KiCad PCB EDA Suite
PolygonTriangulation Class Reference

`#include <polygon_triangulation.h>`

struct  Vertex

## Public Member Functions

PolygonTriangulation (SHAPE_POLY_SET::TRIANGULATED_POLYGON &aResult)

bool TesselatePolygon (const SHAPE_LINE_CHAIN &aPoly)

## Private Member Functions

int32_t zOrder (const double aX, const double aY) const
Calculate the Morton code of the Vertex http://www.graphics.stanford.edu/~seander/bithacks.html#InterleaveBMN. More...

VertexremoveNullTriangles (Vertex *aStart)
Function removeNullTriangles Iterates through the list to remove NULL triangles if they exist. More...

VertexcreateList (const ClipperLib::Path &aPath)
Function createList Takes a Clipper path and converts it into a circular, doubly-linked list for triangulation. More...

VertexcreateList (const SHAPE_LINE_CHAIN &points)
Function createList Takes the SHAPE_LINE_CHAIN and links each point into a circular, doubly-linked list. More...

bool earcutList (Vertex *aPoint, int pass=0)
Function: earcutList Walks through a circular linked list starting at aPoint. More...

bool isEar (Vertex *aEar) const
Function isEar Checks whether the given vertex is in the middle of an ear. More...

void splitPolygon (Vertex *start)
Function splitPolygon If we cannot find an ear to slice in the current polygon list, we use this to split the polygon into two separate lists and slice them each independently. More...

bool goodSplit (const Vertex *a, const Vertex *b) const
Check if a segment joining two vertices lies fully inside the polygon. More...

double area (const Vertex *p, const Vertex *q, const Vertex *r) const
Function area Returns the twice the signed area of the triangle formed by vertices p, q, r. More...

bool intersects (const Vertex *p1, const Vertex *q1, const Vertex *p2, const Vertex *q2) const
Function intersects Checks for intersection between two segments, end points included. More...

bool intersectsPolygon (const Vertex *a, const Vertex *b) const
Function intersectsPolygon Checks whether the segment from vertex a -> vertex b crosses any of the segments of the polygon of which vertex a is a member. More...

bool locallyInside (const Vertex *a, const Vertex *b) const
Function locallyInside Checks whether the segment from vertex a -> vertex b is inside the polygon around the immediate area of vertex a. More...

VertexinsertVertex (const VECTOR2I &pt, Vertex *last)
Function insertVertex Creates an entry in the vertices lookup and optionally inserts the newly created vertex into an existing linked list. More...

## Private Attributes

BOX2I m_bbox

std::deque< Vertexm_vertices

SHAPE_POLY_SET::TRIANGULATED_POLYGONm_result

## Detailed Description

Definition at line 56 of file polygon_triangulation.h.

## ◆ PolygonTriangulation()

 PolygonTriangulation::PolygonTriangulation ( SHAPE_POLY_SET::TRIANGULATED_POLYGON & aResult )
inline

Definition at line 61 of file polygon_triangulation.h.

61  :
62  m_result( aResult )
63  {};
SHAPE_POLY_SET::TRIANGULATED_POLYGON & m_result

## ◆ area()

 double PolygonTriangulation::area ( const Vertex * p, const Vertex * q, const Vertex * r ) const
inlineprivate

Function area Returns the twice the signed area of the triangle formed by vertices p, q, r.

Definition at line 567 of file polygon_triangulation.h.

568  {
569  return ( q->y - p->y ) * ( r->x - q->x ) - ( q->x - p->x ) * ( r->y - q->y );
570  }

References PolygonTriangulation::Vertex::x, and PolygonTriangulation::Vertex::y.

Referenced by intersects(), isEar(), locallyInside(), and removeNullTriangles().

## ◆ createList() [1/2]

 Vertex* PolygonTriangulation::createList ( const ClipperLib::Path & aPath )
inlineprivate

Function createList Takes a Clipper path and converts it into a circular, doubly-linked list for triangulation.

