* 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)

1 files changed, 354 insertions, 0 deletions

diff --git a/test/geo_transformations.cpp b/test/geo_transformations.cpp
new file mode 100644
index 000000000..35ecdb47b
--- /dev/null
+++ b/test/geo_transformations.cpp
@@ -0,0 +1,354 @@
+// 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 transformations(void)
+{
+  /* this test covers the following files:
+     Cross.h Quaternion.h, Transform.cpp
+  */
+
+  typedef Matrix<Scalar,2,2> Matrix2;
+  typedef Matrix<Scalar,3,3> Matrix3;
+  typedef Matrix<Scalar,4,4> Matrix4;
+  typedef Matrix<Scalar,2,1> Vector2;
+  typedef Matrix<Scalar,3,1> Vector3;
+  typedef Matrix<Scalar,4,1> Vector4;
+  typedef Quaternion<Scalar> Quaternionx;
+  typedef AngleAxis<Scalar> AngleAxisx;
+  typedef Transform<Scalar,2> Transform2;
+  typedef Transform<Scalar,3> Transform3;
+  typedef DiagonalMatrix<Scalar,2> AlignedScaling2;
+  typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
+  typedef Translation<Scalar,2> Translation2;
+  typedef Translation<Scalar,3> Translation3;
+
+  Scalar largeEps = test_precision<Scalar>();
+  if (ei_is_same_type<Scalar,float>::ret)
+    largeEps = 1e-2f;
+
+  Vector3 v0 = Vector3::Random(),
+    v1 = Vector3::Random(),
+    v2 = Vector3::Random();
+  Vector2 u0 = Vector2::Random();
+  Matrix3 matrot1, m;
+
+  Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+
+  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));
+  m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
+  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());
+
+  // rotation matrix conversion
+  matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
+          * AngleAxisx(Scalar(0.2), Vector3::UnitY())
+          * AngleAxisx(Scalar(0.3), Vector3::UnitZ());
+  VERIFY_IS_APPROX(matrot1 * v1,
+       AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
+    * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
+    * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * 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);
+
+  // AngleAxis
+  VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
+    Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
+
+  AngleAxisx aa1;
+  m = q1.toRotationMatrix();
+  aa1 = m;
+  VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
+    Quaternionx(m).toRotationMatrix());
+
+  // Transform
+  // TODO complete the tests !
+  a = 0;
+  while (ei_abs(a)<Scalar(0.1))
+    a = ei_random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
+  q1 = AngleAxisx(a, v0.normalized());
+  Transform3 t0, t1, t2;
+  t0.setIdentity();
+  t0.linear() = q1.toRotationMatrix();
+  t1.setIdentity();
+  t1.linear() = q1.toRotationMatrix();
+
+  v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5));
+  t0.scale(v0);
+  t1.prescale(v0);
+
+  VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x());
+  //VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x()));
+
+  t0.setIdentity();
+  t1.setIdentity();
+  v1 << 1, 2, 3;
+  t0.linear() = q1.toRotationMatrix();
+  t0.pretranslate(v0);
+  t0.scale(v1);
+  t1.linear() = q1.conjugate().toRotationMatrix();
+  t1.prescale(v1.cwise().inverse());
+  t1.translate(-v0);
+
+  VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>()));
+
+  t1.fromPositionOrientationScale(v0, q1, v1);
+  VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
+  VERIFY_IS_APPROX(t1*v1, t0*v1);
+
+  t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
+  t1.setIdentity(); t1.scale(v0).rotate(q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
+  VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
+
+  // More transform constructors, operator=, operator*=
+
+  Matrix3 mat3 = Matrix3::Random();
+  Matrix4 mat4;
+  mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
+  Transform3 tmat3(mat3), tmat4(mat4);
+  tmat4.matrix()(3,3) = Scalar(1);
+  VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
+
+  Scalar a3 = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+  Vector3 v3 = Vector3::Random().normalized();
+  AngleAxisx aa3(a3, v3);
+  Transform3 t3(aa3);
+  Transform3 t4;
+  t4 = aa3;
+  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
+  t4.rotate(AngleAxisx(-a3,v3));
+  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
+  t4 *= aa3;
+  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
+
+  v3 = Vector3::Random();
+  Translation3 tv3(v3);
+  Transform3 t5(tv3);
+  t4 = tv3;
+  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
+  t4.translate(-v3);
+  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
+  t4 *= tv3;
+  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
+
+  AlignedScaling3 sv3(v3);
+  Transform3 t6(sv3);
+  t4 = sv3;
+  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
+  t4.scale(v3.cwise().inverse());
+  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
+  t4 *= sv3;
+  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
+
+  // matrix * transform
+  VERIFY_IS_APPROX(Transform3(t3.matrix()*t4).matrix(), Transform3(t3*t4).matrix());
+
+  // chained Transform product
+  VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
+
+  // check that Transform product doesn't have aliasing problems
+  t5 = t4;
+  t5 = t5*t5;
+  VERIFY_IS_APPROX(t5, t4*t4);
+
+  // 2D transformation
+  Transform2 t20, t21;
+  Vector2 v20 = Vector2::Random();
+  Vector2 v21 = Vector2::Random();
+  for (int k=0; k<2; ++k)
+    if (ei_abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
+  t21.setIdentity();
