You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
645 lines
23 KiB
645 lines
23 KiB
// This file is part of Eigen, a lightweight C++ template library |
|
// for linear algebra. |
|
// |
|
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> |
|
// |
|
// 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> |
|
Matrix<T,2,1> angleToVec(T a) |
|
{ |
|
return Matrix<T,2,1>(std::cos(a), std::sin(a)); |
|
} |
|
|
|
// This permits to workaround a bug in clang/llvm code generation. |
|
template<typename T> |
|
EIGEN_DONT_INLINE |
|
void dont_over_optimize(T& x) { volatile typename T::Scalar tmp = x(0); x(0) = tmp; } |
|
|
|
template<typename Scalar, int Mode, int Options> void non_projective_only() |
|
{ |
|
/* this test covers the following files: |
|
Cross.h Quaternion.h, Transform.cpp |
|
*/ |
|
typedef Matrix<Scalar,3,1> Vector3; |
|
typedef Quaternion<Scalar> Quaternionx; |
|
typedef AngleAxis<Scalar> AngleAxisx; |
|
typedef Transform<Scalar,3,Mode,Options> Transform3; |
|
typedef DiagonalMatrix<Scalar,3> AlignedScaling3; |
|
typedef Translation<Scalar,3> Translation3; |
|
|
|
Vector3 v0 = Vector3::Random(), |
|
v1 = Vector3::Random(); |
|
|
|
Transform3 t0, t1, t2; |
|
|
|
Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); |
|
|
|
Quaternionx q1, q2; |
|
|
|
q1 = AngleAxisx(a, v0.normalized()); |
|
|
|
t0 = Transform3::Identity(); |
|
VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); |
|
|
|
t0.linear() = q1.toRotationMatrix(); |
|
|
|
v0 << 50, 2, 1; |
|
t0.scale(v0); |
|
|
|
VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).template head<3>().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.cwiseInverse()); |
|
t1.translate(-v0); |
|
|
|
VERIFY((t0 * 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); |
|
|
|
// translation * vector |
|
t0.setIdentity(); |
|
t0.translate(v0); |
|
VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1); |
|
|
|
// AlignedScaling * vector |
|
t0.setIdentity(); |
|
t0.scale(v0); |
|
VERIFY_IS_APPROX((t0 * v1).template head<3>(), AlignedScaling3(v0) * v1); |
|
} |
|
|
|
template<typename Scalar, int Mode, int Options> void transformations() |
|
{ |
|
/* this test covers the following files: |
|
Cross.h Quaternion.h, Transform.cpp |
|
*/ |
|
using std::cos; |
|
using std::abs; |
|
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,Mode,Options> Transform2; |
|
typedef Transform<Scalar,3,Mode,Options> Transform3; |
|
typedef typename Transform3::MatrixType MatrixType; |
|
typedef DiagonalMatrix<Scalar,3> AlignedScaling3; |
|
typedef Translation<Scalar,2> Translation2; |
|
typedef Translation<Scalar,3> Translation3; |
|
|
|
Vector3 v0 = Vector3::Random(), |
|
v1 = Vector3::Random(); |
|
Matrix3 matrot1, m; |
|
|
|
Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); |
|
Scalar s0 = internal::random<Scalar>(), s1 = internal::random<Scalar>(); |
|
|
|
while(v0.norm() < test_precision<Scalar>()) v0 = Vector3::Random(); |
|
while(v1.norm() < test_precision<Scalar>()) v1 = Vector3::Random(); |
|
|
|
VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0); |
|
VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(EIGEN_PI), v0.unitOrthogonal()) * v0); |
|
if(abs(cos(a)) > test_precision<Scalar>()) |
|
{ |
|
VERIFY_IS_APPROX(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 = AngleAxisx(q1); |
|
VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); |
|
|
|
// The following test is stable only if 2*angle != angle and v1 is not colinear with axis |
|
