seg.cpp

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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 <[email protected]>
 * Copyright The KiCad Developers, see AUTHORS.txt for contributors.
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 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
 */
 
#include <algorithm>        // for min
#include <geometry/seg.h>
#include <math/util.h>      // for rescale
#include <math/vector2d.h>  // for VECTOR2I, VECTOR2
#include <trigo.h>          // for RAD2DEG
 
template <typename T>
int sgn( T aVal )
{
    return ( T( 0 ) < aVal ) - ( aVal < T( 0 ) );
}
 
template <typename T>
constexpr T sqrt_helper(T x, T lo, T hi)
{
  if (lo == hi)
    return lo;
 
  const T mid = (lo + hi + 1) / 2;
  if (x / mid < mid)
    return sqrt_helper<T>(x, lo, mid - 1);
  else
    return sqrt_helper(x, mid, hi);
}
 
template <typename T>
constexpr T ct_sqrt(T x)
{
  return sqrt_helper<T>(x, 0, x / 2 + 1);
}
 
template <typename T>
static constexpr T sqrt_max_typed = ct_sqrt( std::numeric_limits<T>::max() );
 
template <typename T>
T isqrt(T x)
{
  T sqrt_max = sqrt_max_typed<T>;
 
  if( x < 0 )
    return sqrt_max;
 
  T r = (T) std::sqrt( (double) x );
 
  while( r < sqrt_max && r * r < x )
    r++;
 
  while( r > sqrt_max || r * r > x )
    r--;
 
  return r;
}
 
 
SEG::ecoord SEG::SquaredDistance( const SEG& aSeg ) const
{
    if( Intersects( aSeg ) )
        return 0;
 
    const VECTOR2I pts[4] =
    {
        aSeg.NearestPoint( A ) - A,
        aSeg.NearestPoint( B ) - B,
        NearestPoint( aSeg.A ) - aSeg.A,
        NearestPoint( aSeg.B ) - aSeg.B
    };
 
    ecoord m = VECTOR2I::ECOORD_MAX;
 
    for( int i = 0; i < 4; i++ )
        m = std::min( m, pts[i].SquaredEuclideanNorm() );
 
    return m;
}
 
 
EDA_ANGLE SEG::Angle( const SEG& aOther ) const
{
    EDA_ANGLE thisAngle = EDA_ANGLE( A - B ).Normalize180();
    EDA_ANGLE otherAngle = EDA_ANGLE( aOther.A - aOther.B ).Normalize180();
 
    EDA_ANGLE angle = std::abs( ( thisAngle - otherAngle ).Normalize180() );
 
    return std::min( ANGLE_180 - angle, angle );
}
 
 
const VECTOR2I SEG::NearestPoint( const SEG& aSeg ) const
{
    if( OPT_VECTOR2I p = Intersect( aSeg ) )
        return *p;
 
    const VECTOR2I pts_origin[4] =
    {
        aSeg.NearestPoint( A ),
        aSeg.NearestPoint( B ),
        NearestPoint( aSeg.A ),
        NearestPoint( aSeg.B )
    };
 
 
    const VECTOR2I* pts_out[4] =
    {
        &A,
        &B,
        &pts_origin[2],
        &pts_origin[3]
    };
 
    const ecoord pts_dist[4] =
    {
        ( pts_origin[0] - A ).SquaredEuclideanNorm(),
        ( pts_origin[1] - B ).SquaredEuclideanNorm(),
        ( pts_origin[2] - aSeg.A ).SquaredEuclideanNorm(),
        ( pts_origin[3] - aSeg.B ).SquaredEuclideanNorm()
    };
 
    int min_i = 0;
 
    for( int i = 0; i < 4; i++ )
    {
        if( pts_dist[i] < pts_dist[min_i] )
            min_i = i;
    }
 
    return *pts_out[min_i];
}
 
 
bool SEG::NearestPoints( const SEG& aSeg, VECTOR2I& aPtA, VECTOR2I& aPtB, int64_t& aDistSq ) const
{
    if( OPT_VECTOR2I p = Intersect( aSeg ) )
    {
        aPtA = aPtB = *p;
        aDistSq = 0;
 