+  t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
+  VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
+    t21.pretranslate(v20).scale(v21).matrix());
+
+  t21.setIdentity();
+  t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
+  VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
+        * (t21.prescale(v21.cwise().inverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
+
+  // Transform - new API
+  // 3D
+  t0.setIdentity();
+  t0.rotate(q1).scale(v0).translate(v0);
+  // mat * aligned scaling and mat * translation
+  t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  t1 = (Matrix3(q1) * Scaling(v0)) * Translation3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  t1 = (q1 * Scaling(v0)) * Translation3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // mat * transformation and aligned scaling * translation
+  t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  t0.setIdentity();
+  t0.prerotate(q1).prescale(v0).pretranslate(v0);
+  // translation * aligned scaling and transformation * mat
+  t1 = (Translation3(v0) * AlignedScaling3(v0)) * Matrix3(q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // scaling * mat and translation * mat
+  t1 = Translation3(v0) * (AlignedScaling3(v0) * Matrix3(q1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  t0.setIdentity();
+  t0.scale(v0).translate(v0).rotate(q1);
+  // translation * mat and aligned scaling * transformation
+  t1 = AlignedScaling3(v0) * (Translation3(v0) * Matrix3(q1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // transformation * aligned scaling
+  t0.scale(v0);
+  t1 = t1 * AlignedScaling3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // transformation * translation
+  t0.translate(v0);
+  t1 = t1 * Translation3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // translation * transformation
+  t0.pretranslate(v0);
+  t1 = Translation3(v0) * t1;
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // transform * quaternion
+  t0.rotate(q1);
+  t1 = t1 * q1;
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // translation * quaternion
+  t0.translate(v1).rotate(q1);
+  t1 = t1 * (Translation3(v1) * q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // aligned scaling * quaternion
+  t0.scale(v1).rotate(q1);
+  t1 = t1 * (AlignedScaling3(v1) * q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // quaternion * transform
+  t0.prerotate(q1);
+  t1 = q1 * t1;
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // quaternion * translation
+  t0.rotate(q1).translate(v1);
+  t1 = t1 * (q1 * Translation3(v1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // quaternion * aligned scaling
+  t0.rotate(q1).scale(v1);
+  t1 = t1 * (q1 * AlignedScaling3(v1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // translation * vector
+  t0.setIdentity();
+  t0.translate(v0);
+  VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1);
+
+  // AlignedScaling * vector
+  t0.setIdentity();
+  t0.scale(v0);
+  VERIFY_IS_APPROX(t0 * v1, AlignedScaling3(v0) * v1);
+
+  // test transform inversion
+  t0.setIdentity();
+  t0.translate(v0);
+  t0.linear().setRandom();
+  VERIFY_IS_APPROX(t0.inverse(Affine), t0.matrix().inverse());
+  t0.setIdentity();
+  t0.translate(v0).rotate(q1);
+  VERIFY_IS_APPROX(t0.inverse(Isometry), t0.matrix().inverse());
+
+  // test extract rotation and aligned scaling
+//   t0.setIdentity();
+//   t0.translate(v0).rotate(q1).scale(v1);
+//   VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1);
+
+  Matrix3 mat_rotation, mat_scaling;
+  t0.setIdentity();
+  t0.translate(v0).rotate(q1).scale(v1);
+  t0.computeRotationScaling(&mat_rotation, &mat_scaling);
+  VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
+  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
+  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
+  t0.computeScalingRotation(&mat_scaling, &mat_rotation);
+  VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
+  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
+  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
+
+  // test casting
+  Transform<float,3> t1f = t1.template cast<float>();
+  VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
+  Transform<double,3> t1d = t1.template cast<double>();
+  VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
+
+  Translation3 tr1(v0);
+  Translation<float,3> tr1f = tr1.template cast<float>();
+  VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
+  Translation<double,3> tr1d = tr1.template cast<double>();
+  VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
+
+  AlignedScaling3 sc1(v0);
+  DiagonalMatrix<float,3> sc1f; sc1f = sc1.template cast<float>();
+  VERIFY_IS_APPROX(sc1f.template cast<Scalar>(),sc1);
+  DiagonalMatrix<double,3> sc1d; sc1d = (sc1.template cast<double>());
+  VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1);
+
+  AngleAxis<float> aa1f = aa1.template cast<float>();
+  VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
+  AngleAxis<double> aa1d = aa1.template cast<double>();
+  VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
+
+  Rotation2D<Scalar> r2d1(ei_random<Scalar>());
+  Rotation2D<float> r2d1f = r2d1.template cast<float>();
+  VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
+  Rotation2D<double> r2d1d = r2d1.template cast<double>();
+  VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
+}
+
+void test_geo_transformations()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( transformations<float>() );
+    CALL_SUBTEST( transformations<double>() );
+  }
+}