if( (abs(aa.angle()) > test_precision<Scalar>()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision<Scalar>())) ) |
|
{ |
|
VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) ); |
|
} |
|
|
|
aa.fromRotationMatrix(aa.toRotationMatrix()); |
|
VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); |
|
// The following test is stable only if 2*angle != angle and v1 is not colinear with axis |
|
if( (abs(aa.angle()) > test_precision<Scalar>()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision<Scalar>())) ) |
|
{ |
|
VERIFY( !(q1 * v1).isApprox(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 (abs(a)<Scalar(0.1)) |
|
a = internal::random<Scalar>(-Scalar(0.4)*Scalar(EIGEN_PI), Scalar(0.4)*Scalar(EIGEN_PI)); |
|
q1 = AngleAxisx(a, v0.normalized()); |
|
Transform3 t0, t1, t2; |
|
|
|
// first test setIdentity() and Identity() |
|
t0.setIdentity(); |
|
VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); |
|
t0.matrix().setZero(); |
|
t0 = Transform3::Identity(); |
|
VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); |
|
|
|
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.cwiseInverse()); |
|
t1.translate(-v0); |
|
|
|
VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>())); |
|
|
|
t1.fromPositionOrientationScale(v0, q1, v1); |
|
VERIFY_IS_APPROX(t1.matrix(), t0.matrix()); |
|
|
|
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); |
|
if(Mode!=int(AffineCompact)) |
|
tmat4.matrix()(3,3) = Scalar(1); |
|
VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix()); |
|
|
|
Scalar a3 = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_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(), MatrixType::Identity()); |
|
t4 *= aa3; |
|
VERIFY_IS_APPROX(t3.matrix(), t4.matrix()); |
|
|
|
do { |
|
v3 = Vector3::Random(); |
|
dont_over_optimize(v3); |
|
} while (v3.cwiseAbs().minCoeff()<NumTraits<Scalar>::epsilon()); |
|
Translation3 tv3(v3); |
|
Transform3 t5(tv3); |
|
t4 = tv3; |
|
VERIFY_IS_APPROX(t5.matrix(), t4.matrix()); |
|
t4.translate((-v3).eval()); |
|
VERIFY_IS_APPROX(t4.matrix(), MatrixType::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.cwiseInverse()); |
|
VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity()); |
|
t4 *= sv3; |
|
VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); |
|
|
|
// matrix * transform |
|
VERIFY_IS_APPROX((t3.matrix()*t4).matrix(), (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 (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.cwiseInverse()).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) * Eigen::Scaling(v0)) * Translation3(v0); |
|
VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); |
|
t1 = (q1 * Eigen::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.scale(s0).translate(v0); |
|
t1 = Eigen::Scaling(s0) * Translation3(v0); |
|
VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); |
|
t0.prescale(s0); |
|
t1 = Eigen::Scaling(s0) * t1; |
|
VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); |
|
|
|
t0 = t3; |
|
t0.scale(s0); |
|
t1 = t3 * Eigen::Scaling(s0,s0,s0); |
|
VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); |
|
t0.prescale(s0); |
|
t1 = Eigen::Scaling(s0,s0,s0) * t1; |
|
VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); |
|
|
|
t0 = t3; |
|
t0.scale(s0); |
|
t1 = t3 * Eigen::Scaling(s0); |
|
VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); |
|
t0.prescale(s0); |
|
t1 = Eigen::Scaling(s0) * t1; |
|
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)) * Transform3(q1); |
|
VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); |
|
// scaling * mat and translation * mat |
|
t1 = Translation3(v0) * (AlignedScaling3(v0) * Transform3(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) * Transform3(q1)); |
|
VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); |
|
// transformation * aligned scaling |
|
t0.scale(v0); |
|
t1 *= AlignedScaling3(v0); |
|
VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); |
|
t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1)); |
|
t1 = t1 * v0.asDiagonal(); |
|
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()); |
|
|
|
// test transform inversion |
|
t0.setIdentity(); |
|
t0.translate(v0); |
|
do { |
|
t0.linear().setRandom(); |
|
} while(t0.linear().jacobiSvd().singularValues()(2)<test_precision<Scalar>()); |
|
Matrix4 t044 = Matrix4::Zero(); |
|
t044(3,3) = 1; |
|
t044.block(0,0,t0.matrix().rows(),4) = t0.matrix(); |
|
VERIFY_IS_APPROX(t0.inverse(Affine).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4)); |
|
t0.setIdentity(); |
|
t0.translate(v0).rotate(q1); |
|
t044 = Matrix4::Zero(); |
|
t044(3,3) = 1; |
|
t044.block(0,0,t0.matrix().rows(),4) = t0.matrix(); |
|
VERIFY_IS_APPROX(t0.inverse(Isometry).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4)); |
|
|
|
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,Mode> t1f = t1.template cast<float>(); |
|
VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1); |
|
Transform<double,3,Mode> 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); |
|
|
|
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(internal::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); |
|
|
|
for(int k=0; k<100; ++k) |
|
{ |
|
Scalar angle = internal::random<Scalar>(-100,100); |
|
Rotation2D<Scalar> rot2(angle); |
|
VERIFY( rot2.smallestPositiveAngle() >= 0 ); |
|
VERIFY( rot2.smallestPositiveAngle() <= Scalar(2)*Scalar(EIGEN_PI) ); |
|
VERIFY_IS_APPROX( angleToVec(rot2.smallestPositiveAngle()), angleToVec(rot2.angle()) ); |
|
|
|
VERIFY( rot2.smallestAngle() >= -Scalar(EIGEN_PI) ); |
|
VERIFY( rot2.smallestAngle() <= Scalar(EIGEN_PI) ); |
|
VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()), angleToVec(rot2.angle()) ); |
|
|
|
Matrix<Scalar,2,2> rot2_as_mat(rot2); |
|
Rotation2D<Scalar> rot3(rot2_as_mat); |
|
VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()), angleToVec(rot3.angle()) ); |
|
} |
|
|
|
s0 = internal::random<Scalar>(-100,100); |
|
s1 = internal::random<Scalar>(-100,100); |
|
Rotation2D<Scalar> R0(s0), R1(s1); |
|
|
|
t20 = Translation2(v20) * (R0 * Eigen::Scaling(s0)); |
|
t21 = Translation2(v20) * R0 * Eigen::Scaling(s0); |
|
VERIFY_IS_APPROX(t20,t21); |
|
|
|
t20 = Translation2(v20) * (R0 * R0.inverse() * Eigen::Scaling(s0)); |
|
t21 = Translation2(v20) * Eigen::Scaling(s0); |
|
VERIFY_IS_APPROX(t20,t21); |
|
|
|
VERIFY_IS_APPROX(s0, (R0.slerp(0, R1)).angle()); |
|
VERIFY_IS_APPROX( angleToVec(R1.smallestPositiveAngle()), angleToVec((R0.slerp(1, R1)).smallestPositiveAngle()) ); |
|
VERIFY_IS_APPROX(R0.smallestPositiveAngle(), (R0.slerp(0.5, R0)).smallestPositiveAngle()); |
|
|
|
if(std::cos(s0)>0) |
|
VERIFY_IS_MUCH_SMALLER_THAN((R0.slerp(0.5, R0.inverse())).smallestAngle(), Scalar(1)); |
|
else |
|
VERIFY_IS_APPROX(Scalar(EIGEN_PI), (R0.slerp(0.5, R0.inverse())).smallestPositiveAngle()); |
|
|
|
// Check path length |
|
Scalar l = 0; |
|
int path_steps = 100; |
|
for(int k=0; k<path_steps; ++k) |
|
{ |
|
Scalar a1 = R0.slerp(Scalar(k)/Scalar(path_steps), R1).angle(); |
|