Definition at line 301 of file polygon_triangulation.h.

302  {
303  Vertex* tail = nullptr;
304  double sum = 0.0;
305  auto len = aPath.size();
306
307  // Check for winding order
308  for( size_t i = 0; i < len; i++ )
309  {
310  auto p1 = aPath.at( i );
311  auto p2 = aPath.at( ( i + 1 ) < len ? i + 1 : 0 );
312
313  sum += ( ( p2.X - p1.X ) * ( p2.Y + p1.Y ) );
314  }
315
316  if( sum <= 0.0 )
317  {
318  for( auto point : aPath )
319  tail = insertVertex( VECTOR2I( point.X, point.Y ), tail );
320  }
321  else
322  {
323  for( size_t i = 0; i < len; i++ )
324  {
325  auto p = aPath.at( len - i - 1 );
326  tail = insertVertex( VECTOR2I( p.X, p.Y ), tail );
327  }
328  }
329
330  if( tail && ( *tail == *tail->next ) )
331  {
332  tail->next->remove();
333  }
334
335  return tail;
336
337  }
VECTOR2< int > VECTOR2I
Definition: vector2d.h:587
size_t i
Definition: json11.cpp:597
Vertex * insertVertex(const VECTOR2I &pt, Vertex *last)
Function insertVertex Creates an entry in the vertices lookup and optionally inserts the newly create...

Referenced by TesselatePolygon().

## ◆ createList() [2/2]

 Vertex* PolygonTriangulation::createList ( const SHAPE_LINE_CHAIN & points )
inlineprivate

Function createList Takes the SHAPE_LINE_CHAIN and links each point into a circular, doubly-linked list.

Definition at line 344 of file polygon_triangulation.h.

345  {
346  Vertex* tail = nullptr;
347  double sum = 0.0;
348
349  // Check for winding order
350  for( int i = 0; i < points.PointCount(); i++ )
351  {
352  VECTOR2D p1 = points.CPoint( i );
353  VECTOR2D p2 = points.CPoint( i + 1 );
354
355  sum += ( ( p2.x - p1.x ) * ( p2.y + p1.y ) );
356  }
357
358  if( sum > 0.0 )
359  for( int i = points.PointCount() - 1; i >= 0; i--)
360  tail = insertVertex( points.CPoint( i ), tail );
361  else
362  for( int i = 0; i < points.PointCount(); i++ )
363  tail = insertVertex( points.CPoint( i ), tail );
364
365  if( tail && ( *tail == *tail->next ) )
366  {
367  tail->next->remove();
368  }
369
370  return tail;
371  }
void remove()
Function remove Removes the node from the linked list and z-ordered linked list.
int PointCount() const
Function PointCount()
const VECTOR2I & CPoint(int aIndex) const
Function CPoint()
size_t i
Definition: json11.cpp:597
Vertex * insertVertex(const VECTOR2I &pt, Vertex *last)
Function insertVertex Creates an entry in the vertices lookup and optionally inserts the newly create...

## ◆ earcutList()

 bool PolygonTriangulation::earcutList ( Vertex * aPoint, int pass = `0` )
inlineprivate

Function: earcutList Walks through a circular linked list starting at aPoint.

For each point, test to see if the adjacent points form a triangle that is completely enclosed by the remaining polygon (an "ear" sticking off the polygon). If the three points form an ear, we log the ear's location and remove the center point from the linked list.

This function can be called recursively in the case of difficult polygons. In cases where there is an intersection (not technically allowed by KiCad, but could exist in an edited file), we create a single triangle and remove both vertices before attempting to

We've searched the entire polygon for available ears and there are still un-sliced nodes remaining

At this point, our polygon should be fully tesselated.

Definition at line 384 of file polygon_triangulation.h.

