polygon_triangulation.h

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/*
 * This program source code file is part of KiCad, a free EDA CAD application.
 *
 * Copyright (C) 2018 KiCad Developers, see AUTHORS.TXT for contributors.
 *
 * 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 3
 * 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, you may find one here:
 * http://www.gnu.org/licenses/gpl-3.0.html
 * or you may search the http://www.gnu.org website for the version 3 license,
 * or you may write to the Free Software Foundation, Inc.,
 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
 *
 * Based on Uniform Plane Subdivision algorithm from Lamot, Marko, and Borut Žalik.
 * "A fast polygon triangulation algorithm based on uniform plane subdivision."
 * Computers & graphics 27, no. 2 (2003): 239-253.
 *
 * Code derived from:
 * K-3D which is Copyright (c) 2005-2006, Romain Behar, GPL-2, license above
 * earcut which is Copyright (c) 2016, Mapbox, ISC
 *
 * ISC License:
 * Permission to use, copy, modify, and/or distribute this software for any purpose
 * with or without fee is hereby granted, provided that the above copyright notice
 * and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
 * REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
 * FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
 * INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
 * OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
 * TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
 * THIS SOFTWARE.
 *
 */
 
#ifndef __POLYGON_TRIANGULATION_H
#define __POLYGON_TRIANGULATION_H
 
#include <algorithm>
#include <deque>
#include <cmath>
 
#include <advanced_config.h>
#include <clipper.hpp>
#include <geometry/shape_line_chain.h>
#include <geometry/shape_poly_set.h>
#include <geometry/vertex_set.h>
#include <math/box2.h>
#include <math/vector2d.h>
 
#include <wx/log.h>
 
#define TRIANGULATE_TRACE "triangulate"
class POLYGON_TRIANGULATION : public VERTEX_SET
{
public:
 POLYGON_TRIANGULATION( SHAPE_POLY_SET::TRIANGULATED_POLYGON& aResult ) :
 VERTEX_SET( ADVANCED_CFG::GetCfg().m_TriangulateSimplificationLevel ),
 m_vertices_original_size( 0 ), m_result( aResult )
 {};
 
 bool TesselatePolygon( const SHAPE_LINE_CHAIN& aPoly,
 SHAPE_POLY_SET::TRIANGULATED_POLYGON* aHintData )
 {
 m_bbox = aPoly.BBox();
 m_result.Clear();
 
 if( !m_bbox.GetWidth() || !m_bbox.GetHeight() )
 return true;
 
 VERTEX* firstVertex = createList( aPoly );
 
 for( const VECTOR2I& pt : aPoly.CPoints() )
 m_result.AddVertex( pt );
 
 if( !firstVertex || firstVertex->prev == firstVertex->next )
 return true;
 
 wxLogTrace( TRIANGULATE_TRACE, "Created list with %f area", firstVertex->area() );
 
 m_vertices_original_size = m_vertices.size();
 firstVertex->updateList();
 
 if( aHintData && aHintData->Vertices().size() == m_vertices.size() )
 {
 m_result.SetTriangles( aHintData->Triangles() );
 return true;
 }
 else
 {
 auto retval = earcutList( firstVertex );
 
 if( !retval )
 {
 wxLogTrace( TRIANGULATE_TRACE, "Tesselation failed, logging remaining vertices" );
 logRemaining();
 }
 
 m_vertices.clear();
 return retval;
 }
 }
 
private:
 
 void logRemaining()
 {
 std::set<VERTEX*> seen;
 wxLog::EnableLogging();
 for( VERTEX& p : m_vertices )
 {
 if( !p.next || p.next == &p || seen.find( &p ) != seen.end() )
 continue;
 
 logVertices( &p, &seen );
 }
 }
 
 void logVertices( VERTEX* aStart, std::set<VERTEX*>* aSeen )
 {
 if( aSeen && aSeen->count( aStart ) )
 return;
 
