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

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/*
* This program source code file is part of KiCad, a free EDA CAD application.
*
* Copyright (C) 2013 CERN
* @author Tomasz Wlostowski <tomasz.wlostowski@cern.ch>
*
* 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
*/
#ifndef __SEG_H
#define __SEG_H
#include <math.h> // for sqrt
#include <stdlib.h> // for abs
#include <ostream> // for operator<<, ostream, basic_os...
#include <type_traits> // for swap
#include <core/optional.h>
#include <math/util.h> // for rescale
#include <math/vector2d.h>
typedef OPT<VECTOR2I> OPT_VECTOR2I;
class SEG
{
public:
using ecoord = VECTOR2I::extended_type;
friend inline std::ostream& operator<<( std::ostream& aStream, const SEG& aSeg );
/* Start and the of the segment. Public, to make access simpler.
*/
VECTOR2I A;
VECTOR2I B;
/** Default constructor
* Creates an empty (0, 0) segment
*/
SEG()
{
m_index = -1;
}
/**
* Constructor
* Creates a segment between (aX1, aY1) and (aX2, aY2)
*/
SEG( int aX1, int aY1, int aX2, int aY2 ) :
A( VECTOR2I( aX1, aY1 ) ),
B( VECTOR2I( aX2, aY2 ) )
{
m_index = -1;
}
/**
* Constructor
* Creates a segment between (aA) and (aB)
*/
SEG( const VECTOR2I& aA, const VECTOR2I& aB ) :
A( aA ),
B( aB )
{
m_index = -1;
}
/**
* Constructor
* Creates a segment between (aA) and (aB), referenced to a multi-segment shape
* @param aA reference to the start point in the parent shape
* @param aB reference to the end point in the parent shape
* @param aIndex index of the segment within the parent shape
*/
SEG( const VECTOR2I& aA, const VECTOR2I& aB, int aIndex ) :
A( aA ),
B( aB )
{
m_index = aIndex;
}
/**
* Copy constructor
*/
SEG( const SEG& aSeg ) :
A( aSeg.A ),
B( aSeg.B ),
m_index( aSeg.m_index )
{
}
SEG& operator=( const SEG& aSeg )
{
A = aSeg.A;
B = aSeg.B;
m_index = aSeg.m_index;
return *this;
}
bool operator==( const SEG& aSeg ) const
{
return (A == aSeg.A && B == aSeg.B) ;
}
bool operator!=( const SEG& aSeg ) const
{
return (A != aSeg.A || B != aSeg.B);
}
static SEG::ecoord Square( int a )
{
return ecoord( a ) * a;
}
/**
* Function LineProject()
*
* Computes the perpendicular projection point of aP on a line passing through
* ends of the segment.
* @param aP point to project
* @return projected point
*/
VECTOR2I LineProject( const VECTOR2I& aP ) const;
/**
* Function Side()
*
* Determines on which side of directed line passing via segment ends point aP lies.
* @param aP point to determine the orientation wrs to self
* @return: < 0: left, 0 : on the line, > 0 : right
*/
int Side( const VECTOR2I& aP ) const
{
const ecoord det = ( B - A ).Cross( aP - A );
return det < 0 ? -1 : ( det > 0 ? 1 : 0 );
}
/**
* Function LineDistance()
*
* Returns the closest Euclidean distance between point aP and the line defined by
* the ends of segment (this).
* @param aP the point to test
* @param aDetermineSide: when true, the sign of the returned value indicates
* the side of the line at which we are (negative = left)
* @return the distance
*/
int LineDistance( const VECTOR2I& aP, bool aDetermineSide = false ) const;
/**
* Function NearestPoint()
*
* Computes a point on the segment (this) that is closest to point aP.
* @return the nearest point
*/
const VECTOR2I NearestPoint( const VECTOR2I &aP ) const;
/**
* Computes a point on the segment (this) that is closest to any point on aSeg.
* @return the nearest point
*/
const VECTOR2I NearestPoint( const SEG &aSeg ) const;
/**
* Function Intersect()
*
* Computes intersection point of segment (this) with segment aSeg.
* @param aSeg: segment to intersect with
* @param aIgnoreEndpoints: don't treat corner cases (i.e. end of one segment touching the
* other) as intersections.
* @param aLines: treat segments as infinite lines
* @return intersection point, if exists
*/
OPT_VECTOR2I Intersect( const SEG& aSeg, bool aIgnoreEndpoints = false,
bool aLines = false ) const;
/**
* Function IntersectLines()
*
* Computes the intersection point of lines passing through ends of (this) and aSeg
* @param aSeg segment defining the line to intersect with
* @return intersection point, if exists
*/
OPT_VECTOR2I IntersectLines( const SEG& aSeg ) const
{
return Intersect( aSeg, false, true );
}
bool Collide( const SEG& aSeg, int aClearance, int* aActual = nullptr ) const;
ecoord SquaredDistance( const SEG& aSeg ) const;
/**
* Function Distance()
*
* Computes minimum Euclidean distance to segment aSeg.
* @param aSeg other segment
* @return minimum distance
*/
int Distance( const SEG& aSeg ) const
{
return sqrt( SquaredDistance( aSeg ) );
}
ecoord SquaredDistance( const VECTOR2I& aP ) const
{
return ( NearestPoint( aP ) - aP ).SquaredEuclideanNorm();
}
/**
* Function Distance()
*
* Computes minimum Euclidean distance to point aP.
* @param aP the point
* @return minimum distance
*/
int Distance( const VECTOR2I& aP ) const
{
return sqrt( SquaredDistance( aP ) );
}
void CanonicalCoefs( ecoord& qA, ecoord& qB, ecoord& qC ) const
{
qA = ecoord{ A.y } - B.y;
qB = ecoord{ B.x } - A.x;
qC = -qA * A.x - qB * A.y;
}
/**
* Function Collinear()
*
* Checks if segment aSeg lies on the same line as (this).
* @param aSeg the segment to chech colinearity with
* @return true, when segments are collinear.
*/
bool Collinear( const SEG& aSeg ) const
{
ecoord qa, qb, qc;
CanonicalCoefs( qa, qb, qc );
ecoord d1 = std::abs( aSeg.A.x * qa + aSeg.A.y * qb + qc );
ecoord d2 = std::abs( aSeg.B.x * qa + aSeg.B.y * qb + qc );
return ( d1 <= 1 && d2 <= 1 );
}
bool ApproxCollinear( const SEG& aSeg ) const
{
ecoord p, q, r;
CanonicalCoefs( p, q, r );
ecoord dist1 = ( p * aSeg.A.x + q * aSeg.A.y + r ) / sqrt( p * p + q * q );
ecoord dist2 = ( p * aSeg.B.x + q * aSeg.B.y + r ) / sqrt( p * p + q * q );
return std::abs( dist1 ) <= 1 && std::abs( dist2 ) <= 1;
}
bool ApproxParallel ( const SEG& aSeg ) const
{
ecoord p, q, r;
CanonicalCoefs( p, q, r );
ecoord dist1 = ( p * aSeg.A.x + q * aSeg.A.y + r ) / sqrt( p * p + q * q );
ecoord dist2 = ( p * aSeg.B.x + q * aSeg.B.y + r ) / sqrt( p * p + q * q );
return std::abs( dist1 - dist2 ) <= 1;
}
bool Overlaps( const SEG& aSeg ) const
{
if( aSeg.A == aSeg.B ) // single point corner case
{
if( A == aSeg.A || B == aSeg.A )
return false;
return Contains( aSeg.A );
}
if( !Collinear( aSeg ) )
return false;
if( Contains( aSeg.A ) || Contains( aSeg.B ) )
return true;
if( aSeg.Contains( A ) || aSeg.Contains( B ) )
return true;
return false;
}
bool Contains( const SEG& aSeg ) const
{
if( aSeg.A == aSeg.B ) // single point corner case
return Contains( aSeg.A );
if( !Collinear( aSeg ) )
return false;
if( Contains( aSeg.A ) && Contains( aSeg.B ) )
return true;
return false;
}
/**
* Function Length()
*
* Returns the length (this)
* @return length
*/
int Length() const
{
return ( A - B ).EuclideanNorm();
}
ecoord SquaredLength() const
{
return ( A - B ).SquaredEuclideanNorm();
}
ecoord TCoef( const VECTOR2I& aP ) const;
/**
* Function Index()
*
* Return the index of this segment in its parent shape (applicable only to non-local segments)
* @return index value
*/
int Index() const
{
return m_index;
}
bool Contains( const VECTOR2I& aP ) const;
void Reverse()
{
std::swap( A, B );
}
SEG Reversed() const
{
return SEG( B, A );
}
///> Returns the center point of the line
VECTOR2I Center() const
{
return A + ( B - A ) / 2;
}
private:
bool ccw( const VECTOR2I& aA, const VECTOR2I& aB, const VECTOR2I &aC ) const;
private:
///> index withing the parent shape (used when m_is_local == false)
int m_index;
};
inline VECTOR2I SEG::LineProject( const VECTOR2I& aP ) const
{
VECTOR2I d = B - A;
ecoord l_squared = d.Dot( d );
if( l_squared == 0 )
return A;
ecoord t = d.Dot( aP - A );
int xp = rescale( t, ecoord{ d.x }, l_squared );
int yp = rescale( t, ecoord{ d.y }, l_squared );
return A + VECTOR2I( xp, yp );
}
inline int SEG::LineDistance( const VECTOR2I& aP, bool aDetermineSide ) const
{
ecoord p = ecoord{ A.y } - B.y;
ecoord q = ecoord{ B.x } - A.x;
ecoord r = -p * A.x - q * A.y;
ecoord dist = ( p * aP.x + q * aP.y + r ) / sqrt( p * p + q * q );
return aDetermineSide ? dist : std::abs( dist );
}
inline SEG::ecoord SEG::TCoef( const VECTOR2I& aP ) const
{
VECTOR2I d = B - A;
return d.Dot( aP - A);
}
inline const VECTOR2I SEG::NearestPoint( const VECTOR2I& aP ) const
{
VECTOR2I d = B - A;
ecoord l_squared = d.Dot( d );
if( l_squared == 0 )
return A;
ecoord t = d.Dot( aP - A );
if( t < 0 )
return A;
else if( t > l_squared )
return B;
int xp = rescale( t, (ecoord)d.x, l_squared );
int yp = rescale( t, (ecoord)d.y, l_squared );
return A + VECTOR2I( xp, yp );
}
inline std::ostream& operator<<( std::ostream& aStream, const SEG& aSeg )
{
aStream << "[ " << aSeg.A << " - " << aSeg.B << " ]";
return aStream;
}
#endif // __SEG_H
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