rename

Eigen'源码分析/Rotation2D_test.cpp → 1-Eigen'源码分析/Rotation2D_test.cpp

@@ -23,6 +23,8 @@ int main()
 
     sout(a.angle()<<"=="<< M_PI/3);
 
+    sout(a.inverse().angle()<<"=="<<-M_PI/3);
+
     sout(a.Identity().toRotationMatrix());
 
 

1-Eigen'源码分析/geo_quaternion.cpp

@@ -0,0 +1,289 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <[email protected]>
+// Copyright (C) 2009 Mathieu Gautier <[email protected]>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+
+template<typename T> T bounded_acos(T v)
+{
+  using std::acos;
+  using std::min;
+  using std::max;
+  return acos((max)(T(-1),(min)(v,T(1))));
+}
+
+template<typename QuatType> void check_slerp(const QuatType& q0, const QuatType& q1)
+{
+  using std::abs;
+  typedef typename QuatType::Scalar Scalar;
+  typedef AngleAxis<Scalar> AA;
+
+  Scalar largeEps = test_precision<Scalar>();
+
+  Scalar theta_tot = AA(q1*q0.inverse()).angle();
+  if(theta_tot>Scalar(EIGEN_PI))
+    theta_tot = Scalar(2.)*Scalar(EIGEN_PI)-theta_tot;
+  for(Scalar t=0; t<=Scalar(1.001); t+=Scalar(0.1))
+  {
+    QuatType q = q0.slerp(t,q1);
+    Scalar theta = AA(q*q0.inverse()).angle();
+    VERIFY(abs(q.norm() - 1) < largeEps);
+    if(theta_tot==0)  VERIFY(theta_tot==0);
+    else              VERIFY(abs(theta - t * theta_tot) < largeEps);
+  }
+}
+
+template<typename Scalar, int Options> void quaternion(void)
+{
+  /* this test covers the following files:
+     Quaternion.h
+  */
+  using std::abs;
+  typedef Matrix<Scalar,3,1> Vector3;
+  typedef Matrix<Scalar,3,3> Matrix3;
+  typedef Quaternion<Scalar,Options> Quaternionx;
+  typedef AngleAxis<Scalar> AngleAxisx;
+
+  Scalar largeEps = test_precision<Scalar>();
+  if (internal::is_same<Scalar,float>::value)
+    largeEps = Scalar(1e-3);
+
+  Scalar eps = internal::random<Scalar>() * Scalar(1e-2);
+
+  Vector3 v0 = Vector3::Random(),
+          v1 = Vector3::Random(),
+          v2 = Vector3::Random(),
+          v3 = Vector3::Random();
+
+  Scalar  a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)),
+          b = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_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());
+
+  // concatenation
+  q1 *= q2;
+
+  q1 = AngleAxisx(a, v0.normalized());
+  q2 = AngleAxisx(a, v1.normalized());
+
+  // angular distance
+  Scalar refangle = abs(AngleAxisx(q1.inverse()*q2).angle());
+  if (refangle>Scalar(EIGEN_PI))
+    refangle = Scalar(2)*Scalar(EIGEN_PI) - refangle;
+
+  if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
+  {
+    VERIFY_IS_MUCH_SMALLER_THAN(abs(q1.angularDistance(q2) - refangle), Scalar(1));
+  }
+
+  // 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);
+
+  Matrix3 rot1(q1);
+  VERIFY_IS_APPROX(q1*v1,rot1*v1);
+  Quaternionx q3(rot1.transpose()*rot1);
+  VERIFY_IS_APPROX(q3*v1,v1);
+
+
+  // angle-axis conversion
+  AngleAxisx aa = AngleAxisx(q1);
+  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
+
+  // Do not execute the test if the rotation angle is almost zero, or
+  // the rotation axis and v1 are almost parallel.