 if( aSeen )
 aSeen->insert( aStart );
 
 int count = 1;
 VERTEX* p = aStart->next;
 wxString msg = wxString::Format( "Vertices: %d,%d,", static_cast<int>( aStart->x ),
 static_cast<int>( aStart->y ) );
 
 do
 {
 msg += wxString::Format( "%d,%d,", static_cast<int>( p->x ), static_cast<int>( p->y ) );
 
 if( aSeen )
 aSeen->insert( p );
 
 p = p->next;
 count++;
 } while( p != aStart );
 
 if( count < 3 ) // Don't log anything that only has 2 or fewer points
 return;
 
 msg.RemoveLast();
 wxLogTrace( TRIANGULATE_TRACE, msg );
 }
 
 VERTEX* simplifyList( VERTEX* aStart )
 {
 if( !aStart || aStart->next == aStart->prev )
 return aStart;
 
 VERTEX* p = aStart;
 VERTEX* next = p->next;
 VERTEX* retval = aStart;
 int count = 0;
 
 double sq_dist = ADVANCED_CFG::GetCfg().m_TriangulateSimplificationLevel;
 sq_dist *= sq_dist;
 
 do
 {
 VECTOR2D diff = VECTOR2D( next->x - p->x, next->y - p->y );
 
 if( diff.SquaredEuclideanNorm() < sq_dist )
 {
 if( next == aStart )
 {
 retval = p;
 aStart->remove();
 count++;
 break;
 }
 
 next = next->next;
 p->next->remove();
 count++;
 retval = p;
 }
 else
 {
 p = next;
 next = next->next;
 }
 } while( p != aStart && next && p );
 
 wxLogTrace( TRIANGULATE_TRACE, "Removed %d points in simplifyList", count );
 
 if( count )
 return retval;
 
 return nullptr;
 }
 
 
 VERTEX* removeNullTriangles( VERTEX* aStart )
 {
 VERTEX* retval = nullptr;
 size_t count = 0;
 
 if( ( retval = simplifyList( aStart ) ) )
 aStart = retval;
 
 wxASSERT( aStart->next && aStart->prev );
 
 VERTEX* p = aStart->next;
 
 while( p != aStart && p->next && p->prev )
 {
 // We make a dummy triangle that is actually part of the existing line segment
 // and measure its area. This will not be exactly zero due to floating point
 // errors. We then look for areas that are less than 4 times the area of the
 // dummy triangle. For small triangles, this is a small number
 VERTEX tmp( 0, 0.5 * ( p->prev->x + p->next->x ), 0.5 * ( p->prev->y + p->next->y ), this );
 double null_area = 4.0 * std::abs( area( p->prev, &tmp, p->next ) );
 
 if( *p == *( p->next ) || std::abs( area( p->prev, p, p->next ) ) <= null_area )
 {
 // This is a spike, remove it, leaving only one point
 if( *( p->next ) == *( p->prev ) )
 p->next->remove();
 
 p = p->prev;
 p->next->remove();
 retval = p;
 ++count;
 
 if( p == p->next )
 break;
 
 // aStart was removed above, so we need to reset it
 if( !aStart->next )
 aStart = p->prev;
 
 continue;
 }
 
 p = p->next;
 };
 
 if( !p->next || p->next == p || p->next == p->prev )
 return p;
 
 // We needed an end point above that wouldn't be removed, so
 // here we do the final check for this as a Steiner point
 VERTEX tmp( 0, 0.5 * ( p->prev->x + p->next->x ),
 0.5 * ( p->prev->y + p->next->y ), this );
 double null_area = 4.0 * std::abs( area( p->prev, &tmp, p->next ) );
 
 if( std::abs( area( p->prev, p, p->next ) ) <= null_area )
 {
 retval = p->next;
 p->remove();
 ++count;
 }
 
 wxLogTrace( TRIANGULATE_TRACE, "Removed %zu NULL triangles", count );
 
 return retval;
 }
 
 bool earcutList( VERTEX* aPoint, int pass = 0 )
 {
 wxLogTrace( TRIANGULATE_TRACE, "earcutList starting at %p for pass %d", aPoint, pass );
 
 if( !aPoint )
 return true;
 
