From fc10fdb7db22c4f74d7a82e0351131ed85f44783 Mon Sep 17 00:00:00 2001
From: Giles Bathgate <giles.bathgate@gmail.com>
Date: Wed, 15 Sep 2021 08:55:12 +0100
Subject: [PATCH] Implement transposed_inverse for homogeneous plane
 transformations

---
 .../CGAL/Homogeneous/Aff_transformationH3.h   | 55 +++++++++++++++++--
 1 file changed, 51 insertions(+), 4 deletions(-)

diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
index fa0ba377b4d..f0c74e0d883 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
@@ -70,6 +70,9 @@ public:
   virtual  Plane_3
            transform(const Plane_3&) const = 0;
 
+  virtual  Plane_3
+           transform(const Plane_3&, bool, const Aff_transformation_3&) const = 0;
+
   virtual  Aff_transformation_3
            inverse() const = 0;
 
@@ -134,6 +137,9 @@ public:
   virtual  Plane_3
            transform(const Plane_3& pl) const;
 
+  virtual  Plane_3
+           transform(const Plane_3& pl, bool is_even, const Aff_transformation_3& transposed_inverse) const;
+
   virtual  Aff_transformation_3
            inverse() const;
 
@@ -207,6 +213,10 @@ public:
            transform(const Plane_3& pl) const
            { return pl; }
 
+  virtual  Plane_3
+           transform(const Plane_3& pl, bool, const Aff_transformation_3&) const
+           { return pl; }
+
   virtual  Aff_transformation_3
            inverse() const
            { return Aff_transformation_3( IDENTITY); }
@@ -289,6 +299,12 @@ class Scaling_repH3 : public Aff_transformation_rep_baseH3<R>
                return Plane_3(p.a()*_sf_den, p.b()*_sf_den, p.c()*_sf_den, p.d()*_sf_num);
              }
 
+    virtual  Plane_3
+             transform(const Plane_3& p, bool, const Aff_transformation_3&) const
+             {
+               return transform(p);
+             }
+
     virtual  Aff_transformation_3
              inverse() const
              { return Aff_transformation_3(SCALING, _sf_den, _sf_num); }
@@ -386,6 +402,9 @@ public:
   virtual  Plane_3
            transform(const Plane_3& pl) const;
 
+  virtual  Plane_3
+           transform(const Plane_3& pl, bool is_even, const Aff_transformation_3& transposed_inverse) const;
+
   virtual  Aff_transformation_3
            inverse() const;
 
@@ -471,6 +490,9 @@ public:
   Plane_3
   transform(const Plane_3& pl) const;
 
+  Plane_3
+  transform(const Plane_3& pl, bool is_even, const Aff_transformation_3& transposed_inverse) const;
+
   Aff_transformation_3
   inverse()   const;
 
@@ -577,22 +599,31 @@ template < class R >
 CGAL_KERNEL_INLINE
 typename Aff_transformation_repH3<R>::Plane_3
 Aff_transformation_repH3<R>::
-transform(const typename Aff_transformation_repH3<R>::Plane_3& pl) const
+transform(const typename Aff_transformation_repH3<R>::Plane_3& pl, bool is_even, const typename Aff_transformation_repH3<R>::Aff_transformation_3& transposed_inverse) const
 {
-  if ( is_even() )
+  if ( is_even )
   {
       return Plane_3(
                transform(pl.point() ),
-               transpose().inverse().transform(pl.orthogonal_direction() ));
+               transposed_inverse.transform(pl.orthogonal_direction() ));
   }
   else
   {
      return Plane_3(
                transform(pl.point() ),
-               -(transpose().inverse().transform(pl.orthogonal_direction() )));
+               -(transposed_inverse.transform(pl.orthogonal_direction() )));
   }
 }
 
+template < class R >
+CGAL_KERNEL_INLINE
+typename Aff_transformation_repH3<R>::Plane_3
+Aff_transformation_repH3<R>::
+transform(const typename Aff_transformation_repH3<R>::Plane_3& pl) const
+{
+  return transform(pl, is_even(), transpose().inverse());
+}
+
 template < class R >
 CGAL_KERNEL_INLINE
 typename Aff_transformation_repH3<R>::Aff_transformation_3
@@ -805,6 +836,15 @@ transform(const typename Translation_repH3<R>::Plane_3& pl) const
   return Plane_3( transform( pl.point() ), pl.orthogonal_vector() );
 }
 
+template < class R >
+inline
+typename Translation_repH3<R>::Plane_3
+Translation_repH3<R>::
+transform(const typename Translation_repH3<R>::Plane_3& pl, bool, const typename Translation_repH3<R>::Aff_transformation_3&) const
+{
+  return transform(pl);
+}
+
 template < class R >
 inline
 typename Translation_repH3<R>::Aff_transformation_3
@@ -1018,6 +1058,13 @@ Aff_transformationH3<R>::
 transform(const typename Aff_transformationH3<R>::Plane_3& pl) const
 { return this->Ptr()->transform(pl); }
 
+template < class R >
+inline
+typename Aff_transformationH3<R>::Plane_3
+Aff_transformationH3<R>::
+transform(const typename Aff_transformationH3<R>::Plane_3& pl, bool is_even, const typename Aff_transformationH3<R>::Aff_transformation_3& transposed_inverse) const
+{ return this->Ptr()->transform(pl, is_even, transposed_inverse); }
+
 template < class R >
 inline
 typename Aff_transformationH3<R>::Aff_transformation_3