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Revise triangulation 

- Avoid double-splitting a single point
- Check for mid-line intersections
- Avoid splitting zero-area polygons
- Keep full z-list for intersection checks

Fixes https://gitlab.com/kicad/code/kicad/-/issues/16241
This commit is contained in:
Seth Hillbrand 2023-12-13 13:35:10 -08:00
parent 8687d5092f
commit 0a67dd3fdd
1 changed files with 123 additions and 28 deletions
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151
libs/kimath/include/geometry/polygon_triangulation.h
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@ -66,6 +66,8 @@ public:
bool TesselatePolygon( const SHAPE_LINE_CHAIN& aPoly )
{
m_bbox = aPoly.BBox();
m_prefactor_x = 32767.0 / m_bbox.GetWidth();
m_prefactor_y = 32767.0 / m_bbox.GetHeight();
m_result.Clear();
if( !m_bbox.GetWidth() || !m_bbox.GetHeight() )
@ -271,8 +273,8 @@ private:
*/
int32_t zOrder( const double aX, const double aY ) const
{
int32_t x = static_cast<int32_t>( 32767.0 * ( aX - m_bbox.GetX() ) / m_bbox.GetWidth() );
int32_t y = static_cast<int32_t>( 32767.0 * ( aY - m_bbox.GetY() ) / m_bbox.GetHeight() );
int32_t x = static_cast<int32_t>( m_prefactor_x * ( aX - m_bbox.GetX() ) );
int32_t y = static_cast<int32_t>( m_prefactor_y * ( aY - m_bbox.GetY() ) );
x = ( x | ( x << 8 ) ) & 0x00FF00FF;
x = ( x | ( x << 4 ) ) & 0x0F0F0F0F;
@ -301,7 +303,7 @@ private:
while( p != aStart )
{
if( area( p->prev, p, p->next ) == 0.0 )
if( *p == *( p->next ) || area( p->prev, p, p->next ) == 0.0 )
{
p = p->prev;
p->next->remove();
@ -310,6 +312,7 @@ private:
if( p == p->next )
break;
}
p = p->next;
};
@ -436,26 +439,38 @@ private:
continue;
}
Vertex* nextNext = next->next;
Vertex* p = next;
bool removed = false;
if( *prev != *nextNext && intersects( prev, aPoint, next, nextNext ) &&
locallyInside( prev, nextNext ) &&
locallyInside( nextNext, prev ) )
do
{
m_result.AddTriangle( prev->i, aPoint->i, nextNext->i );
Vertex* nextNext = p->next->next;
prev = p->prev;
// remove two nodes involved
next->remove();
aPoint->remove();
if( *prev != *nextNext && intersects( prev, p, p->next, nextNext ) &&
locallyInside( prev, nextNext ) &&
locallyInside( nextNext, prev ) )
{
m_result.AddTriangle( prev->i, p->i, nextNext->i );
aPoint = nextNext;
stop = nextNext;
// remove two nodes involved
p->next->remove();
p->remove();
continue;
}
next = nextNext;
p = nextNext;
removed = true;
}
p = p->next;
} while ( p != next );
aPoint = next;
if( removed )
continue;
/*
* We've searched the entire polygon for available ears and there are still
* un-sliced nodes remaining.