 VERTEX* stop = aPoint;
 VERTEX* prev;
 VERTEX* next;
 int internal_pass = 1;
 
 while( aPoint->prev != aPoint->next )
 {
 prev = aPoint->prev;
 next = aPoint->next;
 
 if( aPoint->isEar() )
 {
 // Tiny ears cannot be seen on the screen
 if( !isTooSmall( aPoint ) )
 {
 m_result.AddTriangle( prev->i, aPoint->i, next->i );
 }
 else
 {
 wxLogTrace( TRIANGULATE_TRACE, "Ignoring tiny ear with area %f",
 area( prev, aPoint, next ) );
 }
 
 aPoint->remove();
 
 // Skip one vertex as the triangle will account for the prev node
 aPoint = next->next;
 stop = next->next;
 
 continue;
 }
 
 VERTEX* nextNext = next->next;
 
 if( *prev != *nextNext && intersects( prev, aPoint, next, nextNext ) &&
 locallyInside( prev, nextNext ) &&
 locallyInside( nextNext, prev ) )
 {
 wxLogTrace( TRIANGULATE_TRACE,
 "Local intersection detected. Merging minor triangle with area %f",
 area( prev, aPoint, nextNext ) );
 m_result.AddTriangle( prev->i, aPoint->i, nextNext->i );
 
 // remove two nodes involved
 next->remove();
 aPoint->remove();
 
 aPoint = nextNext;
 stop = nextNext;
 
 continue;
 }
 
 aPoint = next;
 
 /*
 * We've searched the entire polygon for available ears and there are still
 * un-sliced nodes remaining.
 */
 if( aPoint == stop && aPoint->prev != aPoint->next )
 {
 VERTEX* newPoint;
 
 // Removing null triangles will remove steiner points as well as colinear points
 // that are three in a row. Because our next step is to subdivide the polygon,
 // we need to allow it to add the subdivided points first. This is why we only
 // run the RemoveNullTriangles function after the first pass.
 if( ( internal_pass == 2 ) && ( newPoint = removeNullTriangles( aPoint ) ) )
 {
 // There are no remaining triangles in the list
 if( newPoint->next == newPoint->prev )
 break;
 
 aPoint = newPoint;
 stop = newPoint;
 continue;
 }
 
 ++internal_pass;
 
 // This will subdivide the polygon 2 times. The first pass will add enough points
 // such that each edge is less than the average edge length. If this doesn't work
 // The next pass will remove the null triangles (above) and subdivide the polygon
 // again, this time adding one point to each long edge (and thereby changing the locations)
 if( internal_pass < 4 )
 {
 wxLogTrace( TRIANGULATE_TRACE, "Subdividing polygon" );
 subdividePolygon( aPoint, internal_pass );
 continue;
 }
 
 // If we don't have any NULL triangles left, cut the polygon in two and try again
 wxLogTrace( TRIANGULATE_TRACE, "Splitting polygon" );
 
 if( !splitPolygon( aPoint ) )
 return false;
 
 break;
 }
 }
 
 // Check to see if we are left with only three points in the polygon
 if( aPoint->next && aPoint->prev == aPoint->next->next )
 {
 // Three concave points will never be able to be triangulated because they were
 // created by an intersecting polygon, so just drop them.
 if( area( aPoint->prev, aPoint, aPoint->next ) >= 0 )
 return true;
 }
 