Scalar a2 = R0.slerp(Scalar(k+1)/Scalar(path_steps), R1).angle(); |
|
l += std::abs(a2-a1); |
|
} |
|
VERIFY(l<=Scalar(EIGEN_PI)*(Scalar(1)+NumTraits<Scalar>::epsilon()*Scalar(path_steps/2))); |
|
|
|
// check basic features |
|
{ |
|
Rotation2D<Scalar> r1; // default ctor |
|
r1 = Rotation2D<Scalar>(s0); // copy assignment |
|
VERIFY_IS_APPROX(r1.angle(),s0); |
|
Rotation2D<Scalar> r2(r1); // copy ctor |
|
VERIFY_IS_APPROX(r2.angle(),s0); |
|
} |
|
|
|
{ |
|
Transform3 t32(Matrix4::Random()), t33, t34; |
|
t34 = t33 = t32; |
|
t32.scale(v0); |
|
t33*=AlignedScaling3(v0); |
|
VERIFY_IS_APPROX(t32.matrix(), t33.matrix()); |
|
t33 = t34 * AlignedScaling3(v0); |
|
VERIFY_IS_APPROX(t32.matrix(), t33.matrix()); |
|
} |
|
|
|
} |
|
|
|
template<typename A1, typename A2, typename P, typename Q, typename V, typename H> |
|
void transform_associativity_left(const A1& a1, const A2& a2, const P& p, const Q& q, const V& v, const H& h) |
|
{ |
|
VERIFY_IS_APPROX( q*(a1*v), (q*a1)*v ); |
|
VERIFY_IS_APPROX( q*(a2*v), (q*a2)*v ); |
|
VERIFY_IS_APPROX( q*(p*h).hnormalized(), ((q*p)*h).hnormalized() ); |
|
} |
|
|
|
template<typename A1, typename A2, typename P, typename Q, typename V, typename H> |
|
void transform_associativity2(const A1& a1, const A2& a2, const P& p, const Q& q, const V& v, const H& h) |
|
{ |
|
VERIFY_IS_APPROX( a1*(q*v), (a1*q)*v ); |
|
VERIFY_IS_APPROX( a2*(q*v), (a2*q)*v ); |
|
VERIFY_IS_APPROX( p *(q*v).homogeneous(), (p *q)*v.homogeneous() ); |
|
|
|
transform_associativity_left(a1, a2,p, q, v, h); |
|
} |
|
|
|
template<typename Scalar, int Dim, int Options,typename RotationType> |
|
void transform_associativity(const RotationType& R) |
|
{ |
|
typedef Matrix<Scalar,Dim,1> VectorType; |
|
typedef Matrix<Scalar,Dim+1,1> HVectorType; |
|
typedef Matrix<Scalar,Dim,Dim> LinearType; |
|
typedef Matrix<Scalar,Dim+1,Dim+1> MatrixType; |
|
typedef Transform<Scalar,Dim,AffineCompact,Options> AffineCompactType; |
|
typedef Transform<Scalar,Dim,Affine,Options> AffineType; |
|
typedef Transform<Scalar,Dim,Projective,Options> ProjectiveType; |
|
typedef DiagonalMatrix<Scalar,Dim> ScalingType; |
|
typedef Translation<Scalar,Dim> TranslationType; |
|
|
|
AffineCompactType A1c; A1c.matrix().setRandom(); |
|
AffineCompactType A2c; A2c.matrix().setRandom(); |
|
AffineType A1(A1c); |
|
AffineType A2(A2c); |
|
ProjectiveType P1; P1.matrix().setRandom(); |
|
VectorType v1 = VectorType::Random(); |
|
VectorType v2 = VectorType::Random(); |
|
HVectorType h1 = HVectorType::Random(); |
|
Scalar s1 = internal::random<Scalar>(); |
|
LinearType L = LinearType::Random(); |
|
MatrixType M = MatrixType::Random(); |
|
|
|
CALL_SUBTEST( transform_associativity2(A1c, A1, P1, A2, v2, h1) ); |
|
CALL_SUBTEST( transform_associativity2(A1c, A1, P1, A2c, v2, h1) ); |
|
CALL_SUBTEST( transform_associativity2(A1c, A1, P1, v1.asDiagonal(), v2, h1) ); |
|
CALL_SUBTEST( transform_associativity2(A1c, A1, P1, ScalingType(v1), v2, h1) ); |
|
CALL_SUBTEST( transform_associativity2(A1c, A1, P1, Scaling(v1), v2, h1) ); |
|
CALL_SUBTEST( transform_associativity2(A1c, A1, P1, Scaling(s1), v2, h1) ); |
|
CALL_SUBTEST( transform_associativity2(A1c, A1, P1, TranslationType(v1), v2, h1) ); |
|
CALL_SUBTEST( transform_associativity_left(A1c, A1, P1, L, v2, h1) ); |
|
CALL_SUBTEST( transform_associativity2(A1c, A1, P1, R, v2, h1) ); |
|
|
|
VERIFY_IS_APPROX( A1*(M*h1), (A1*M)*h1 ); |
|
VERIFY_IS_APPROX( A1c*(M*h1), (A1c*M)*h1 ); |
|
VERIFY_IS_APPROX( P1*(M*h1), (P1*M)*h1 ); |
|
|
|
VERIFY_IS_APPROX( M*(A1*h1), (M*A1)*h1 ); |