+  if (abs(aa.angle()) > 5*test_precision<Scalar>()
+      && (aa.axis() - v1.normalized()).norm() < Scalar(1.99)
+      && (aa.axis() + v1.normalized()).norm() < Scalar(1.99))
+  {
+    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());
+  if (internal::is_same<Scalar,double>::value)
+  {
+    v3 = (v1.array()+eps).matrix();
+    VERIFY_IS_APPROX( v3.normalized(),(q2.setFromTwoVectors(v1, v3)*v1).normalized());
+    VERIFY_IS_APPROX(-v3.normalized(),(q2.setFromTwoVectors(v1,-v3)*v1).normalized());
+  }
+
+  // from two vector creation static function
+  VERIFY_IS_APPROX( v2.normalized(),(Quaternionx::FromTwoVectors(v1, v2)*v1).normalized());
+  VERIFY_IS_APPROX( v1.normalized(),(Quaternionx::FromTwoVectors(v1, v1)*v1).normalized());
+  VERIFY_IS_APPROX(-v1.normalized(),(Quaternionx::FromTwoVectors(v1,-v1)*v1).normalized());
+  if (internal::is_same<Scalar,double>::value)
+  {
+    v3 = (v1.array()+eps).matrix();
+    VERIFY_IS_APPROX( v3.normalized(),(Quaternionx::FromTwoVectors(v1, v3)*v1).normalized());
+    VERIFY_IS_APPROX(-v3.normalized(),(Quaternionx::FromTwoVectors(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);
+
+  // test bug 369 - improper alignment.
+  Quaternionx *q = new Quaternionx;
+  delete q;
+
+  q1 = Quaternionx::UnitRandom();
+  q2 = Quaternionx::UnitRandom();
+  check_slerp(q1,q2);
+
+  q1 = AngleAxisx(b, v1.normalized());
+  q2 = AngleAxisx(b+Scalar(EIGEN_PI), v1.normalized());
+  check_slerp(q1,q2);
+
+  q1 = AngleAxisx(b,  v1.normalized());
+  q2 = AngleAxisx(-b, -v1.normalized());
+  check_slerp(q1,q2);
+
+  q1 = Quaternionx::UnitRandom();
+  q2.coeffs() = -q1.coeffs();
+  check_slerp(q1,q2);
+}
+
+template<typename Scalar> void mapQuaternion(void){
+  typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA;
+  typedef Map<const Quaternion<Scalar>, Aligned> MCQuaternionA;
+  typedef Map<Quaternion<Scalar> > MQuaternionUA;
+  typedef Map<const Quaternion<Scalar> > MCQuaternionUA;
+  typedef Quaternion<Scalar> Quaternionx;
+  typedef Matrix<Scalar,3,1> Vector3;
+  typedef AngleAxis<Scalar> AngleAxisx;
+
+  Vector3 v0 = Vector3::Random(),
+          v1 = Vector3::Random();
+  Scalar  a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
+
+  EIGEN_ALIGN_MAX Scalar array1[4];
+  EIGEN_ALIGN_MAX Scalar array2[4];
+  EIGEN_ALIGN_MAX Scalar array3[4+1];
+  Scalar* array3unaligned = array3+1;
+
+  MQuaternionA    mq1(array1);
+  MCQuaternionA   mcq1(array1);
+  MQuaternionA    mq2(array2);
+  MQuaternionUA   mq3(array3unaligned);
+  MCQuaternionUA  mcq3(array3unaligned);
+
+//  std::cerr << array1 << " " << array2 << " " << array3 << "\n";
+  mq1 = AngleAxisx(a, v0.normalized());
+  mq2 = mq1;
+  mq3 = mq1;
+
+  Quaternionx q1 = mq1;
+  Quaternionx q2 = mq2;
+  Quaternionx q3 = mq3;
+  Quaternionx q4 = MCQuaternionUA(array3unaligned);
+
+  VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs());
+  VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs());
+  VERIFY_IS_APPROX(q4.coeffs(), q3.coeffs());
+  #ifdef EIGEN_VECTORIZE