        return true;
    }
 
    const VECTOR2I pts_origin[4] =
    {
        aSeg.NearestPoint( A ),
        aSeg.NearestPoint( B ),
        NearestPoint( aSeg.A ),
        NearestPoint( aSeg.B )
    };
 
    const VECTOR2I* pts_a_out[4] =
    {
        &A,
        &B,
        &pts_origin[2],
        &pts_origin[3]
    };
 
    const VECTOR2I* pts_b_out[4] =
    {
        &pts_origin[0],
        &pts_origin[1],
        &aSeg.A,
        &aSeg.B
    };
 
    const ecoord pts_dist[4] =
    {
        ( pts_origin[0] - A ).SquaredEuclideanNorm(),
        ( pts_origin[1] - B ).SquaredEuclideanNorm(),
        ( pts_origin[2] - aSeg.A ).SquaredEuclideanNorm(),
        ( pts_origin[3] - aSeg.B ).SquaredEuclideanNorm()
    };
 
    int min_i = 0;
 
    for( int i = 0; i < 4; i++ )
    {
        if( pts_dist[i] < pts_dist[min_i] )
            min_i = i;
    }
 
    aPtA = *pts_a_out[min_i];
    aPtB = *pts_b_out[min_i];
    aDistSq = pts_dist[min_i];
 
    return true;
}
 
 
bool SEG::intersects( const SEG& aSeg, bool aIgnoreEndpoints, bool aLines, VECTOR2I* aPt ) const
{
    const VECTOR2<ecoord> e = VECTOR2<ecoord>( B.x - A.x, B.y - A.y );
    const VECTOR2<ecoord> f = VECTOR2<ecoord>( aSeg.B.x - aSeg.A.x, aSeg.B.y - aSeg.A.y );
    const VECTOR2<ecoord> ac = VECTOR2<ecoord>( aSeg.A.x - A.x, aSeg.A.y - A.y );
 
    ecoord d = f.Cross( e );
    ecoord p = f.Cross( ac );
    ecoord q = e.Cross( ac );
 
    if( d == 0 )
        return false;
 
    if( !aLines && d > 0 && ( q < 0 || q > d || p < 0 || p > d ) )
        return false;
 
    if( !aLines && d < 0 && ( q < d || p < d || p > 0 || q > 0 ) )
        return false;
 
    if( !aLines && aIgnoreEndpoints && ( q == 0 || q == d ) && ( p == 0 || p == d ) )
        return false;
 
    if( aPt )
    {
        VECTOR2<ecoord> result( aSeg.A.x + rescale( q, (ecoord) f.x, d ),
                                aSeg.A.y + rescale( q, (ecoord) f.y, d ) );
 
        if( abs( result.x ) > std::numeric_limits<VECTOR2I::coord_type>::max()
            || abs( result.y ) > std::numeric_limits<VECTOR2I::coord_type>::max() )
        {
            return false;
        }
 
        *aPt = VECTOR2I( (int) result.x, (int) result.y );
    }
 
    return true;
}
 
 
bool SEG::Intersects( const SEG& aSeg ) const
{
    return intersects( aSeg );
}
 
 
OPT_VECTOR2I SEG::Intersect( const SEG& aSeg, bool aIgnoreEndpoints, bool aLines ) const
{
    VECTOR2I ip;
 
    if( intersects( aSeg, aIgnoreEndpoints, aLines, &ip ) )
        return ip;
    else
        return OPT_VECTOR2I();
}
 
 
SEG SEG::PerpendicularSeg( const VECTOR2I& aP ) const
{
    VECTOR2I slope( B - A );
    VECTOR2I endPoint = slope.Perpendicular() + aP;
 
    return SEG( aP, endPoint );
}
 
 
SEG SEG::ParallelSeg( const VECTOR2I& aP ) const
{
    VECTOR2I slope( B - A );
    VECTOR2I endPoint = slope + aP;
 
    return SEG( aP, endPoint );
}
 
 
bool SEG::ccw( const VECTOR2I& aA, const VECTOR2I& aB, const VECTOR2I& aC ) const
{
    return (ecoord) ( aC.y - aA.y ) * ( aB.x - aA.x ) > (ecoord) ( aB.y - aA.y ) * ( aC.x - aA.x );
}
 
