484 lines
12 KiB
C++
484 lines
12 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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* Copyright (C) 2013 CERN
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* Copyright (C) 2021 KiCad Developers, see AUTHORS.txt for contributors.
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*
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* @author Tomasz Wlostowski <tomasz.wlostowski@cern.ch>
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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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#ifndef __SEG_H
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#define __SEG_H
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#include <math.h> // for sqrt
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#include <stdlib.h> // for abs
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#include <ostream> // for operator<<, ostream, basic_os...
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#include <type_traits> // for swap
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#include <core/optional.h>
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#include <math/util.h> // for rescale
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#include <math/vector2d.h>
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typedef OPT<VECTOR2I> OPT_VECTOR2I;
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class SEG
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{
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public:
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using ecoord = VECTOR2I::extended_type;
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friend inline std::ostream& operator<<( std::ostream& aStream, const SEG& aSeg );
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/* Start and the of the segment. Public, to make access simpler.
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*/
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VECTOR2I A;
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VECTOR2I B;
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/**
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* Create an empty (0, 0) segment.
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*/
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SEG()
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{
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m_index = -1;
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}
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/**
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* Create a segment between (aX1, aY1) and (aX2, aY2).
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*/
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SEG( int aX1, int aY1, int aX2, int aY2 ) :
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A( VECTOR2I( aX1, aY1 ) ),
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B( VECTOR2I( aX2, aY2 ) )
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{
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m_index = -1;
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}
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/**
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* Create a segment between (aA) and (aB).
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*/
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SEG( const VECTOR2I& aA, const VECTOR2I& aB ) :
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A( aA ),
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B( aB )
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{
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m_index = -1;
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}
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/**
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* Create a segment between (aA) and (aB), referenced to a multi-segment shape.
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*
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* @param aA reference to the start point in the parent shape
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* @param aB reference to the end point in the parent shape
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* @param aIndex index of the segment within the parent shape
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*/
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SEG( const VECTOR2I& aA, const VECTOR2I& aB, int aIndex ) :
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A( aA ),
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B( aB )
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{
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m_index = aIndex;
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}
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/**
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* Copy constructor.
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*/
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SEG( const SEG& aSeg ) :
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A( aSeg.A ),
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B( aSeg.B ),
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m_index( aSeg.m_index )
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{
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}
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SEG& operator=( const SEG& aSeg )
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{
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A = aSeg.A;
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B = aSeg.B;
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m_index = aSeg.m_index;
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return *this;
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}
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bool operator==( const SEG& aSeg ) const
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{
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return (A == aSeg.A && B == aSeg.B) ;
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}
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bool operator!=( const SEG& aSeg ) const
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{
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return (A != aSeg.A || B != aSeg.B);
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}
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static SEG::ecoord Square( int a )
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{
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return ecoord( a ) * a;
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}
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/**
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* Compute the perpendicular projection point of aP on a line passing through
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* ends of the segment.
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*
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* @param aP point to project
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* @return projected point
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*/
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VECTOR2I LineProject( const VECTOR2I& aP ) const;
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/**
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* Determine on which side of directed line passing via segment ends point aP lies.
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*
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* @param aP point to determine the orientation wrs to self
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* @return: < 0: left, 0 : on the line, > 0 : right
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*/
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int Side( const VECTOR2I& aP ) const
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{
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const ecoord det = ( B - A ).Cross( aP - A );
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return det < 0 ? -1 : ( det > 0 ? 1 : 0 );
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}
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/**
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* Return the closest Euclidean distance between point aP and the line defined by
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* the ends of segment (this).
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*
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* @param aP the point to test
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* @param aDetermineSide: when true, the sign of the returned value indicates
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* the side of the line at which we are (negative = left)
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* @return the distance
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*/
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int LineDistance( const VECTOR2I& aP, bool aDetermineSide = false ) const;
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/**
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* Determine the smallest angle between two segments (result in degrees)
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*
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* @param aOther point to determine the orientation wrs to self
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* @return smallest angle between this and aOther (degrees)
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*/
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double AngleDegrees( const SEG& aOther ) const;
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/**
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* Compute a point on the segment (this) that is closest to point \a aP.
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*
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* @return the nearest point
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*/
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const VECTOR2I NearestPoint( const VECTOR2I &aP ) const;
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/**
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* Compute a point on the segment (this) that is closest to any point on \a aSeg.
