fix #1 : need to nest by value the affine part in homogeneous product

Eigen/src/Geometry/Homogeneous.h

diff --git a/Eigen/src/Geometry/Homogeneous.h b/Eigen/src/Geometry/Homogeneous.h
index 0041ca5..34d4d07 100644
--- a/Eigen/src/Geometry/Homogeneous.h
+++ b/Eigen/src/Geometry/Homogeneous.h
@@ -102,11 +102,11 @@
 
     template<typename Scalar, int Dim, int Mode> friend
     inline const ei_homogeneous_left_product_impl<Homogeneous,
-      typename Transform<Scalar,Dim,Mode>::AffinePart>
+      typename Transform<Scalar,Dim,Mode>::AffinePartNested>
     operator* (const Transform<Scalar,Dim,Mode>& tr, const Homogeneous& rhs)
     {
       ei_assert(Direction==Vertical);
-      return ei_homogeneous_left_product_impl<Homogeneous,typename Transform<Scalar,Dim,Mode>::AffinePart>
+      return ei_homogeneous_left_product_impl<Homogeneous,typename Transform<Scalar,Dim,Mode>::AffinePartNested >
         (tr.affine(),rhs.m_matrix);
     }
 

Eigen/src/Geometry/Transform.h

diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
index 186580a..77a06fe 100644
--- a/Eigen/src/Geometry/Transform.h
+++ b/Eigen/src/Geometry/Transform.h
@@ -184,6 +184,10 @@
   typedef typename ei_meta_if<int(Mode)==int(AffineCompact),
                               MatrixType&,
                               Block<MatrixType,Dim,HDim> >::ret AffinePart;
+  /** type of read/write reference to the affine part of the transformation */
+  typedef typename ei_meta_if<int(Mode)==int(AffineCompact),
+                              MatrixType&,
+                              NestByValue<Block<MatrixType,Dim,HDim> > >::ret AffinePartNested;
   /** type of a vector */
   typedef Matrix<Scalar,Dim,1> VectorType;
   /** type of a read/write reference to the translation part of the rotation */

test/geo_homogeneous.cpp

diff --git a/test/geo_homogeneous.cpp b/test/geo_homogeneous.cpp
index 5deb0d5..bf568bb 100644
--- a/test/geo_homogeneous.cpp
+++ b/test/geo_homogeneous.cpp
@@ -33,10 +33,10 @@
 
   typedef Matrix<Scalar,Size,Size> MatrixType;
   typedef Matrix<Scalar,Size,1> VectorType;
-  
+
   typedef Matrix<Scalar,Size+1,Size> HMatrixType;
   typedef Matrix<Scalar,Size+1,1> HVectorType;
-  
+
   typedef Matrix<Scalar,Size,Size+1>   T1MatrixType;
   typedef Matrix<Scalar,Size+1,Size+1> T2MatrixType;
   typedef Matrix<Scalar,Size+1,Size> T3MatrixType;
@@ -51,17 +51,17 @@
 
   HVectorType hv0 = HVectorType::Random(),
               hv1 = HVectorType::Random();
-  
+
   MatrixType m0 = MatrixType::Random(),
              m1 = MatrixType::Random();
-  
+
   HMatrixType hm0 = HMatrixType::Random(),
               hm1 = HMatrixType::Random();
 
   hv0 << v0, 1;
   VERIFY_IS_APPROX(v0.homogeneous(), hv0);
   VERIFY_IS_APPROX(v0, hv0.hnormalized());
-  
+
   hm0 << m0, ones.transpose();
   VERIFY_IS_APPROX(m0.colwise().homogeneous(), hm0);
   VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
@@ -69,16 +69,16 @@
   for(int j=0; j<Size; ++j)
     m0.col(j) = hm0.col(j).start(Size) / hm0(Size,j);
   VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
-  
+
   T1MatrixType t1 = T1MatrixType::Random();
   VERIFY_IS_APPROX(t1 * (v0.homogeneous().eval()), t1 * v0.homogeneous());
   VERIFY_IS_APPROX(t1 * (m0.colwise().homogeneous().eval()), t1 * m0.colwise().homogeneous());
-  
+
   T2MatrixType t2 = T2MatrixType::Random();
   VERIFY_IS_APPROX(t2 * (v0.homogeneous().eval()), t2 * v0.homogeneous());
   VERIFY_IS_APPROX(t2 * (m0.colwise().homogeneous().eval()), t2 * m0.colwise().homogeneous());
-  
-  VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t2, 
+
+  VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t2,
                     v0.transpose().rowwise().homogeneous() * t2);
   VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t2,
                     m0.transpose().rowwise().homogeneous() * t2);
@@ -88,6 +88,17 @@
                     v0.transpose().rowwise().homogeneous() * t3);
   VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t3,
                     m0.transpose().rowwise().homogeneous() * t3);
+
+  // test product with a Transform object
+  Transform<Scalar, Size, Affine> Rt;
+  Matrix<Scalar, Size, Dynamic> pts, Rt_pts1;
+
+  Rt.setIdentity();
+  pts.setRandom(Size,5);
+
+  Rt_pts1 = Rt * pts.colwise().homogeneous();
+  std::cerr << (Rt_pts1 - pts).sum() << "\n";
+  VERIFY_IS_MUCH_SMALLER_THAN( (Rt_pts1 - pts).sum(), Scalar(1));
 }
 
 void test_geo_homogeneous()

test/sparse_solvers.cpp

diff --git a/test/sparse_solvers.cpp b/test/sparse_solvers.cpp
index 1f15980..de308e0 100644
--- a/test/sparse_solvers.cpp
+++ b/test/sparse_solvers.cpp
@@ -72,12 +72,12 @@
     initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
     VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().solveTriangular(vec2),
                      m2.template triangular<UpperTriangular>().solve(vec3));
-    
+
     // TODO test row major
-    
+
     SparseMatrix<Scalar> matB(rows, rows);
     DenseMatrix refMatB = DenseMatrix::Zero(rows, rows);
-    
+
     // lower - sparse
     initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular);
     initSparse<Scalar>(density, refMatB, matB);
@@ -91,7 +91,7 @@
     refMat2.template marked<UpperTriangular>().solveTriangularInPlace(refMatB);
     m2.template triangular<UpperTriangular>().solveInPlace(matB);
     VERIFY_IS_APPROX(matB, refMatB);
-    
+
     // test deprecated API
     initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
     VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().solveTriangular(vec2),
@@ -122,7 +122,7 @@
     SparseLLT<SparseSelfAdjointMatrix,Cholmod>(m2).solveInPlace(x);
     VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod");
     #endif
-      
+
     #ifdef EIGEN_TAUCS_SUPPORT
     x = b;
     SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,IncompleteFactorization).solveInPlace(x);