 
bool SEG::Collide( const SEG& aSeg, int aClearance, int* aActual ) const
{
    // check for intersection
    // fixme: move to a method
    if( ccw( A, aSeg.A, aSeg.B ) != ccw( B, aSeg.A, aSeg.B ) &&
            ccw( A, B, aSeg.A ) != ccw( A, B, aSeg.B ) )
    {
        if( aActual )
            *aActual = 0;
 
        return true;
    }
 
    ecoord dist_sq = VECTOR2I::ECOORD_MAX;
    ecoord clearance_sq = (ecoord) aClearance * aClearance;
 
    auto checkCollision =
            [&]( bool aFinal )
            {
                if( dist_sq == 0 )
                {
                    if( aActual )
                        *aActual = 0;
 
                    return true;
                }
                else if( dist_sq < clearance_sq )
                {
                    if( aActual )
                    {
                        if( aFinal )
                        {
                            *aActual = int( isqrt( dist_sq ) );
                            return true;
                        }
                        else
                        {
                            // We have to keep going to ensure we have the lowest value
                            // for aActual
                            return false;
                        }
                    }
 
                    return true;
                }
 
                return false;
            };
 
    dist_sq = std::min( dist_sq, SquaredDistance( aSeg.A ) );
 
    if( checkCollision( false ) )
        return true;
 
    dist_sq = std::min( dist_sq, SquaredDistance( aSeg.B ) );
 
    if( checkCollision( false ) )
        return true;
 
    dist_sq = std::min( dist_sq, aSeg.SquaredDistance( A ) );
 
    if( checkCollision( false ) )
        return true;
 
    dist_sq = std::min( dist_sq, aSeg.SquaredDistance( B ) );
 
    return checkCollision( true );
}
 
 
bool SEG::Contains( const VECTOR2I& aP ) const
{
    return SquaredDistance( aP ) <= 3;
}
 
 
const VECTOR2I SEG::NearestPoint( const VECTOR2I& aP ) const
{
    // Inlined for performance reasons
    VECTOR2L d;
    d.x = static_cast<int64_t>( B.x ) - A.x;
    d.y = static_cast<int64_t>( B.y ) - A.y;
 
    ecoord   l_squared( d.x * d.x + d.y * d.y );
 
    if( l_squared == 0 )
        return A;
 
    // Inlined for performance reasons
    VECTOR2L pa;
    pa.x = static_cast<int64_t>( aP.x ) - A.x;
    pa.y = static_cast<int64_t>( aP.y ) - A.y;
 
    ecoord t = d.Dot( pa );
 
    if( t < 0 )
        return A;
    else if( t > l_squared )
        return B;
 
    ecoord xp = rescale( t, (ecoord) d.x, l_squared );
    ecoord yp = rescale( t, (ecoord) d.y, l_squared );
 
    return VECTOR2<ecoord>( A.x + xp, A.y + yp );
}
 
 
const VECTOR2I SEG::ReflectPoint( const VECTOR2I& aP ) const
{
    VECTOR2I                d = B - A;
    VECTOR2I::extended_type l_squared = d.Dot( d );
    VECTOR2I::extended_type t = d.Dot( aP - A );
    VECTOR2<ecoord>         c;
 
    if( !l_squared )
    {
        c = aP;
    }
    else
    {
        c.x = A.x + rescale( t, static_cast<VECTOR2I::extended_type>( d.x ), l_squared );
        c.y = A.y + rescale( t, static_cast<VECTOR2I::extended_type>( d.y ), l_squared );
    }
 
    return VECTOR2<ecoord>( 2 * c.x - aP.x, 2 * c.y - aP.y );
}
 
 
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 );
 
    ecoord xp = rescale( t, ecoord{ d.x }, l_squared );
    ecoord yp = rescale( t, ecoord{ d.y }, l_squared );
 
    return VECTOR2<ecoord>( A.x + xp, A.y + yp );
}
 
 
int SEG::Distance( const SEG& aSeg ) const
{
    return int( isqrt( SquaredDistance( aSeg ) ) );
}
 
 
int SEG::Distance( const VECTOR2I& aP ) const
{
    return int( isqrt( SquaredDistance( aP ) ) );
}
 
