++ ) {
Polygon_2 P;
P.push_back( gA.pointN( i ).toPoint_2() );
P.push_back( gA.pointN( i+1 ).toPoint_2() );
//
// We want to compute the "minkowski sum" on each segment of the line string
// This is not very well defined. But it appears CGAL supports it.
// However we must use the explicit "full convolution" method for that particular case in CGAL >= 4.7
#if CGAL_VERSION_NR < 1040701000 // version 4.7
Polygon_with_holes_2 part = minkowski_sum_2( P, gB );
#else
Polygon_with_holes_2 part = minkowski_sum_by_full_convolution_2( P, gB );
#endif
// merge into a polygon set
if ( polygonSet.is_empty() ) {
polygonSet.insert( part );
}
else {
polygonSet.join( part );
}
}
}
/*
* append gA+gB into the polygonSet
*/
void minkowskiSum( const Point& gA, const Polygon_2& gB, Polygon_set_2& polygonSet )
{
BOOST_ASSERT( gB.size() );
CGAL::Aff_transformation_2< Kernel > translate(
CGAL::TRANSLATION,
gA.toVector_2()
);
Polygon_2 sum ;
for ( Polygon_2::Vertex_const_iterator it = gB.vertices_begin();
it != gB.vertices_end(); ++it ) {
sum.push_back( translate.transform( *it ) );
}
if ( sum.is_clockwise_oriented() ) {
sum.reverse_orientation() ;
}
if ( polygonSet.is_empty() ) {
polygonSet.insert( sum );
}
else {
polygonSet.join( sum );
}
}
void minkowskiSum( const Polygon& gA, const Polygon_2& gB, Polygon_set_2& polygonSet )
{
if ( gA.isEmpty() ) {
return ;
}
/*
* Invoke minkowski_sum_2 for exterior ring
*/
{
Polygon_with_holes_2 sum = minkowski_sum_2( gA.exteriorRing().toPolygon_2(), gB ) ;
if ( polygonSet.is_empty() ) {
polygonSet.insert( sum );
}
else {
polygonSet.join( sum );
}
}
/*
* Compute the Minkowski sum for each segment of the interior rings
* and perform the union of the result. The result is a polygon, and its holes
* correspond to the inset.
*
*/
if ( gA.hasInteriorRings() ) {
Polygon_set_2 sumInteriorRings ;
for ( size_t i = 0; i < gA.numInteriorRings(); i++ ) {
minkowskiSum( gA.interiorRingN( i ), gB, sumInteriorRings ) ;
}
/*
* compute the difference for each hole of the resulting polygons
*/
std::list<Polygon_with_holes_2> interiorPolygons ;
sumInteriorRings.polygons_with_holes( std::back_inserter( interiorPolygons ) ) ;
for ( std::list<Polygon_with_holes_2>::iterator it_p = interiorPolygons.begin();
it_p != interiorPolygons.end(); ++it_p ) {
for ( Polygon_with_holes_2::Hole_iterator it_hole = it_p->holes_begin();
it_hole != it_p->holes_end(); ++it_hole ) {
it_hole->reverse_orientation() ;
polygonSet.difference( *it_hole ) ;
} // foreach hole
}// foreach polygon
}
}
void minkowskiSum( const LineString& gA, const Polygon_2 & gB, Polygon_set_2 & polygonSet ){
if ( gA.isEmpty() ){
return ;
}
int npt = gA.numPoints() ;
for ( int i = 0; i < npt - 1 ; i++ ){
Polygon_2 P;
P.push_back( gA.pointN(i).toPoint_2() );
P.push_back( gA.pointN(i+1).toPoint_2() );
Polygon_with_holes_2 part = minkowski_sum_2( P, gB );
// merge into a polygon set
if ( polygonSet.is_empty() ){
polygonSet.insert( part );
}else{
polygonSet.join( part );
}
}
}
bool is_empty(Polygon_set_2 S) {
return S.is_empty();
}
