771 lines
23 KiB
C++
771 lines
23 KiB
C++
/*
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* This program source code file is part of KiCad, a free EDA CAD application.
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*
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* Modifications Copyright (C) 2018-2023 KiCad Developers
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 2
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* of the License, or (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, you may find one here:
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* http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
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* or you may search the http://www.gnu.org website for the version 2 license,
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* or you may write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
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*
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* Based on Uniform Plane Subdivision algorithm from Lamot, Marko, and Borut Žalik.
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* "A fast polygon triangulation algorithm based on uniform plane subdivision."
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* Computers & graphics 27, no. 2 (2003): 239-253.
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*
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* Code derived from:
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* K-3D which is Copyright (c) 2005-2006, Romain Behar, GPL-2, license above
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* earcut which is Copyright (c) 2016, Mapbox, ISC
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*
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* ISC License:
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* Permission to use, copy, modify, and/or distribute this software for any purpose
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* with or without fee is hereby granted, provided that the above copyright notice
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* and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
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* REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
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* FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
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* INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
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* OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
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* TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
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* THIS SOFTWARE.
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*
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*/
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#ifndef __POLYGON_TRIANGULATION_H
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#define __POLYGON_TRIANGULATION_H
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#include <algorithm>
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#include <deque>
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#include <cmath>
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#include <clipper.hpp>
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#include <geometry/shape_line_chain.h>
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#include <geometry/shape_poly_set.h>
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#include <math/box2.h>
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#include <math/vector2d.h>
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class POLYGON_TRIANGULATION
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{
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public:
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POLYGON_TRIANGULATION( SHAPE_POLY_SET::TRIANGULATED_POLYGON& aResult ) :
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m_result( aResult )
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{};
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bool TesselatePolygon( const SHAPE_LINE_CHAIN& aPoly )
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{
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m_bbox = aPoly.BBox();
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m_result.Clear();
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if( !m_bbox.GetWidth() || !m_bbox.GetHeight() )
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return false;
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/// Place the polygon Vertices into a circular linked list
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/// and check for lists that have only 0, 1 or 2 elements and
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/// therefore cannot be polygons
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VERTEX* firstVertex = createList( aPoly );
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if( !firstVertex || firstVertex->prev == firstVertex->next )
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return false;
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firstVertex->updateList();
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auto retval = earcutList( firstVertex );
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m_vertices.clear();
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return retval;
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}
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private:
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struct VERTEX
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{
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VERTEX( size_t aIndex, double aX, double aY, POLYGON_TRIANGULATION* aParent ) :
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i( aIndex ),
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x( aX ),
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y( aY ),
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parent( aParent )
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{
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}
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VERTEX& operator=( const VERTEX& ) = delete;
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VERTEX& operator=( VERTEX&& ) = delete;
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bool operator==( const VERTEX& rhs ) const
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{
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return this->x == rhs.x && this->y == rhs.y;
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}
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bool operator!=( const VERTEX& rhs ) const { return !( *this == rhs ); }
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/**
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* Split the referenced polygon between the reference point and
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* vertex b, assuming they are in the same polygon. Notes that while we
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* create a new vertex pointer for the linked list, we maintain the same
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* vertex index value from the original polygon. In this way, we have
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* two polygons that both share the same vertices.
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*
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* @return the newly created vertex in the polygon that does not include the
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* reference vertex.
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*/
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VERTEX* split( VERTEX* b )
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{
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parent->m_vertices.emplace_back( i, x, y, parent );
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VERTEX* a2 = &parent->m_vertices.back();
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parent->m_vertices.emplace_back( b->i, b->x, b->y, parent );
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VERTEX* b2 = &parent->m_vertices.back();
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VERTEX* an = next;
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VERTEX* bp = b->prev;
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next = b;
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b->prev = this;
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a2->next = an;
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an->prev = a2;
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b2->next = a2;
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a2->prev = b2;
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bp->next = b2;
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b2->prev = bp;
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return b2;
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}
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/**
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* Remove the node from the linked list and z-ordered linked list.
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*/
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void remove()
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{
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next->prev = prev;
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prev->next = next;
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if( prevZ )
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prevZ->nextZ = nextZ;
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if( nextZ )
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nextZ->prevZ = prevZ;
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next = nullptr;
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prev = nullptr;
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nextZ = nullptr;
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prevZ = nullptr;
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}
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void updateOrder()
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{
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if( !z )
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z = parent->zOrder( x, y );
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}
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/**
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* After inserting or changing nodes, this function should be called to
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* remove duplicate vertices and ensure z-ordering is correct.