385  {
386  if( !aPoint )
387  return true;
388
389  Vertex* stop = aPoint;
390  Vertex* prev;
391  Vertex* next;
392
393  while( aPoint->prev != aPoint->next )
394  {
395  prev = aPoint->prev;
396  next = aPoint->next;
397
398  if( isEar( aPoint ) )
399  {
400  m_result.AddTriangle( prev->i, aPoint->i, next->i );
401  aPoint->remove();
402
403  // Skip one vertex as the triangle will account for the prev node
404  aPoint = next->next;
405  stop = next->next;
406
407  continue;
408  }
409
410  Vertex* nextNext = next->next;
411
412  if( *prev != *nextNext && intersects( prev, aPoint, next, nextNext ) &&
413  locallyInside( prev, nextNext ) &&
414  locallyInside( nextNext, prev ) )
415  {
416  m_result.AddTriangle( prev->i, aPoint->i, nextNext->i );
417
418  // remove two nodes involved
419  next->remove();
420  aPoint->remove();
421
422  aPoint = nextNext;
423
424  continue;
425  }
426
427  aPoint = next;
428
433  if( aPoint == stop )
434  {
435  // First, try to remove the remaining steiner points
436  // If aPoint is a steiner, we need to re-assign both the start and stop points
437  if( auto newPoint = removeNullTriangles( aPoint ) )
438  {
439  aPoint = newPoint;
440  stop = newPoint;
441  continue;
442  }
443
444  // If we don't have any NULL triangles left, cut the polygon in two and try again
445  splitPolygon( aPoint );
446  break;
447  }
448  }
449
453  return( aPoint->prev == aPoint->next );
454  }
CITER next(CITER it)
Definition: ptree.cpp:130
bool intersects(const Vertex *p1, const Vertex *q1, const Vertex *p2, const Vertex *q2) const
Function intersects Checks for intersection between two segments, end points included.
Vertex * removeNullTriangles(Vertex *aStart)
Function removeNullTriangles Iterates through the list to remove NULL triangles if they exist.
SHAPE_POLY_SET::TRIANGULATED_POLYGON & m_result
bool locallyInside(const Vertex *a, const Vertex *b) const
Function locallyInside Checks whether the segment from vertex a -> vertex b is inside the polygon aro...
bool isEar(Vertex *aEar) const
Function isEar Checks whether the given vertex is in the middle of an ear.
void splitPolygon(Vertex *start)
Function splitPolygon If we cannot find an ear to slice in the current polygon list,...

Referenced by splitPolygon(), and TesselatePolygon().

## ◆ goodSplit()

 bool PolygonTriangulation::goodSplit ( const Vertex * a, const Vertex * b ) const
inlineprivate

Check if a segment joining two vertices lies fully inside the polygon.

To do this, we first ensure that the line isn't along the polygon edge. Next, we know that if the line doesn't intersect the polygon, then it is either fully inside or fully outside the polygon. Finally, by checking whether the segment is enclosed by the local triangles, we distinguish between these two cases and no further checks are needed.

Definition at line 554 of file polygon_triangulation.h.

555  {
556  return a->next->i != b->i &&
557  a->prev->i != b->i &&
558  !intersectsPolygon( a, b ) &&
559  locallyInside( a, b );
560  }
bool intersectsPolygon(const Vertex *a, const Vertex *b) const
Function intersectsPolygon Checks whether the segment from vertex a -> vertex b crosses any of the se...
bool locallyInside(const Vertex *a, const Vertex *b) const
Function locallyInside Checks whether the segment from vertex a -> vertex b is inside the polygon aro...

Referenced by splitPolygon().

## ◆ insertVertex()

 Vertex* PolygonTriangulation::insertVertex ( const VECTOR2I & pt, Vertex * last )
inlineprivate

Function insertVertex Creates an entry in the vertices lookup and optionally inserts the newly created vertex into an existing linked list.

Returns a pointer to the newly created vertex

Definition at line 631 of file polygon_triangulation.h.

