* fix Quaternion::setFromTwoVectors (thanks to "benv" from the forum)

* extend PartialRedux::cross() to any matrix sizes with automatic vectorization when possible * unit tests: add "geo_" prefix to all unit tests related to the geometry module and start splitting the big "geometry.cpp" tests to multiple smaller ones (also include new tests)
2026-04-10 11:34:33 +08:00 · 2009-02-17 09:53:05 +00:00
parent 67b4fab4e3
commit e6f1104b57
16 changed files with 445 additions and 157 deletions
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -129,10 +129,13 @@ ei_add_test(inverse)
 ei_add_test(qr)
 ei_add_test(eigensolver " " "${GSL_LIBRARIES}")
 ei_add_test(svd)
-ei_add_test(geometry)
-ei_add_test(hyperplane)
-ei_add_test(parametrizedline)
-ei_add_test(alignedbox)
+ei_add_test(geo_orthomethods)
+ei_add_test(geo_quaternion)
+ei_add_test(geo_transformations)
+ei_add_test(geo_eulerangles)
+ei_add_test(geo_hyperplane)
+ei_add_test(geo_parametrizedline)
+ei_add_test(geo_alignedbox)
 ei_add_test(regression)
 ei_add_test(stdvector)
 ei_add_test(resize)
--- a/test/geo_alignedbox.cpp
+++ b/test/geo_alignedbox.cpp
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra. Eigen itself is part of the KDE project.
 //
-// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
 //
 // Eigen is free software; you can redistribute it and/or
 // modify it under the terms of the GNU Lesser General Public
@@ -65,7 +65,7 @@ template<typename BoxType> void alignedbox(const BoxType& _box)
  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),b0);
 }

-void test_alignedbox()
+void test_geo_alignedbox()
 {
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST( alignedbox(AlignedBox<float,2>()) );
--- a/test/geo_eulerangles.cpp
+++ b/test/geo_eulerangles.cpp
@@ -0,0 +1,70 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, 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.
+//
+// Eigen 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 Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+
+template<typename Scalar> void eulerangles(void)
+{
+  typedef Matrix<Scalar,3,3> Matrix3;
+  typedef Matrix<Scalar,3,1> Vector3;
+  typedef Quaternion<Scalar> Quaternionx;
+  typedef AngleAxis<Scalar> AngleAxisx;
+
+  Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+  Quaternionx q1;
+  q1 = AngleAxisx(a, Vector3::Random().normalized());
+  Matrix3 m;
+  m = q1;
+
+  #define VERIFY_EULER(I,J,K, X,Y,Z) { \
+    Vector3 ea = m.eulerAngles(I,J,K); \
+    Matrix3 m1 = Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \
+    VERIFY_IS_APPROX(m,  Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \
+  }
+  VERIFY_EULER(0,1,2, X,Y,Z);
+  VERIFY_EULER(0,1,0, X,Y,X);
+  VERIFY_EULER(0,2,1, X,Z,Y);
+  VERIFY_EULER(0,2,0, X,Z,X);
+
+  VERIFY_EULER(1,2,0, Y,Z,X);
+  VERIFY_EULER(1,2,1, Y,Z,Y);
+  VERIFY_EULER(1,0,2, Y,X,Z);
+  VERIFY_EULER(1,0,1, Y,X,Y);
+
+  VERIFY_EULER(2,0,1, Z,X,Y);
+  VERIFY_EULER(2,0,2, Z,X,Z);
+  VERIFY_EULER(2,1,0, Z,Y,X);
+  VERIFY_EULER(2,1,2, Z,Y,Z);
+}
+
+void test_geo_eulerangles()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( eulerangles<float>() );
+    CALL_SUBTEST( eulerangles<double>() );
+  }
+}
--- a/test/geo_hyperplane.cpp
+++ b/test/geo_hyperplane.cpp
@@ -127,7 +127,7 @@ template<typename Scalar> void lines()
  }
 }