@ -472,7 +487,9 @@ private:
}
// If we don't have any NULL triangles left, cut the polygon in two and try again
splitPolygon( aPoint );
if ( !splitPolygon( aPoint ) )
return false;
break;
}
}
@ -557,7 +574,7 @@ private:
* independently. This is assured to generate at least one new ear if the
* split is successful
*/
void splitPolygon( Vertex* start )
bool splitPolygon( Vertex* start )
{
Vertex* origPoly = start;
@ -565,19 +582,29 @@ private:
{
Vertex* marker = origPoly->next->next;
if( m_splits.count( origPoly ) )
{
origPoly = origPoly->next;
continue;
}
while( marker != origPoly->prev )
{
if( m_splits.count( marker ) )
{
marker = marker->next;
continue;
}
// Find a diagonal line that is wholly enclosed by the polygon interior
if( origPoly->i != marker->i && goodSplit( origPoly, marker ) )
{
Vertex* newPoly = origPoly->split( marker );
origPoly->updateList();
newPoly->updateList();
m_splits.insert( origPoly );
m_splits.insert( marker );
earcutList( origPoly );
earcutList( newPoly );
return;
return ( earcutList( origPoly ) && earcutList( newPoly ) );
}
marker = marker->next;
@ -585,6 +612,8 @@ private:
origPoly = origPoly->next;
} while( origPoly != start );
return false;
}
/**
@ -597,10 +626,15 @@ private:
*/
bool goodSplit( const Vertex* a, const Vertex* b ) const
{
return a->next->i != b->i &&
a->prev->i != b->i &&
!intersectsPolygon( a, b ) &&
locallyInside( a, b );
bool a_on_edge = ( a->nextZ && *a == *a->nextZ ) || ( a->prevZ && *a == *a->prevZ );
bool b_on_edge = ( b->nextZ && *b == *b->nextZ ) || ( b->prevZ && *b == *b->prevZ );
bool no_intersect = a->next->i != b->i && a->prev->i != b->i && !intersectsPolygon( a, b );
bool local_split = locallyInside( a, b ) && locallyInside( b, a ) && middleInside( a, b );
bool same_dir = area( a->prev, a, b->prev ) != 0.0 || area( a, b->prev, b ) != 0.0;
bool has_len = ( *a == *b ) && area( a->prev, a, a->next ) > 0 && area( b->prev, b, b->next ) > 0;
return no_intersect && local_split && ( same_dir || has_len ) && !a_on_edge && !b_on_edge;
}
/**
@ -611,6 +645,22 @@ private:
return ( q->y - p->y ) * ( r->x - q->x ) - ( q->x - p->x ) * ( r->y - q->y );
}
constexpr int sign( double aVal ) const
{
return ( aVal > 0 ) - ( aVal < 0 );
}
/**
* If p, q, and r are collinear and r lies between p and q, then return true.
*/
constexpr bool overlapping( const Vertex* p, const Vertex* q, const Vertex* r ) const
{
return q->x <= std::max( p->x, r->x ) &&
q->x >= std::min( p->x, r->x ) &&
q->y <= std::max( p->y, r->y ) &&
q->y >= std::min( p->y, r->y );
}
/**
* Check for intersection between two segments, end points included.
*
@ -621,8 +671,28 @@ private:
if( ( *p1 == *q1 && *p2 == *q2 ) || ( *p1 == *q2 && *p2 == *q1 ) )
return true;
return ( area( p1, q1, p2 ) > 0 ) != ( area( p1, q1, q2 ) > 0 )
&& ( area( p2, q2, p1 ) > 0 ) != ( area( p2, q2, q1 ) > 0 );
int sign1 = sign( area( p1, q1, p2 ) );
int sign2 = sign( area( p1, q1, q2 ) );
int sign3 = sign( area( p2, q2, p1 ) );
int sign4 = sign( area( p2, q2, q1 ) );
if( sign1 != sign2 && sign3 != sign4 )
return true;
if( sign1 == 0 && overlapping( p1, p2, q1 ) )
return true;
if( sign2 == 0 && overlapping( p1, q2, q1 ) )
return true;
if( sign3 == 0 && overlapping( p2, p1, q2 ) )
return true;
if( sign4 == 0 && overlapping( p2, q1, q2 ) )
return true;
return false;
}
/**
@ -666,6 +736,28 @@ private:
return area( a, b, a->prev ) < 0 || area( a, a->next, b ) < 0;
}
/**
* Check to see if the segment halfway point between a and b is inside the polygon
*/
bool middleInside( const Vertex* a, const Vertex* b ) const
{
const Vertex* p = a;
bool inside = false;
double px = ( a->x + b->x ) / 2;
double py = ( a->y + b->y ) / 2;
do
{
if( ( ( p->y > py ) != ( p->next->y > py ) )
&& ( px < ( p->next->x - p->x ) * ( py - p->y ) / ( p->next->y - p->y ) + p->x ) )
inside = !inside;
p = p->next;
} while( p != a );
return inside;
}
/**
* Create an entry in the vertices lookup and optionally inserts the newly created vertex
* into an existing linked list.
@ -696,7 +788,10 @@ private:
private:
BOX2I m_bbox;
double m_prefactor_x;
double m_prefactor_y;
std::deque<Vertex> m_vertices;
std::set<Vertex*> m_splits;
SHAPE_POLY_SET::TRIANGULATED_POLYGON& m_result;
};