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*/
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void updateList()
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{
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VERTEX* p = next;
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while( p != this )
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{
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/**
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* Remove duplicates
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*/
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if( *p == *p->next )
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{
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p = p->prev;
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p->next->remove();
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if( p == p->next )
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break;
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}
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p->updateOrder();
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p = p->next;
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};
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updateOrder();
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zSort();
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}
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/**
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* Sort all vertices in this vertex's list by their Morton code.
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*/
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void zSort()
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{
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std::deque<VERTEX*> queue;
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queue.push_back( this );
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for( auto p = next; p && p != this; p = p->next )
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queue.push_back( p );
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std::sort( queue.begin(), queue.end(), []( const VERTEX* a, const VERTEX* b )
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{
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if( a->z != b->z )
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return a->z < b->z;
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if( a->x != b->x )
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return a->x < b->x;
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if( a->y != b->y )
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return a->y < b->y;
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return a->i < b->i;
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} );
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VERTEX* prev_elem = nullptr;
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for( auto elem : queue )
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{
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if( prev_elem )
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prev_elem->nextZ = elem;
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elem->prevZ = prev_elem;
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prev_elem = elem;
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}
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prev_elem->nextZ = nullptr;
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}
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/**
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* Check to see if triangle surrounds our current vertex
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*/
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bool inTriangle( const VERTEX& a, const VERTEX& b, const VERTEX& c )
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{
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return ( c.x - x ) * ( a.y - y ) - ( a.x - x ) * ( c.y - y ) >= 0
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&& ( a.x - x ) * ( b.y - y ) - ( b.x - x ) * ( a.y - y ) >= 0
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&& ( b.x - x ) * ( c.y - y ) - ( c.x - x ) * ( b.y - y ) >= 0;
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}
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const size_t i;
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const double x;
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const double y;
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POLYGON_TRIANGULATION* parent;
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// previous and next vertices nodes in a polygon ring
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VERTEX* prev = nullptr;
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VERTEX* next = nullptr;
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// z-order curve value
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int32_t z = 0;
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// previous and next nodes in z-order
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VERTEX* prevZ = nullptr;
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VERTEX* nextZ = nullptr;
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};
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/**
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* Calculate the Morton code of the Vertex
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* http://www.graphics.stanford.edu/~seander/bithacks.html#InterleaveBMN
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*
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*/
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int32_t zOrder( const double aX, const double aY ) const
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{
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int32_t x = static_cast<int32_t>( 32767.0 * ( aX - m_bbox.GetX() ) / m_bbox.GetWidth() );
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int32_t y = static_cast<int32_t>( 32767.0 * ( aY - m_bbox.GetY() ) / m_bbox.GetHeight() );
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x = ( x | ( x << 8 ) ) & 0x00FF00FF;
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x = ( x | ( x << 4 ) ) & 0x0F0F0F0F;
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x = ( x | ( x << 2 ) ) & 0x33333333;
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x = ( x | ( x << 1 ) ) & 0x55555555;
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y = ( y | ( y << 8 ) ) & 0x00FF00FF;
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y = ( y | ( y << 4 ) ) & 0x0F0F0F0F;
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y = ( y | ( y << 2 ) ) & 0x33333333;
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y = ( y | ( y << 1 ) ) & 0x55555555;
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return x | ( y << 1 );
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}
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/**
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* Iterate through the list to remove NULL triangles if they exist.
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*
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* This should only be called as a last resort when tesselation fails
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* as the NULL triangles are inserted as Steiner points to improve the
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* triangulation regularity of polygons
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*/
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VERTEX* removeNullTriangles( VERTEX* aStart )
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{
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VERTEX* retval = nullptr;
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VERTEX* p = aStart->next;
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while( p != aStart )
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{
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if( *p == *( p->next ) || area( p->prev, p, p->next ) == 0.0 )
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{
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p = p->prev;
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p->next->remove();
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retval = aStart;
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if( p == p->next )
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break;
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}
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p = p->next;
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};
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// We needed an end point above that wouldn't be removed, so
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// here we do the final check for this as a Steiner point
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if( area( aStart->prev, aStart, aStart->next ) == 0.0 )
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{
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retval = p->next;
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p->remove();
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}
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return retval;
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}
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/**
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* Take a Clipper path and converts it into a circular, doubly-linked list for triangulation.