-void test_hyperplane()
+void test_geo_hyperplane()
 {
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST( hyperplane(Hyperplane<float,2>()) );
--- a/test/geo_orthomethods.cpp
+++ b/test/geo_orthomethods.cpp
@@ -0,0 +1,109 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, 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.
+//
+// Eigen 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 Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+
+/* this test covers the following files:
+   Geometry/OrthoMethods.h
+*/
+
+template<typename Scalar> void orthomethods_3()
+{
+  typedef Matrix<Scalar,3,3> Matrix3;
+  typedef Matrix<Scalar,3,1> Vector3;
+
+  Vector3 v0 = Vector3::Random(),
+          v1 = Vector3::Random(),
+          v2 = Vector3::Random();
+
+  // cross product
+  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
+  Matrix3 mat3;
+  mat3 << v0.normalized(),
+         (v0.cross(v1)).normalized(),
+         (v0.cross(v1).cross(v0)).normalized();
+  VERIFY(mat3.isUnitary());
+
+
+  // colwise/rowwise cross product
+  mat3.setRandom();
+  Vector3 vec3 = Vector3::Random();
+  Matrix3 mcross;
+  int i = ei_random<int>(0,2);
+  mcross = mat3.colwise().cross(vec3);
+  VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
+  mcross = mat3.rowwise().cross(vec3);
+  VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
+
+}
+
+template<typename Scalar, int Size> void orthomethods(int size=Size)
+{
+  typedef Matrix<Scalar,Size,1> VectorType;
+  typedef Matrix<Scalar,3,Size> Matrix3N;
+  typedef Matrix<Scalar,Size,3> MatrixN3;
+  typedef Matrix<Scalar,3,1> Vector3;
+
+  VectorType v0 = VectorType::Random(size),
+             v1 = VectorType::Random(size),
+             v2 = VectorType::Random(size);
+
+  // unitOrthogonal
+  VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
+  VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1));
+
+  // colwise/rowwise cross product
+  Vector3 vec3 = Vector3::Random();
+  int i = ei_random<int>(0,size-1);
+
+  Matrix3N mat3N(3,size), mcross3N(3,size);
+  mat3N.setRandom();
+  mcross3N = mat3N.colwise().cross(vec3);
+  VERIFY_IS_APPROX(mcross3N.col(i), mat3N.col(i).cross(vec3));
+
+  MatrixN3 matN3(size,3), mcrossN3(size,3);
+  matN3.setRandom();
+  mcrossN3 = matN3.rowwise().cross(vec3);
+  VERIFY_IS_APPROX(mcrossN3.row(i), matN3.row(i).cross(vec3));
+
+}
+
+void test_geo_orthomethods()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( orthomethods_3<float>() );
+    CALL_SUBTEST( orthomethods_3<double>() );
+    CALL_SUBTEST( (orthomethods<float,2>()) );
+    CALL_SUBTEST( (orthomethods<double,2>()) );
+    CALL_SUBTEST( (orthomethods<float,3>()) );
+    CALL_SUBTEST( (orthomethods<double,3>()) );
+    CALL_SUBTEST( (orthomethods<float,7>()) );
+    CALL_SUBTEST( (orthomethods<double,8>()) );
+    CALL_SUBTEST( (orthomethods<float,Dynamic>(36)) );
+    CALL_SUBTEST( (orthomethods<double,Dynamic>(35)) );
+  }
+}
--- a/test/geo_parametrizedline.cpp
+++ b/test/geo_parametrizedline.cpp
@@ -66,7 +66,7 @@ template<typename LineType> void parametrizedline(const LineType& _line)
  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),l0);
 }