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*
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* @return the nearest point
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*/
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const VECTOR2I NearestPoint( const SEG &aSeg ) const;
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/**
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* Reflect a point using this segment as axis.
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*
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* @return the reflected point
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*/
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const VECTOR2I ReflectPoint( const VECTOR2I& aP ) const;
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/**
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* Compute intersection point of segment (this) with segment \a aSeg.
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*
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* @param aSeg: segment to intersect with
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* @param aIgnoreEndpoints: don't treat corner cases (i.e. end of one segment touching the
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* other) as intersections.
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* @param aLines: treat segments as infinite lines
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* @return intersection point, if exists
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*/
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OPT_VECTOR2I Intersect( const SEG& aSeg, bool aIgnoreEndpoints = false,
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bool aLines = false ) const;
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/**
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* Compute the intersection point of lines passing through ends of (this) and \a aSeg.
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*
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* @param aSeg segment defining the line to intersect with
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* @return intersection point, if exists
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*/
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OPT_VECTOR2I IntersectLines( const SEG& aSeg ) const
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{
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return Intersect( aSeg, false, true );
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}
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/**
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* Compute a segment perpendicular to this one, passing through point \a aP.
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*
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* @param aP Point through which the new segment will pass
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* @return SEG perpendicular to this passing through point aP
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*/
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SEG PerpendicularSeg( const VECTOR2I& aP ) const;
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/**
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* Compute a segment parallel to this one, passing through point \a aP.
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*
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* @param aP Point through which the new segment will pass
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* @return SEG parallel to this passing through point aP
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*/
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SEG ParallelSeg( const VECTOR2I& aP ) const;
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bool Collide( const SEG& aSeg, int aClearance, int* aActual = nullptr ) const;
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ecoord SquaredDistance( const SEG& aSeg ) const;
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/**
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* Compute minimum Euclidean distance to segment \a aSeg.
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*
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* @param aSeg other segment
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* @return minimum distance
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*/
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int Distance( const SEG& aSeg ) const
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{
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return sqrt( SquaredDistance( aSeg ) );
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}
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ecoord SquaredDistance( const VECTOR2I& aP ) const
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{
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return ( NearestPoint( aP ) - aP ).SquaredEuclideanNorm();
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}
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/**
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* Compute minimum Euclidean distance to point \a aP.
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*
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* @param aP the point
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* @return minimum distance
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*/
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int Distance( const VECTOR2I& aP ) const
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{
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return sqrt( SquaredDistance( aP ) );
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}
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void CanonicalCoefs( ecoord& qA, ecoord& qB, ecoord& qC ) const
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{
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qA = ecoord{ A.y } - B.y;
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qB = ecoord{ B.x } - A.x;
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qC = -qA * A.x - qB * A.y;
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}
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/**
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* Check if segment aSeg lies on the same line as (this).
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*
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* @param aSeg the segment to check colinearity with
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* @return true, when segments are collinear.
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*/
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bool Collinear( const SEG& aSeg ) const
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{
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ecoord qa, qb, qc;
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CanonicalCoefs( qa, qb, qc );
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ecoord d1 = std::abs( aSeg.A.x * qa + aSeg.A.y * qb + qc );
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ecoord d2 = std::abs( aSeg.B.x * qa + aSeg.B.y * qb + qc );
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return ( d1 <= 1 && d2 <= 1 );
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}
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bool ApproxCollinear( const SEG& aSeg ) const
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{
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ecoord p, q, r;
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CanonicalCoefs( p, q, r );
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ecoord dist1 = ( p * aSeg.A.x + q * aSeg.A.y + r ) / sqrt( p * p + q * q );
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ecoord dist2 = ( p * aSeg.B.x + q * aSeg.B.y + r ) / sqrt( p * p + q * q );
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return std::abs( dist1 ) <= 1 && std::abs( dist2 ) <= 1;
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}
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bool ApproxParallel ( const SEG& aSeg ) const
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{
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ecoord p, q, r;
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CanonicalCoefs( p, q, r );
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ecoord dist1 = ( p * aSeg.A.x + q * aSeg.A.y + r ) / sqrt( p * p + q * q );
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ecoord dist2 = ( p * aSeg.B.x + q * aSeg.B.y + r ) / sqrt( p * p + q * q );
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return std::abs( dist1 - dist2 ) <= 1;
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}
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bool ApproxPerpendicular( const SEG& aSeg ) const
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{
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SEG perp = PerpendicularSeg( A );
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return aSeg.ApproxParallel( perp );
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}
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bool Overlaps( const SEG& aSeg ) const
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{
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if( aSeg.A == aSeg.B ) // single point corner case
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{
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if( A == aSeg.A || B == aSeg.A )
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return false;
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return Contains( aSeg.A );
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}
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if( !Collinear( aSeg ) )
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return false;
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if( Contains( aSeg.A ) || Contains( aSeg.B ) )
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return true;
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if( aSeg.Contains( A ) || aSeg.Contains( B ) )
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return true;
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return false;
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}
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bool Contains( const SEG& aSeg ) const
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{
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if( aSeg.A == aSeg.B ) // single point corner case
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return Contains( aSeg.A );
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if( !Collinear( aSeg ) )
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return false;
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if( Contains( aSeg.A ) && Contains( aSeg.B ) )
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return true;
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return false;
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}
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/**
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* Return the length (this).
