From 56f58cf53f3a884e475d639e013390416dbc41be Mon Sep 17 00:00:00 2001
From: Jeff Young <jeff@rokeby.ie>
Date: Wed, 19 Oct 2022 13:49:53 +0100
Subject: [PATCH] Manual cherry-pick of
 6ed3618ce5f86f96a86a2f332bcf530b1cf7b5ff.

---
 libs/kimath/include/geometry/seg.h | 33 +++-------------
 libs/kimath/src/geometry/seg.cpp   | 60 ++++++++++++++++++++++++++++++
 2 files changed, 65 insertions(+), 28 deletions(-)

diff --git a/libs/kimath/include/geometry/seg.h b/libs/kimath/include/geometry/seg.h
index 7e615c7255..dd8d417191 100644
--- a/libs/kimath/include/geometry/seg.h
+++ b/libs/kimath/include/geometry/seg.h
@@ -276,34 +276,9 @@ public:
         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, int aDistanceThreshold = 1 ) 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 ) <= aDistanceThreshold;
-    }
-
-    bool ApproxPerpendicular( const SEG& aSeg ) const
-    {
-        SEG perp = PerpendicularSeg( A );
-
-        return aSeg.ApproxParallel( perp );
-    }
+    bool ApproxCollinear( const SEG& aSeg, int aDistanceThreshold = 1 ) const;
+    bool ApproxParallel( const SEG& aSeg, int aDistanceThreshold = 1 ) const;
+    bool ApproxPerpendicular( const SEG& aSeg ) const;
 
     bool Overlaps( const SEG& aSeg ) const
     {
@@ -394,6 +369,8 @@ private:
     bool intersects( const SEG& aSeg, bool aIgnoreEndpoints = false, bool aLines = false,
                      VECTOR2I* aPt = nullptr ) const;
 
+    bool mutualDistance( const SEG& aSeg, ecoord& aD1, ecoord& aD2 ) const;
+
 private:
     ///< index within the parent shape (used when m_is_local == false)
     int m_index;
diff --git a/libs/kimath/src/geometry/seg.cpp b/libs/kimath/src/geometry/seg.cpp
index 2e5a787407..17dc837441 100644
--- a/libs/kimath/src/geometry/seg.cpp
+++ b/libs/kimath/src/geometry/seg.cpp
@@ -349,3 +349,63 @@ int SEG::LineDistance( const VECTOR2I& aP, bool aDetermineSide ) const
     return aDetermineSide ? dist : std::abs( dist );
 }
 
+
+bool SEG::mutualDistance( 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 ) * isqrt( dsq1 );
+    aD2 = sgn( det2 ) * isqrt( dsq2 );
+
+    return true;
+}
+
+bool SEG::ApproxCollinear( const SEG& aSeg, int aDistanceThreshold ) const
+{
+    ecoord d1, d2;
+
+    if( ! mutualDistance( aSeg, d1, d2 ) )
+        return false;
+
+    return std::abs( d1 ) <= aDistanceThreshold && std::abs( d2 ) <= aDistanceThreshold;
+}
+
+
+bool SEG::ApproxParallel( const SEG& aSeg, int aDistanceThreshold ) const
+{
+    ecoord d1, d2;
+
+    if( ! mutualDistance( aSeg, d1, d2 ) )
+        return false;
+
+    return std::abs( d1 - d2 ) <= (ecoord) aDistanceThreshold;
+}
+
+
+bool SEG::ApproxPerpendicular( const SEG& aSeg ) const
+{
+    SEG perp = PerpendicularSeg( A );
+
+    return aSeg.ApproxParallel( perp );
+}