+  if(internal::packet_traits<Scalar>::Vectorizable)
+    VERIFY_RAISES_ASSERT((MQuaternionA(array3unaligned)));
+  #endif
+
+  VERIFY_IS_APPROX(mq1 * (mq1.inverse() * v1), v1);
+  VERIFY_IS_APPROX(mq1 * (mq1.conjugate() * v1), v1);
+
+  VERIFY_IS_APPROX(mcq1 * (mcq1.inverse() * v1), v1);
+  VERIFY_IS_APPROX(mcq1 * (mcq1.conjugate() * v1), v1);
+
+  VERIFY_IS_APPROX(mq3 * (mq3.inverse() * v1), v1);
+  VERIFY_IS_APPROX(mq3 * (mq3.conjugate() * v1), v1);
+
+  VERIFY_IS_APPROX(mcq3 * (mcq3.inverse() * v1), v1);
+  VERIFY_IS_APPROX(mcq3 * (mcq3.conjugate() * v1), v1);
+
+  VERIFY_IS_APPROX(mq1*mq2, q1*q2);
+  VERIFY_IS_APPROX(mq3*mq2, q3*q2);
+  VERIFY_IS_APPROX(mcq1*mq2, q1*q2);
+  VERIFY_IS_APPROX(mcq3*mq2, q3*q2);
+}
+
+template<typename Scalar> void quaternionAlignment(void){
+  typedef Quaternion<Scalar,AutoAlign> QuaternionA;
+  typedef Quaternion<Scalar,DontAlign> QuaternionUA;
+
+  EIGEN_ALIGN_MAX Scalar array1[4];
+  EIGEN_ALIGN_MAX Scalar array2[4];
+  EIGEN_ALIGN_MAX Scalar array3[4+1];
+  Scalar* arrayunaligned = array3+1;
+
+  QuaternionA *q1 = ::new(reinterpret_cast<void*>(array1)) QuaternionA;
+  QuaternionUA *q2 = ::new(reinterpret_cast<void*>(array2)) QuaternionUA;
+  QuaternionUA *q3 = ::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionUA;
+
+  q1->coeffs().setRandom();
+  *q2 = *q1;
+  *q3 = *q1;
+
+  VERIFY_IS_APPROX(q1->coeffs(), q2->coeffs());
+  VERIFY_IS_APPROX(q1->coeffs(), q3->coeffs());
+  #if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES>0
+  if(internal::packet_traits<Scalar>::Vectorizable && internal::packet_traits<Scalar>::size<=4)
+    VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionA));
+  #endif
+}
+
+template<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)
+{
+  // there's a lot that we can't test here while still having this test compile!
+  // the only possible approach would be to run a script trying to compile stuff and checking that it fails.
+  // CMake can help with that.
+
+  // verify that map-to-const don't have LvalueBit
+  typedef typename internal::add_const<PlainObjectType>::type ConstPlainObjectType;
+  VERIFY( !(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit) );
+  VERIFY( !(internal::traits<Map<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );
+  VERIFY( !(Map<ConstPlainObjectType>::Flags & LvalueBit) );
+  VERIFY( !(Map<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );
+}
+
+void test_geo_quaternion()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1(( quaternion<float,AutoAlign>() ));
+    CALL_SUBTEST_1( check_const_correctness(Quaternionf()) );
+    CALL_SUBTEST_2(( quaternion<double,AutoAlign>() ));
+    CALL_SUBTEST_2( check_const_correctness(Quaterniond()) );
+    CALL_SUBTEST_3(( quaternion<float,DontAlign>() ));
+    CALL_SUBTEST_4(( quaternion<double,DontAlign>() ));
+    CALL_SUBTEST_5(( quaternionAlignment<float>() ));
+    CALL_SUBTEST_6(( quaternionAlignment<double>() ));
+    CALL_SUBTEST_1( mapQuaternion<float>() );
+    CALL_SUBTEST_2( mapQuaternion<double>() );
+  }
+}