|
VERIFY_IS_APPROX( M*(A1c*h1), (M*A1c)*h1 ); |
|
VERIFY_IS_APPROX( M*(P1*h1), ((M*P1)*h1) ); |
|
} |
|
|
|
template<typename Scalar> void transform_alignment() |
|
{ |
|
typedef Transform<Scalar,3,Projective,AutoAlign> Projective3a; |
|
typedef Transform<Scalar,3,Projective,DontAlign> Projective3u; |
|
|
|
EIGEN_ALIGN_MAX Scalar array1[16]; |
|
EIGEN_ALIGN_MAX Scalar array2[16]; |
|
EIGEN_ALIGN_MAX Scalar array3[16+1]; |
|
Scalar* array3u = array3+1; |
|
|
|
Projective3a *p1 = ::new(reinterpret_cast<void*>(array1)) Projective3a; |
|
Projective3u *p2 = ::new(reinterpret_cast<void*>(array2)) Projective3u; |
|
Projective3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Projective3u; |
|
|
|
p1->matrix().setRandom(); |
|
*p2 = *p1; |
|
*p3 = *p1; |
|
|
|
VERIFY_IS_APPROX(p1->matrix(), p2->matrix()); |
|
VERIFY_IS_APPROX(p1->matrix(), p3->matrix()); |
|
|
|
VERIFY_IS_APPROX( (*p1) * (*p1), (*p2)*(*p3)); |
|
|
|
#if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES>0 |
|
if(internal::packet_traits<Scalar>::Vectorizable) |
|
VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Projective3a)); |
|
#endif |
|
} |
|
|
|
template<typename Scalar, int Dim, int Options> void transform_products() |
|
{ |
|
typedef Matrix<Scalar,Dim+1,Dim+1> Mat; |
|
typedef Transform<Scalar,Dim,Projective,Options> Proj; |
|
typedef Transform<Scalar,Dim,Affine,Options> Aff; |
|
typedef Transform<Scalar,Dim,AffineCompact,Options> AffC; |
|
|
|
Proj p; p.matrix().setRandom(); |
|
Aff a; a.linear().setRandom(); a.translation().setRandom(); |
|
AffC ac = a; |
|
|
|
Mat p_m(p.matrix()), a_m(a.matrix()); |
|
|
|
VERIFY_IS_APPROX((p*p).matrix(), p_m*p_m); |
|
VERIFY_IS_APPROX((a*a).matrix(), a_m*a_m); |
|
VERIFY_IS_APPROX((p*a).matrix(), p_m*a_m); |
|
VERIFY_IS_APPROX((a*p).matrix(), a_m*p_m); |
|
VERIFY_IS_APPROX((ac*a).matrix(), a_m*a_m); |
|
VERIFY_IS_APPROX((a*ac).matrix(), a_m*a_m); |
|
VERIFY_IS_APPROX((p*ac).matrix(), p_m*a_m); |
|
VERIFY_IS_APPROX((ac*p).matrix(), a_m*p_m); |
|
} |
|
|
|
void test_geo_transformations() |
|
{ |
|
for(int i = 0; i < g_repeat; i++) { |
|
CALL_SUBTEST_1(( transformations<double,Affine,AutoAlign>() )); |
|
CALL_SUBTEST_1(( non_projective_only<double,Affine,AutoAlign>() )); |
|
|
|
CALL_SUBTEST_2(( transformations<float,AffineCompact,AutoAlign>() )); |
|
CALL_SUBTEST_2(( non_projective_only<float,AffineCompact,AutoAlign>() )); |
|
CALL_SUBTEST_2(( transform_alignment<float>() )); |
|
|
|
CALL_SUBTEST_3(( transformations<double,Projective,AutoAlign>() )); |
|
CALL_SUBTEST_3(( transformations<double,Projective,DontAlign>() )); |
|
CALL_SUBTEST_3(( transform_alignment<double>() )); |
|
|
|
CALL_SUBTEST_4(( transformations<float,Affine,RowMajor|AutoAlign>() )); |
|
CALL_SUBTEST_4(( non_projective_only<float,Affine,RowMajor>() )); |
|
|
|
CALL_SUBTEST_5(( transformations<double,AffineCompact,RowMajor|AutoAlign>() )); |
|
CALL_SUBTEST_5(( non_projective_only<double,AffineCompact,RowMajor>() )); |
|
|
|
CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|AutoAlign>() )); |
|
CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|DontAlign>() )); |
|
|
|
|
|
CALL_SUBTEST_7(( transform_products<double,3,RowMajor|AutoAlign>() )); |
|
CALL_SUBTEST_7(( transform_products<float,2,AutoAlign>() )); |
|
|
|
CALL_SUBTEST_8(( transform_associativity<double,2,ColMajor>(Rotation2D<double>(internal::random<double>()*double(EIGEN_PI))) )); |
|
CALL_SUBTEST_8(( transform_associativity<double,3,ColMajor>(Quaterniond::UnitRandom()) )); |
|
} |
|
}
|
|
|