 /*
 * At this point, our polygon should be fully tessellated.
 */
 if( aPoint->prev != aPoint->next )
 return std::abs( aPoint->area() ) > ADVANCED_CFG::GetCfg().m_TriangulateMinimumArea;
 
 return true;
 }
 
 
 bool isTooSmall( const VERTEX* aPoint ) const
 {
 double min_area = ADVANCED_CFG::GetCfg().m_TriangulateMinimumArea;
 double prev_sq_len = ( aPoint->prev->x - aPoint->x ) * ( aPoint->prev->x - aPoint->x ) +
 ( aPoint->prev->y - aPoint->y ) * ( aPoint->prev->y - aPoint->y );
 double next_sq_len = ( aPoint->next->x - aPoint->x ) * ( aPoint->next->x - aPoint->x ) +
 ( aPoint->next->y - aPoint->y ) * ( aPoint->next->y - aPoint->y );
 double opp_sq_len = ( aPoint->next->x - aPoint->prev->x ) * ( aPoint->next->x - aPoint->prev->x ) +
 ( aPoint->next->y - aPoint->prev->y ) * ( aPoint->next->y - aPoint->prev->y );
 
 return ( prev_sq_len < min_area || next_sq_len < min_area || opp_sq_len < min_area );
 }
 
 void subdividePolygon( VERTEX* aStart, int pass = 0 )
 {
 VERTEX* p = aStart;
 
 struct VertexComparator {
 bool operator()(const std::pair<VERTEX*,double>& a, const std::pair<VERTEX*,double>& b) const {
 return a.second > b.second;
 }
 };
 
 std::set<std::pair<VERTEX*,double>, VertexComparator> longest;
 double avg = 0.0;
 
 do
 {
 double len = ( p->x - p->next->x ) * ( p->x - p->next->x ) +
 ( p->y - p->next->y ) * ( p->y - p->next->y );
 longest.emplace( p, len );
 
 avg += len;
 p = p->next;
 } while (p != aStart);
 
 avg /= longest.size();
 wxLogTrace( TRIANGULATE_TRACE, "Average length: %f", avg );
 
 for( auto it = longest.begin(); it != longest.end() && it->second > avg; ++it )
 {
 wxLogTrace( TRIANGULATE_TRACE, "Subdividing edge with length %f", it->second );
 VERTEX* a = it->first;
 VERTEX* b = a->next;
 VERTEX* last = a;
 
 // We adjust the number of divisions based on the pass in order to progressively
 // subdivide the polygon when triangulation fails
 int divisions = avg / it->second + 2 + pass;
 double step = 1.0 / divisions;
 
 for( int i = 1; i < divisions; i++ )
 {
 double x = a->x * ( 1.0 - step * i ) + b->x * ( step * i );
 double y = a->y * ( 1.0 - step * i ) + b->y * ( step * i );
 last = insertTriVertex( VECTOR2I( x, y ), last );
 }
 }
 
 // update z-order of the vertices
 aStart->updateList();
 }
 
 bool splitPolygon( VERTEX* start )
 {
 VERTEX* origPoly = start;
 
 // If we have fewer than 4 points, we cannot split the polygon
 if( !start || !start->next || start->next == start->prev
 || start->next->next == start->prev )
 {
 return true;
 }
 
 // Our first attempts to split the polygon will be at overlapping points.
 // These are natural split points and we only need to switch the loop directions
 // to generate two new loops. Since they are overlapping, we are do not
 // need to create a new segment to disconnect the two loops.
 do
 {
 std::vector<VERTEX*> overlapPoints;
 VERTEX* z_pt = origPoly;
 
 while ( z_pt->prevZ && *z_pt->prevZ == *origPoly )
 z_pt = z_pt->prevZ;
 
 overlapPoints.push_back( z_pt );
 
 while( z_pt->nextZ && *z_pt->nextZ == *origPoly )
 {
 z_pt = z_pt->nextZ;
 overlapPoints.push_back( z_pt );
 }
 
 if( overlapPoints.size() != 2 || overlapPoints[0]->next == overlapPoints[1]
 || overlapPoints[0]->prev == overlapPoints[1] )
 {
 origPoly = origPoly->next;
 continue;
 }
 