 
SEG::ecoord SEG::SquaredDistance( const VECTOR2I& aP ) const
{
    // Using the VECTOR2L() reflexive c'tor is a performance hit.
    // Even sticking these in a lambda still invokes it.
    VECTOR2L ab, ap;
    ab.x = static_cast<int64_t>( B.x ) - A.x;
    ab.y = static_cast<int64_t>( B.y ) - A.y;
    ap.x = static_cast<int64_t>( aP.x ) - A.x;
    ap.y = static_cast<int64_t>( aP.y ) - A.y;
 
    ecoord e = ap.Dot( ab );
 
    if( e <= 0 )
        return ap.SquaredEuclideanNorm();
 
    ecoord f = ab.SquaredEuclideanNorm();
 
    if( e >= f )
    {
        VECTOR2L bp;
        bp.x = static_cast<int64_t>( aP.x ) - B.x;
        bp.y = static_cast<int64_t>( aP.y ) - B.y;
        return bp.Dot( bp );
    }
 
    const double g = ap.SquaredEuclideanNorm() - ( double( e ) * e ) / f;
 
    // The only way g can be negative is if there was a rounding error since
    // e is the projection of aP onto ab and therefore cannot be greater than
    // the length of ap and f is guaranteed to be greater than e, meaning
    // e * e / f cannot be greater than ap.SquaredEuclideanNorm()
    if( g < 0 || g > static_cast<double>( std::numeric_limits<ecoord>::max() ) )
        return 0;
 
    return KiROUND<double, ecoord>( g );
}
 
 
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 l = p * p + q * q;
    ecoord det = p * aP.x + q * aP.y + r;
    ecoord dist_sq = 0;
 
    if( l > 0 )
    {
        dist_sq  = rescale( det, det, l );
    }
 
    ecoord dist = isqrt( dist_sq );
 
    return static_cast<int>( aDetermineSide ? sgn( det ) * dist : std::abs( dist ) );
}
 
 
bool SEG::mutualDistanceSquared( const SEG& aSeg, ecoord& aD1, ecoord& aD2 ) const
{
    SEG a( *this );
    SEG b( aSeg );
 
    if( a.SquaredLength() < b.SquaredLength() )
        std::swap(a, b);
 
    ecoord p = ecoord{ a.A.y } - a.B.y;
    ecoord q = ecoord{ a.B.x } - a.A.x;
    ecoord r = -p * a.A.x - q * a.A.y;
 
    ecoord l = p * p + q * q;
 
    if( l == 0 )
        return false;
 
    ecoord det1 = p * b.A.x + q * b.A.y + r;
    ecoord det2 = p * b.B.x + q * b.B.y + r;
 
    ecoord dsq1 = rescale( det1, det1, l );
    ecoord dsq2 = rescale( det2, det2, l );
 
    aD1 = sgn( det1 ) * dsq1;
    aD2 = sgn( det2 ) * dsq2;
 
    return true;
}
 
bool SEG::ApproxCollinear( const SEG& aSeg, int aDistanceThreshold ) const
{
    ecoord thresholdSquared = Square( aDistanceThreshold );
    ecoord d1_sq, d2_sq;
 
    if( !mutualDistanceSquared( aSeg, d1_sq, d2_sq ) )
        return false;
 
    return std::abs( d1_sq ) <= thresholdSquared && std::abs( d2_sq ) <= thresholdSquared;
}
 
 
bool SEG::ApproxParallel( const SEG& aSeg, int aDistanceThreshold ) const
{
    ecoord thresholdSquared = Square( aDistanceThreshold );
    ecoord d1_sq, d2_sq;
 
    if( ! mutualDistanceSquared( aSeg, d1_sq, d2_sq ) )
        return false;
 
    return std::abs( d1_sq - d2_sq ) <= thresholdSquared;
}
 
 
bool SEG::ApproxPerpendicular( const SEG& aSeg ) const
{
    SEG perp = PerpendicularSeg( A );
 
    return aSeg.ApproxParallel( perp );
}