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*/
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VERTEX* createList( const ClipperLib::Path& aPath )
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{
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VERTEX* tail = nullptr;
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double sum = 0.0;
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auto len = aPath.size();
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// Check for winding order
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for( size_t i = 0; i < len; i++ )
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{
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auto p1 = aPath.at( i );
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auto p2 = aPath.at( ( i + 1 ) < len ? i + 1 : 0 );
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sum += ( ( p2.X - p1.X ) * ( p2.Y + p1.Y ) );
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}
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if( sum <= 0.0 )
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{
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for( auto point : aPath )
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tail = insertVertex( VECTOR2I( point.X, point.Y ), tail );
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}
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else
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{
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for( size_t i = 0; i < len; i++ )
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{
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auto p = aPath.at( len - i - 1 );
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tail = insertVertex( VECTOR2I( p.X, p.Y ), tail );
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}
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}
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if( tail && ( *tail == *tail->next ) )
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{
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tail->next->remove();
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}
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return tail;
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}
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/**
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* Take a #SHAPE_LINE_CHAIN and links each point into a circular, doubly-linked list.
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*/
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VERTEX* createList( const SHAPE_LINE_CHAIN& points )
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{
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VERTEX* tail = nullptr;
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double sum = 0.0;
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// Check for winding order
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for( int i = 0; i < points.PointCount(); i++ )
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{
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VECTOR2D p1 = points.CPoint( i );
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VECTOR2D p2 = points.CPoint( i + 1 );
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sum += ( ( p2.x - p1.x ) * ( p2.y + p1.y ) );
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}
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if( sum > 0.0 )
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for( int i = points.PointCount() - 1; i >= 0; i--)
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tail = insertVertex( points.CPoint( i ), tail );
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else
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for( int i = 0; i < points.PointCount(); i++ )
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tail = insertVertex( points.CPoint( i ), tail );
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if( tail && ( *tail == *tail->next ) )
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{
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tail->next->remove();
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}
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return tail;
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}
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/**
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* Walk through a circular linked list starting at \a aPoint.
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*
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* For each point, test to see if the adjacent points form a triangle that is completely
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* enclosed by the remaining polygon (an "ear" sticking off the polygon). If the three
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* points form an ear, we log the ear's location and remove the center point from the
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* linked list.
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*
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* This function can be called recursively in the case of difficult polygons. In cases
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* where there is an intersection (not technically allowed by KiCad, but could exist in
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* an edited file), we create a single triangle and remove both vertices before attempting
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* to.
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*/
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bool earcutList( VERTEX* aPoint, int pass = 0 )
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{
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if( !aPoint )
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return true;
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VERTEX* stop = aPoint;
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VERTEX* prev;
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VERTEX* next;
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while( aPoint->prev != aPoint->next )
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{
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prev = aPoint->prev;
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next = aPoint->next;
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if( isEar( aPoint ) )
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{
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m_result.AddTriangle( prev->i, aPoint->i, next->i );
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aPoint->remove();
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// Skip one vertex as the triangle will account for the prev node
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aPoint = next->next;
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stop = next->next;
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continue;
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}
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VERTEX* nextNext = next->next;
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if( *prev != *nextNext && intersects( prev, aPoint, next, nextNext ) &&
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locallyInside( prev, nextNext ) &&
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locallyInside( nextNext, prev ) )
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{
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m_result.AddTriangle( prev->i, aPoint->i, nextNext->i );
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// remove two nodes involved
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next->remove();
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aPoint->remove();
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aPoint = nextNext;
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stop = nextNext;
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continue;
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}
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aPoint = next;
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/*
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* We've searched the entire polygon for available ears and there are still
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* un-sliced nodes remaining.
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*/
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if( aPoint == stop )
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{
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// First, try to remove the remaining steiner points
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// If aPoint is a steiner, we need to re-assign both the start and stop points
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if( auto newPoint = removeNullTriangles( aPoint ) )
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{
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aPoint = newPoint;
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stop = newPoint;
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continue;
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}
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// If we don't have any NULL triangles left, cut the polygon in two and try again
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if( !splitPolygon( aPoint ) )
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return false;
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break;
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}
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}
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// Check to see if we are left with only three points in the polygon
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if( aPoint->next && aPoint->prev == aPoint->next->next )
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{
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// Three concave points will never be able to be triangulated because they were
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// created by an intersecting polygon, so just drop them.
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if( area( aPoint->prev, aPoint, aPoint->next ) >= 0 )
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return true;
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}
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/*
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* At this point, our polygon should be fully tessellated.
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*/
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return( aPoint->prev == aPoint->next );
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}
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/**
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* Check whether the given vertex is in the middle of an ear.
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*
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* This works by walking forward and backward in zOrder to the limits of the minimal
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* bounding box formed around the triangle, checking whether any points are located
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* inside the given triangle.
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*
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* @return true if aEar is the apex point of a ear in the polygon.
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*/
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bool isEar( VERTEX* aEar ) const
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{
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const VERTEX* a = aEar->prev;
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const VERTEX* b = aEar;
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const VERTEX* c = aEar->next;
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// If the area >=0, then the three points for a concave sequence
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// with b as the reflex point
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if( area( a, b, c ) >= 0 )
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return false;
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// triangle bbox
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const double minTX = std::min( a->x, std::min( b->x, c->x ) );
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const double minTY = std::min( a->y, std::min( b->y, c->y ) );
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const double maxTX = std::max( a->x, std::max( b->x, c->x ) );
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const double maxTY = std::max( a->y, std::max( b->y, c->y ) );
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// z-order range for the current triangle bounding box
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const int32_t minZ = zOrder( minTX, minTY );
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const int32_t maxZ = zOrder( maxTX, maxTY );
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// first look for points inside the triangle in increasing z-order
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VERTEX* p = aEar->nextZ;
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while( p && p->z <= maxZ )
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{
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if( p != a && p != c
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&& p->inTriangle( *a, *b, *c )
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&& area( p->prev, p, p->next ) >= 0 )
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return false;
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p = p->nextZ;
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}
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// then look for points in decreasing z-order
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p = aEar->prevZ;
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while( p && p->z >= minZ )
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{
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if( p != a && p != c
|
|
&& p->inTriangle( *a, *b, *c )
|
|
&& area( p->prev, p, p->next ) >= 0 )
|
|
return false;
|
|
|
|
p = p->prevZ;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
/**
|
|
* 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
|
|
*/
|
|
bool splitPolygon( VERTEX* start )
|
|
{
|
|
VERTEX* origPoly = start;
|
|
|
|
do
|
|
{
|
|
VERTEX* marker = origPoly->next->next;
|
|
|
|
while( marker != origPoly->prev )
|
|
{
|
|
// 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();
|
|
|
|
return earcutList( origPoly ) && earcutList( newPoly );
|
|
}
|
|
|
|
marker = marker->next;
|
|
}
|
|
|
|
origPoly = origPoly->next;
|
|
} while( origPoly != start );
|
|
|
|
return false;
|
|
}
|
|
|
|
/**
|
|
* 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. Next, we ensure that
|
|
* the proposed split is inside the local area of the polygon at both ends
|
|
* and the midpoint. Finally, we check to split creates two new polygons,
|
|
* each with positive area.
|
|
*/
|
|
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;
|
|
|
|
|
|
return no_intersect && local_split && ( same_dir || has_len ) && !a_on_edge && !b_on_edge;
|
|
|
|
}
|
|
|
|
/**
|
|
* Return the twice the signed area of the triangle formed by vertices p, q, and r.
|
|
*/
|
|
double area( const VERTEX* p, const VERTEX* q, const VERTEX* r ) const
|
|
{
|
|
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.
|
|
*
|
|
* @return true if p1-p2 intersects q1-q2.
|
|
*/
|
|
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;
|
|
}
|
|
|
|
/**
|
|
* Check 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.
|
|
*/
|
|
bool intersectsPolygon( const VERTEX* a, const VERTEX* b ) const
|
|
{
|
|
const VERTEX* p = a->next;
|
|
|
|
do
|
|
{
|
|
if( p->i != a->i &&
|
|
p->next->i != a->i &&
|
|
p->i != b->i &&
|
|
p->next->i != b->i && intersects( p, p->next, a, b ) )
|
|
return true;
|
|
|
|
p = p->next;
|
|
} while( p != a );
|
|
|
|
return false;
|
|
}
|
|
|
|
/**
|
|
* Check 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.
|
|
*
|
|
* @return true if the segment from a->b is inside a's polygon next to vertex a.
|
|
*/
|
|
bool locallyInside( const VERTEX* a, const VERTEX* b ) const
|
|
{
|
|
if( area( a->prev, a, a->next ) < 0 )
|
|
return area( a, b, a->next ) >= 0 && area( a, a->prev, b ) >= 0;
|
|
else
|
|
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.
|
|
*
|
|
* @return a pointer to the newly created vertex.
|
|
*/
|
|
VERTEX* insertVertex( const VECTOR2I& pt, VERTEX* last )
|
|
{
|
|
m_result.AddVertex( pt );
|
|
m_vertices.emplace_back( m_result.GetVertexCount() - 1, pt.x, pt.y, this );
|
|
|
|
VERTEX* p = &m_vertices.back();
|
|
|
|
if( !last )
|
|
{
|
|
p->prev = p;
|
|
p->next = p;
|
|
}
|
|
else
|
|
{
|
|
p->next = last->next;
|
|
p->prev = last;
|
|
last->next->prev = p;
|
|
last->next = p;
|
|
}
|
|
return p;
|
|
}
|
|
|
|
private:
|
|
BOX2I m_bbox;
|
|
std::deque<VERTEX> m_vertices;
|
|
SHAPE_POLY_SET::TRIANGULATED_POLYGON& m_result;
|
|
};
|
|
|
|
#endif //__POLYGON_TRIANGULATION_H
|