632  {
633  m_result.AddVertex( pt );
634  m_vertices.emplace_back( m_result.GetVertexCount() - 1, pt.x, pt.y, this );
635
636  Vertex* p = &m_vertices.back();
637  if( !last )
638  {
639  p->prev = p;
640  p->next = p;
641  }
642  else
643  {
644  p->next = last->next;
645  p->prev = last;
646  last->next->prev = p;
647  last->next = p;
648  }
649  return p;
650  }
SHAPE_POLY_SET::TRIANGULATED_POLYGON & m_result
void AddVertex(const VECTOR2I &aP)
std::deque< Vertex > m_vertices

Referenced by createList().

## ◆ intersects()

 bool PolygonTriangulation::intersects ( const Vertex * p1, const Vertex * q1, const Vertex * p2, const Vertex * q2 ) const
inlineprivate

Function intersects Checks for intersection between two segments, end points included.

Returns true if p1-p2 intersects q1-q2

Definition at line 577 of file polygon_triangulation.h.

578  {
579  if( ( *p1 == *q1 && *p2 == *q2 ) || ( *p1 == *q2 && *p2 == *q1 ) )
580  return true;
581
582  return ( area( p1, q1, p2 ) > 0 ) != ( area( p1, q1, q2 ) > 0 )
583  && ( area( p2, q2, p1 ) > 0 ) != ( area( p2, q2, q1 ) > 0 );
584  }
double area(const Vertex *p, const Vertex *q, const Vertex *r) const
Function area Returns the twice the signed area of the triangle formed by vertices p,...

References area().

Referenced by earcutList(), and intersectsPolygon().

## ◆ intersectsPolygon()

 bool PolygonTriangulation::intersectsPolygon ( const Vertex * a, const Vertex * b ) const
inlineprivate

Function intersectsPolygon Checks whether the segment from vertex a -> vertex b crosses any of the segments of the polygon of which vertex a is a member.

Return true if the segment intersects the edge of the polygon

Definition at line 592 of file polygon_triangulation.h.

593  {
594  const Vertex* p = a->next;
595  do
596  {
597  if( p->i != a->i &&
598  p->next->i != a->i &&
599  p->i != b->i &&
600  p->next->i != b->i && intersects( p, p->next, a, b ) )
601  return true;
602
603  p = p->next;
604  } while( p != a );
605
606  return false;
607  }
bool intersects(const Vertex *p1, const Vertex *q1, const Vertex *p2, const Vertex *q2) const
Function intersects Checks for intersection between two segments, end points included.

Referenced by goodSplit().

## ◆ isEar()

 bool PolygonTriangulation::isEar ( Vertex * aEar ) const
inlineprivate

Function isEar Checks whether the given vertex is in the middle of an ear.

This works by walking forward and backward in zOrder to the limits of the minimal bounding box formed around the triangle, checking whether any points are located inside the given triangle.

Returns true if aEar is the apex point of a ear in the polygon

Definition at line 465 of file polygon_triangulation.h.

466  {
467  const Vertex* a = aEar->prev;
468  const Vertex* b = aEar;
469  const Vertex* c = aEar->next;
470
471  // If the area >=0, then the three points for a concave sequence
472  // with b as the reflex point
473  if( area( a, b, c ) >= 0 )
474  return false;
475
476  // triangle bbox
477  const double minTX = std::min( a->x, std::min( b->x, c->x ) );
478  const double minTY = std::min( a->y, std::min( b->y, c->y ) );
479  const double maxTX = std::max( a->x, std::max( b->x, c->x ) );
480  const double maxTY = std::max( a->y, std::max( b->y, c->y ) );
481
482  // z-order range for the current triangle bounding box
483  const int32_t minZ = zOrder( minTX, minTY );
484  const int32_t maxZ = zOrder( maxTX, maxTY );
485
486  // first look for points inside the triangle in increasing z-order
487  Vertex* p = aEar->nextZ;
488
489  while( p && p->z <= maxZ )
490  {
491  if( p != a && p != c
492  && p->inTriangle( *a, *b, *c )
493  && area( p->prev, p, p->next ) >= 0 )
494  return false;
495  p = p->nextZ;
496  }
497
498  // then look for points in decreasing z-order
499  p = aEar->prevZ;
500
501  while( p && p->z >= minZ )
502  {
503  if( p != a && p != c
504  && p->inTriangle( *a, *b, *c )
505  && area( p->prev, p, p->next ) >= 0 )
506  return false;
507  p = p->prevZ;
508  }
509
510  return true;
511  }
int32_t zOrder(const double aX, const double aY) const
Calculate the Morton code of the Vertex http://www.graphics.stanford.edu/~seander/bithacks....
#define max(a, b)
Definition: auxiliary.h:86
double area(const Vertex *p, const Vertex *q, const Vertex *r) const
Function area Returns the twice the signed area of the triangle formed by vertices p,...
#define min(a, b)
Definition: auxiliary.h:85