 if( overlapPoints[0]->area( overlapPoints[1] ) < 0 || overlapPoints[1]->area( overlapPoints[0] ) < 0 )
 {
 wxLogTrace( TRIANGULATE_TRACE, "Split generated a hole, skipping" );
 origPoly = origPoly->next;
 continue;
 }
 
 wxLogTrace( TRIANGULATE_TRACE, "Splitting at overlap point %f, %f", overlapPoints[0]->x, overlapPoints[0]->y );
 std::swap( overlapPoints[0]->next, overlapPoints[1]->next );
 overlapPoints[0]->next->prev = overlapPoints[0];
 overlapPoints[1]->next->prev = overlapPoints[1];
 
 overlapPoints[0]->updateList();
 overlapPoints[1]->updateList();
 logVertices( overlapPoints[0], nullptr );
 logVertices( overlapPoints[1], nullptr );
 bool retval = earcutList( overlapPoints[0] ) && earcutList( overlapPoints[1] );
 
 wxLogTrace( TRIANGULATE_TRACE, "%s at first overlap split", retval ? "Success" : "Failed" );
 return retval;
 
 
 } while ( origPoly != start );
 
 // If we've made it through the split algorithm and we still haven't found a
 // set of overlapping points, we need to create a new segment to split the polygon
 // into two separate polygons. We do this by finding the two vertices that form
 // a valid line (does not cross the existing polygon)
 do
 {
 VERTEX* marker = origPoly->next->next;
 
 while( marker != origPoly->prev )
 {
 // Find a diagonal line that is wholly enclosed by the polygon interior
 if( origPoly->next && origPoly->i != marker->i && goodSplit( origPoly, marker ) )
 {
 VERTEX* newPoly = origPoly->split( marker );
 
 origPoly->updateList();
 newPoly->updateList();
 
 bool retval = earcutList( origPoly ) && earcutList( newPoly );
 
 wxLogTrace( TRIANGULATE_TRACE, "%s at split", retval ? "Success" : "Failed" );
 return retval;
 }
 
 marker = marker->next;
 }
 
 origPoly = origPoly->next;
 } while( origPoly != start );
 
 wxLogTrace( TRIANGULATE_TRACE, "Could not find a valid split point" );
 return false;
 }
 
 bool goodSplit( const VERTEX* a, const VERTEX* b ) const
 {
 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;
 bool pos_area = a->area( b ) > 0 && b->area( a ) > 0;
 
 return no_intersect && local_split && ( same_dir || has_len ) && !a_on_edge && !b_on_edge && pos_area;
 
 }
 
 
 constexpr int sign( double aVal ) const
 {
 return ( aVal > 0 ) - ( aVal < 0 );
 }
 
 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 );
 }
 
 bool intersects( const VERTEX* p1, const VERTEX* q1, const VERTEX* p2, const VERTEX* q2 ) const
 {
 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;
 }
 
 bool intersectsPolygon( const VERTEX* a, const VERTEX* b ) const
 {
 for( size_t ii = 0; ii < m_vertices_original_size; ii++ )
 {
 const VERTEX* p = &m_vertices[ii];
 const VERTEX* q = &m_vertices[( ii + 1 ) % m_vertices_original_size];
 
 if( p->i == a->i || p->i == b->i || q->i == a->i || q->i == b->i )
 continue;
 
 if( intersects( p, q, a, b ) )
 return true;
 }
 
 return false;
 }
 
 VERTEX* insertTriVertex( const VECTOR2I& pt, VERTEX* last )
 {
 m_result.AddVertex( pt );
 return insertVertex( m_result.GetVertexCount() - 1, pt, nullptr );
 }
 
private:
 size_t m_vertices_original_size;
 SHAPE_POLY_SET::TRIANGULATED_POLYGON& m_result;
};
 
#endif //__POLYGON_TRIANGULATION_H