-void test_parametrizedline()
+void test_geo_parametrizedline()
 {
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST( parametrizedline(ParametrizedLine<float,2>()) );
--- a/test/geo_quaternion.cpp
+++ b/test/geo_quaternion.cpp
@@ -0,0 +1,116 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, 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.
+//
+// Eigen 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 Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+
+template<typename Scalar> void quaternion(void)
+{
+  /* this test covers the following files:
+     Quaternion.h
+  */
+
+  typedef Matrix<Scalar,3,3> Matrix3;
+  typedef Matrix<Scalar,3,1> Vector3;
+  typedef Quaternion<Scalar> Quaternionx;
+  typedef AngleAxis<Scalar> AngleAxisx;
+
+  Scalar largeEps = test_precision<Scalar>();
+  if (ei_is_same_type<Scalar,float>::ret)
+    largeEps = 1e-3f;
+
+  Scalar eps = ei_random<Scalar>() * 1e-2;
+
+  Vector3 v0 = Vector3::Random(),
+          v1 = Vector3::Random(),
+          v2 = Vector3::Random(),
+          v3 = Vector3::Random();
+
+  Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+
+  // Quaternion: Identity(), setIdentity();
+  Quaternionx q1, q2;
+  q2.setIdentity();
+  VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
+  q1.coeffs().setRandom();
+  VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
+
+  q1 = AngleAxisx(a, v0.normalized());
+  q2 = AngleAxisx(a, v1.normalized());
+
+  // angular distance
+  Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle());
+  if (refangle>Scalar(M_PI))
+    refangle = Scalar(2)*Scalar(M_PI) - refangle;
+
+  if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
+  {
+    VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps));
+  }
+
+  // rotation matrix conversion
+  VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
+  VERIFY_IS_APPROX(q1 * q2 * v2,
+    q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
+
+  VERIFY(  (q2*q1).isApprox(q1*q2, largeEps)
+        || !(q2 * q1 * v2).isApprox(q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
+
+  q2 = q1.toRotationMatrix();
+  VERIFY_IS_APPROX(q1*v1,q2*v1);
+
+
+  // angle-axis conversion
+  AngleAxisx aa = q1;
+  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
+  VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
+
+  // from two vector creation
+  VERIFY_IS_APPROX( v2.normalized(),(q2.setFromTwoVectors(v1, v2)*v1).normalized());
+  VERIFY_IS_APPROX( v1.normalized(),(q2.setFromTwoVectors(v1, v1)*v1).normalized());
+  VERIFY_IS_APPROX(-v1.normalized(),(q2.setFromTwoVectors(v1,-v1)*v1).normalized());
+  v3 = v1.cwise()+eps;
+  VERIFY_IS_APPROX( v3.normalized(),(q2.setFromTwoVectors(v1, v3)*v1).normalized());
+  VERIFY_IS_APPROX(-v3.normalized(),(q2.setFromTwoVectors(v1,-v3)*v1).normalized());
+
+  // inverse and conjugate
+  VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
+  VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
+
+  // test casting
+  Quaternion<float> q1f = q1.template cast<float>();
+  VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
+  Quaternion<double> q1d = q1.template cast<double>();
+  VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
+}
+
+void test_geo_quaternion()
+{
+  for(int i = 0; i < g_repeat; i++) {
+//     CALL_SUBTEST( quaternion<float>() );
+    CALL_SUBTEST( quaternion<double>() );
+  }
+}
--- a/test/geo_transformations.cpp
+++ b/test/geo_transformations.cpp
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra. Eigen itself is part of the KDE project.
 //
-// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
 //
 // Eigen is free software; you can redistribute it and/or
 // modify it under the terms of the GNU Lesser General Public
@@ -27,7 +27,7 @@
 #include <Eigen/LU>
 #include <Eigen/SVD>

-template<typename Scalar> void geometry(void)
+template<typename Scalar> void transformations(void)
 {
  /* this test covers the following files:
     Cross.h Quaternion.h, Transform.cpp
@@ -56,32 +56,10 @@ template<typename Scalar> void geometry(void)
    v1 = Vector3::Random(),
    v2 = Vector3::Random();
  Vector2 u0 = Vector2::Random();
-  Matrix3 matrot1;
+  Matrix3 matrot1, m;

  Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));

-  // cross product
-  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
-  Matrix3 m;
-  m << v0.normalized(),
-      (v0.cross(v1)).normalized(),
-      (v0.cross(v1).cross(v0)).normalized();
-  VERIFY(m.isUnitary());
-
-  // Quaternion: Identity(), setIdentity();
-  Quaternionx q1, q2;
-  q2.setIdentity();
-  VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
-  q1.coeffs().setRandom();
-  VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
-
-  // unitOrthogonal
-  VERIFY_IS_MUCH_SMALLER_THAN(u0.unitOrthogonal().dot(u0), Scalar(1));
-  VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
-  VERIFY_IS_APPROX(u0.unitOrthogonal().norm(), Scalar(1));
-  VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1));
-
-
  VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
  VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
  VERIFY_IS_APPROX(ei_cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
@@ -89,30 +67,11 @@ template<typename Scalar> void geometry(void)
  VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
  VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);

+  Quaternionx q1, q2;
  q1 = AngleAxisx(a, v0.normalized());
  q2 = AngleAxisx(a, v1.normalized());