Referenced by earcutList().

## ◆ locallyInside()

 bool PolygonTriangulation::locallyInside ( const Vertex * a, const Vertex * b ) const
inlineprivate

Function locallyInside Checks whether the segment from vertex a -> vertex b is inside the polygon around the immediate area of vertex a.

We don't define the exact area over which the segment is inside but it is guaranteed to be inside the polygon immediately adjacent to vertex a. Returns true if the segment from a->b is inside a's polygon next to vertex a

Definition at line 617 of file polygon_triangulation.h.

618  {
619  if( area( a->prev, a, a->next ) < 0 )
620  return area( a, b, a->next ) >= 0 && area( a, a->prev, b ) >= 0;
621  else
622  return area( a, b, a->prev ) < 0 || area( a, a->next, b ) < 0;
623  }
double area(const Vertex *p, const Vertex *q, const Vertex *r) const
Function area Returns the twice the signed area of the triangle formed by vertices p,...

Referenced by earcutList(), and goodSplit().

## ◆ removeNullTriangles()

 Vertex* PolygonTriangulation::removeNullTriangles ( Vertex * aStart )
inlineprivate

Function removeNullTriangles Iterates through the list to remove NULL triangles if they exist.

This should only be called as a last resort when tesselation fails as the NULL triangles are inserted as Steiner points to improve the triangulation regularity of polygons

Definition at line 266 of file polygon_triangulation.h.

267  {
268  Vertex* retval = nullptr;
269  Vertex* p = aStart->next;
270
271  while( p != aStart )
272  {
273  if( area( p->prev, p, p->next ) == 0.0 )
274  {
275  p = p->prev;
276  p->next->remove();
277  retval = aStart;
278
279  if( p == p->next )
280  break;
281  }
282  p = p->next;
283  };
284
285  // We needed an end point above that wouldn't be removed, so
286  // here we do the final check for this as a Steiner point
287  if( area( aStart->prev, aStart, aStart->next ) == 0.0 )
288  {
289  retval = p->next;
290  p->remove();
291  }
292
293  return retval;
294  }
double area(const Vertex *p, const Vertex *q, const Vertex *r) const
Function area Returns the twice the signed area of the triangle formed by vertices p,...

Referenced by earcutList().

## ◆ splitPolygon()

 void PolygonTriangulation::splitPolygon ( Vertex * start )
inlineprivate

Function splitPolygon If we cannot find an ear to slice in the current polygon list, we use this to split the polygon into two separate lists and slice them each independently.

This is assured to generate at least one new ear if the split is successful

Definition at line 520 of file polygon_triangulation.h.

521  {
522  Vertex* origPoly = start;
523  do
524  {
525  Vertex* marker = origPoly->next->next;
526  while( marker != origPoly->prev )
527  {
528  // Find a diagonal line that is wholly enclosed by the polygon interior
529  if( origPoly->i != marker->i && goodSplit( origPoly, marker ) )
530  {
531  Vertex* newPoly = origPoly->split( marker );
532
533  origPoly->updateList();
534  newPoly->updateList();
535
536  earcutList( origPoly );
537  earcutList( newPoly );
538  return;
539  }
540  marker = marker->next;
541  }
542  origPoly = origPoly->next;
543  } while( origPoly != start );
544  }
bool earcutList(Vertex *aPoint, int pass=0)
Function: earcutList Walks through a circular linked list starting at aPoint.
bool goodSplit(const Vertex *a, const Vertex *b) const
Check if a segment joining two vertices lies fully inside the polygon.