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*
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* @return length
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*/
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int Length() const
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{
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return ( A - B ).EuclideanNorm();
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}
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ecoord SquaredLength() const
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{
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return ( A - B ).SquaredEuclideanNorm();
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}
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ecoord TCoef( const VECTOR2I& aP ) const;
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/**
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* Return the index of this segment in its parent shape (applicable only to non-local
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* segments).
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*
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* @return index value
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*/
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int Index() const
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{
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return m_index;
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}
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bool Contains( const VECTOR2I& aP ) const;
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void Reverse()
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{
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std::swap( A, B );
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}
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SEG Reversed() const
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{
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return SEG( B, A );
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}
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///< Returns the center point of the line
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VECTOR2I Center() const
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{
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return A + ( B - A ) / 2;
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}
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private:
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bool ccw( const VECTOR2I& aA, const VECTOR2I& aB, const VECTOR2I &aC ) const;
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private:
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///< index withing the parent shape (used when m_is_local == false)
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int m_index;
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};
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inline VECTOR2I SEG::LineProject( const VECTOR2I& aP ) const
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{
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VECTOR2I d = B - A;
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ecoord l_squared = d.Dot( d );
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if( l_squared == 0 )
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return A;
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ecoord t = d.Dot( aP - A );
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int xp = rescale( t, ecoord{ d.x }, l_squared );
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int yp = rescale( t, ecoord{ d.y }, l_squared );
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return A + VECTOR2I( xp, yp );
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}
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inline int SEG::LineDistance( const VECTOR2I& aP, bool aDetermineSide ) const
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{
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ecoord p = ecoord{ A.y } - B.y;
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ecoord q = ecoord{ B.x } - A.x;
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ecoord r = -p * A.x - q * A.y;
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ecoord dist = ( p * aP.x + q * aP.y + r ) / sqrt( p * p + q * q );
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return aDetermineSide ? dist : std::abs( dist );
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}
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inline SEG::ecoord SEG::TCoef( const VECTOR2I& aP ) const
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{
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VECTOR2I d = B - A;
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return d.Dot( aP - A);
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}
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inline const VECTOR2I SEG::NearestPoint( const VECTOR2I& aP ) const
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{
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VECTOR2I d = B - A;
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ecoord l_squared = d.Dot( d );
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if( l_squared == 0 )
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return A;
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ecoord t = d.Dot( aP - A );
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if( t < 0 )
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return A;
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else if( t > l_squared )
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return B;
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int xp = rescale( t, (ecoord)d.x, l_squared );
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int yp = rescale( t, (ecoord)d.y, l_squared );
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return A + VECTOR2I( xp, yp );
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}
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inline const VECTOR2I SEG::ReflectPoint( const VECTOR2I& aP ) const
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{
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VECTOR2I d = B - A;
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VECTOR2I::extended_type l_squared = d.Dot( d );
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VECTOR2I::extended_type t = d.Dot( aP - A );
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VECTOR2I c;
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if( !l_squared )
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c = aP;
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else
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{
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c.x = A.x + rescale( t, static_cast<VECTOR2I::extended_type>( d.x ), l_squared );
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c.y = A.y + rescale( t, static_cast<VECTOR2I::extended_type>( d.y ), l_squared );
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}
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return 2 * c - aP;
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}
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inline std::ostream& operator<<( std::ostream& aStream, const SEG& aSeg )
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{
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aStream << "[ " << aSeg.A << " - " << aSeg.B << " ]";
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return aStream;
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}
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#endif // __SEG_H
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