-  // angular distance
-  Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle());
-  if (refangle>Scalar(M_PI))
-    refangle = Scalar(2)*Scalar(M_PI) - refangle;
-  
-  if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
-  {
-    VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps));
-  }
-
  // rotation matrix conversion
-  VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
-  VERIFY_IS_APPROX(q1 * q2 * v2,
-    q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
-
-  VERIFY( (q2*q1).isApprox(q1*q2, largeEps) || !(q2 * q1 * v2).isApprox(
-    q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
-
-  q2 = q1.toRotationMatrix();
-  VERIFY_IS_APPROX(q1*v1,q2*v1);
-
  matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
          * AngleAxisx(Scalar(0.2), Vector3::UnitY())
          * AngleAxisx(Scalar(0.3), Vector3::UnitZ());
@@ -126,14 +85,6 @@ template<typename Scalar> void geometry(void)
  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
  VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);

-  // from two vector creation
-  VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
-  VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
-
-  // inverse and conjugate
-  VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
-  VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
-
  // AngleAxis
  VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
    Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
@@ -382,11 +333,6 @@ template<typename Scalar> void geometry(void)
  DiagonalMatrix<double,3> sc1d; sc1d = (sc1.template cast<double>());
  VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1);

-  Quaternion<float> q1f = q1.template cast<float>();
-  VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
-  Quaternion<double> q1d = q1.template cast<double>();
-  VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
-
  AngleAxis<float> aa1f = aa1.template cast<float>();
  VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
  AngleAxis<double> aa1d = aa1.template cast<double>();
@@ -397,47 +343,12 @@ template<typename Scalar> void geometry(void)
  VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
  Rotation2D<double> r2d1d = r2d1.template cast<double>();
  VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
-
-  m = q1;
-//   m.col(1) = Vector3(0,ei_random<Scalar>(),ei_random<Scalar>()).normalized();
-//   m.col(0) = Vector3(-1,0,0).normalized();
-//   m.col(2) = m.col(0).cross(m.col(1));
-  #define VERIFY_EULER(I,J,K, X,Y,Z) { \
-    Vector3 ea = m.eulerAngles(I,J,K); \
-    Matrix3 m1 = Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \
-    VERIFY_IS_APPROX(m,  Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \
-  }
-  VERIFY_EULER(0,1,2, X,Y,Z);
-  VERIFY_EULER(0,1,0, X,Y,X);
-  VERIFY_EULER(0,2,1, X,Z,Y);
-  VERIFY_EULER(0,2,0, X,Z,X);
-
-  VERIFY_EULER(1,2,0, Y,Z,X);
-  VERIFY_EULER(1,2,1, Y,Z,Y);
-  VERIFY_EULER(1,0,2, Y,X,Z);
-  VERIFY_EULER(1,0,1, Y,X,Y);
-
-  VERIFY_EULER(2,0,1, Z,X,Y);
-  VERIFY_EULER(2,0,2, Z,X,Z);
-  VERIFY_EULER(2,1,0, Z,Y,X);
-  VERIFY_EULER(2,1,2, Z,Y,Z);
-
-  // colwise/rowwise cross product
-  mat3.setRandom();
-  Vector3 vec3 = Vector3::Random();
-  Matrix3 mcross;
-  int i = ei_random<int>(0,2);
-  mcross = mat3.colwise().cross(vec3);
-  VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
-  mcross = mat3.rowwise().cross(vec3);
-  VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
-
 }

-void test_geometry()
+void test_geo_transformations()
 {
  for(int i = 0; i < g_repeat; i++) {
-    CALL_SUBTEST( geometry<float>() );
-    CALL_SUBTEST( geometry<double>() );
+    CALL_SUBTEST( transformations<float>() );
+    CALL_SUBTEST( transformations<double>() );
  }
 }
--- a/test/sparse_product.cpp
+++ b/test/sparse_product.cpp
@@ -34,7 +34,6 @@ template<typename SparseMatrixType> void sparse_product(const SparseMatrixType&
  double density = std::max(8./(rows*cols), 0.01);
  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
  typedef Matrix<Scalar,Dynamic,1> DenseVector;
-  Scalar eps = 1e-6;

  // test matrix-matrix product
  {