Referenced by earcutList().

## ◆ TesselatePolygon()

 bool PolygonTriangulation::TesselatePolygon ( const SHAPE_LINE_CHAIN & aPoly )
inline

Place the polygon Vertices into a circular linked list and check for lists that have only 0, 1 or 2 elements and therefore cannot be polygons

Definition at line 655 of file polygon_triangulation.h.

656  {
657  m_bbox = aPoly.BBox();
658  m_result.Clear();
659
660  if( !m_bbox.GetWidth() || !m_bbox.GetHeight() )
661  return false;
662
666  Vertex* firstVertex = createList( aPoly );
667  if( !firstVertex || firstVertex->prev == firstVertex->next )
668  return false;
669
670  firstVertex->updateList();
671
672  auto retval = earcutList( firstVertex );
673  m_vertices.clear();
674  return retval;
675  }
Vertex * createList(const ClipperLib::Path &aPath)
Function createList Takes a Clipper path and converts it into a circular, doubly-linked list for tria...
bool earcutList(Vertex *aPoint, int pass=0)
Function: earcutList Walks through a circular linked list starting at aPoint.
const BOX2I BBox(int aClearance=0) const override
Function BBox()
coord_type GetWidth() const
Definition: box2.h:195
SHAPE_POLY_SET::TRIANGULATED_POLYGON & m_result
coord_type GetHeight() const
Definition: box2.h:196
std::deque< Vertex > m_vertices

## ◆ zOrder()

 int32_t PolygonTriangulation::zOrder ( const double aX, const double aY ) const
inlineprivate

Calculate the Morton code of the Vertex http://www.graphics.stanford.edu/~seander/bithacks.html#InterleaveBMN.

Definition at line 241 of file polygon_triangulation.h.

242  {
243  int32_t x = static_cast<int32_t>( 32767.0 * ( aX - m_bbox.GetX() ) / m_bbox.GetWidth() );
244  int32_t y = static_cast<int32_t>( 32767.0 * ( aY - m_bbox.GetY() ) / m_bbox.GetHeight() );
245
246  x = ( x | ( x << 8 ) ) & 0x00FF00FF;
247  x = ( x | ( x << 4 ) ) & 0x0F0F0F0F;
248  x = ( x | ( x << 2 ) ) & 0x33333333;
249  x = ( x | ( x << 1 ) ) & 0x55555555;
250
251  y = ( y | ( y << 8 ) ) & 0x00FF00FF;
252  y = ( y | ( y << 4 ) ) & 0x0F0F0F0F;
253  y = ( y | ( y << 2 ) ) & 0x33333333;
254  y = ( y | ( y << 1 ) ) & 0x55555555;
255
256  return x | ( y << 1 );
257  }
coord_type GetX() const
Definition: box2.h:188
coord_type GetWidth() const
Definition: box2.h:195
coord_type GetY() const
Definition: box2.h:189
coord_type GetHeight() const
Definition: box2.h:196

Referenced by isEar(), and PolygonTriangulation::Vertex::updateOrder().

## ◆ m_bbox

 BOX2I PolygonTriangulation::m_bbox
private

Definition at line 232 of file polygon_triangulation.h.

Referenced by TesselatePolygon(), and zOrder().

## ◆ m_result

 SHAPE_POLY_SET::TRIANGULATED_POLYGON& PolygonTriangulation::m_result
private

Definition at line 234 of file polygon_triangulation.h.

Referenced by earcutList(), insertVertex(), and TesselatePolygon().

## ◆ m_vertices

 std::deque PolygonTriangulation::m_vertices
private

The documentation for this class was generated from the following file: