kicad/libs/kimath/include/geometry/polygon_triangulation.h

695 lines
21 KiB
C++

/*
* This program source code file is part of KiCad, a free EDA CAD application.
*
* Modifications Copyright (C) 2018-2021 KiCad Developers
*
* 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 2
* 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/old-licenses/gpl-2.0.html
* or you may search the http://www.gnu.org website for the version 2 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 <clipper.hpp>
#include <geometry/shape_line_chain.h>
#include <geometry/shape_poly_set.h>
#include <math/box2.h>
#include <math/vector2d.h>
class PolygonTriangulation
{
public:
PolygonTriangulation( SHAPE_POLY_SET::TRIANGULATED_POLYGON& aResult ) :
m_result( aResult )
{};
bool TesselatePolygon( const SHAPE_LINE_CHAIN& aPoly )
{
m_bbox = aPoly.BBox();
m_result.Clear();
if( !m_bbox.GetWidth() || !m_bbox.GetHeight() )
return false;
/// 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
Vertex* firstVertex = createList( aPoly );
if( !firstVertex || firstVertex->prev == firstVertex->next )
return false;
firstVertex->updateList();
auto retval = earcutList( firstVertex );
m_vertices.clear();
return retval;
}
private:
struct Vertex
{
Vertex( size_t aIndex, double aX, double aY, PolygonTriangulation* aParent ) :
i( aIndex ),
x( aX ),
y( aY ),
parent( aParent )
{
}
Vertex& operator=( const Vertex& ) = delete;
Vertex& operator=( Vertex&& ) = delete;
bool operator==( const Vertex& rhs ) const
{
return this->x == rhs.x && this->y == rhs.y;
}
bool operator!=( const Vertex& rhs ) const { return !( *this == rhs ); }
/**
* Split the referenced polygon between the reference point and
* vertex b, assuming they are in the same polygon. Notes that while we
* create a new vertex pointer for the linked list, we maintain the same
* vertex index value from the original polygon. In this way, we have
* two polygons that both share the same vertices.
*
* @return the newly created vertex in the polygon that does not include the
* reference vertex.
*/
Vertex* split( Vertex* b )
{
parent->m_vertices.emplace_back( i, x, y, parent );
Vertex* a2 = &parent->m_vertices.back();
parent->m_vertices.emplace_back( b->i, b->x, b->y, parent );
Vertex* b2 = &parent->m_vertices.back();
Vertex* an = next;
Vertex* bp = b->prev;
next = b;
b->prev = this;
a2->next = an;
an->prev = a2;
b2->next = a2;
a2->prev = b2;
bp->next = b2;
b2->prev = bp;
return b2;
}
/**
* Remove the node from the linked list and z-ordered linked list.
*/
void remove()
{
next->prev = prev;
prev->next = next;
if( prevZ )
prevZ->nextZ = nextZ;
if( nextZ )
nextZ->prevZ = prevZ;
next = nullptr;
prev = nullptr;
nextZ = nullptr;
prevZ = nullptr;
}
void updateOrder()
{
if( !z )
z = parent->zOrder( x, y );
}
/**
* After inserting or changing nodes, this function should be called to
* remove duplicate vertices and ensure z-ordering is correct.
*/
void updateList()
{
Vertex* p = next;
while( p != this )
{
/**
* Remove duplicates
*/
if( *p == *p->next )
{
p = p->prev;
p->next->remove();
if( p == p->next )
break;
}
p->updateOrder();
p = p->next;
};
updateOrder();
zSort();
}
/**
* Sort all vertices in this vertex's list by their Morton code.
*/
void zSort()
{
std::deque<Vertex*> queue;
queue.push_back( this );
for( auto p = next; p && p != this; p = p->next )
queue.push_back( p );
std::sort( queue.begin(), queue.end(), []( const Vertex* a, const Vertex* b )
{
return a->z < b->z;
} );
Vertex* prev_elem = nullptr;
for( auto elem : queue )
{
if( prev_elem )
prev_elem->nextZ = elem;
elem->prevZ = prev_elem;
prev_elem = elem;
}
prev_elem->nextZ = nullptr;
}
/**
* Check to see if triangle surrounds our current vertex
*/
bool inTriangle( const Vertex& a, const Vertex& b, const Vertex& c )
{
return ( c.x - x ) * ( a.y - y ) - ( a.x - x ) * ( c.y - y ) >= 0
&& ( a.x - x ) * ( b.y - y ) - ( b.x - x ) * ( a.y - y ) >= 0
&& ( b.x - x ) * ( c.y - y ) - ( c.x - x ) * ( b.y - y ) >= 0;
}
const size_t i;
const double x;
const double y;
PolygonTriangulation* parent;
// previous and next vertices nodes in a polygon ring
Vertex* prev = nullptr;
Vertex* next = nullptr;
// z-order curve value
int32_t z = 0;
// previous and next nodes in z-order
Vertex* prevZ = nullptr;
Vertex* nextZ = nullptr;
};
/**
* Calculate the Morton code of the Vertex
* http://www.graphics.stanford.edu/~seander/bithacks.html#InterleaveBMN
*
*/
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() );
x = ( x | ( x << 8 ) ) & 0x00FF00FF;
x = ( x | ( x << 4 ) ) & 0x0F0F0F0F;
x = ( x | ( x << 2 ) ) & 0x33333333;
x = ( x | ( x << 1 ) ) & 0x55555555;
y = ( y | ( y << 8 ) ) & 0x00FF00FF;
y = ( y | ( y << 4 ) ) & 0x0F0F0F0F;
y = ( y | ( y << 2 ) ) & 0x33333333;
y = ( y | ( y << 1 ) ) & 0x55555555;
return x | ( y << 1 );
}
/**
* Iterate 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
*/
Vertex* removeNullTriangles( Vertex* aStart )
{
Vertex* retval = nullptr;
Vertex* p = aStart->next;
while( p != aStart )
{
if( area( p->prev, p, p->next ) == 0.0 )
{
p = p->prev;
p->next->remove();
retval = aStart;
if( p == p->next )
break;
}
p = p->next;
};
// We needed an end point above that wouldn't be removed, so
// here we do the final check for this as a Steiner point
if( area( aStart->prev, aStart, aStart->next ) == 0.0 )
{
retval = p->next;
p->remove();
}
return retval;
}
/**
* Take a Clipper path and converts it into a circular, doubly-linked list for triangulation.
*/
Vertex* createList( const ClipperLib::Path& aPath )
{
Vertex* tail = nullptr;
double sum = 0.0;
auto len = aPath.size();
// Check for winding order
for( size_t i = 0; i < len; i++ )
{
auto p1 = aPath.at( i );
auto p2 = aPath.at( ( i + 1 ) < len ? i + 1 : 0 );
sum += ( ( p2.X - p1.X ) * ( p2.Y + p1.Y ) );
}
if( sum <= 0.0 )
{
for( auto point : aPath )
tail = insertVertex( VECTOR2I( point.X, point.Y ), tail );
}
else
{
for( size_t i = 0; i < len; i++ )
{
auto p = aPath.at( len - i - 1 );
tail = insertVertex( VECTOR2I( p.X, p.Y ), tail );
}
}
if( tail && ( *tail == *tail->next ) )
{
tail->next->remove();
}
return tail;
}
/**
* Take a #SHAPE_LINE_CHAIN and links each point into a circular, doubly-linked list.
*/
Vertex* createList( const SHAPE_LINE_CHAIN& points )
{
Vertex* tail = nullptr;
double sum = 0.0;
// Check for winding order
for( int i = 0; i < points.PointCount(); i++ )
{
VECTOR2D p1 = points.CPoint( i );
VECTOR2D p2 = points.CPoint( i + 1 );
sum += ( ( p2.x - p1.x ) * ( p2.y + p1.y ) );
}
if( sum > 0.0 )
for( int i = points.PointCount() - 1; i >= 0; i--)
tail = insertVertex( points.CPoint( i ), tail );
else
for( int i = 0; i < points.PointCount(); i++ )
tail = insertVertex( points.CPoint( i ), tail );
if( tail && ( *tail == *tail->next ) )
{
tail->next->remove();
}
return tail;
}
/**
* Walk through a circular linked list starting at \a 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.
*/
bool earcutList( Vertex* aPoint, int pass = 0 )
{
if( !aPoint )
return true;
Vertex* stop = aPoint;
Vertex* prev;
Vertex* next;
while( aPoint->prev != aPoint->next )
{
prev = aPoint->prev;
next = aPoint->next;
if( isEar( aPoint ) )
{
m_result.AddTriangle( prev->i, aPoint->i, next->i );
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 ) )
{
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 )
{
// First, try to remove the remaining steiner points
// If aPoint is a steiner, we need to re-assign both the start and stop points
if( auto newPoint = removeNullTriangles( aPoint ) )
{
aPoint = newPoint;
stop = newPoint;
continue;
}
// If we don't have any NULL triangles left, cut the polygon in two and try again
splitPolygon( aPoint );
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.
*/
return( aPoint->prev == aPoint->next );
}
/**
* Check 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.
*
* @return true if aEar is the apex point of a ear in the polygon.
*/
bool isEar( Vertex* aEar ) const
{
const Vertex* a = aEar->prev;
const Vertex* b = aEar;
const Vertex* c = aEar->next;
// If the area >=0, then the three points for a concave sequence
// with b as the reflex point
if( area( a, b, c ) >= 0 )
return false;
// triangle bbox
const double minTX = std::min( a->x, std::min( b->x, c->x ) );
const double minTY = std::min( a->y, std::min( b->y, c->y ) );
const double maxTX = std::max( a->x, std::max( b->x, c->x ) );
const double maxTY = std::max( a->y, std::max( b->y, c->y ) );
// z-order range for the current triangle bounding box
const int32_t minZ = zOrder( minTX, minTY );
const int32_t maxZ = zOrder( maxTX, maxTY );
// first look for points inside the triangle in increasing z-order
Vertex* p = aEar->nextZ;
while( p && p->z <= maxZ )
{
if( p != a && p != c
&& p->inTriangle( *a, *b, *c )
&& area( p->prev, p, p->next ) >= 0 )
return false;
p = p->nextZ;
}
// then look for points in decreasing z-order
p = aEar->prevZ;
while( p && p->z >= minZ )
{
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
*/
void 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();
earcutList( origPoly );
earcutList( newPoly );
return;
}
marker = marker->next;
}
origPoly = origPoly->next;
} while( origPoly != start );
}
/**
* 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.
*/
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 );
}
/**
* 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 );
}
/**
* 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
{
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 );
}
/**
* 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;
}
/**
* 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