| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2023 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are met: |
| // |
| // * Redistributions of source code must retain the above copyright notice, |
| // this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright notice, |
| // this list of conditions and the following disclaimer in the documentation |
| // and/or other materials provided with the distribution. |
| // * Neither the name of Google Inc. nor the names of its contributors may be |
| // used to endorse or promote products derived from this software without |
| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| |
| #include "ceres/rotation.h" |
| |
| #include <algorithm> |
| #include <array> |
| #include <cmath> |
| #include <limits> |
| #include <random> |
| #include <string> |
| #include <utility> |
| |
| #include "absl/log/log.h" |
| #include "ceres/constants.h" |
| #include "ceres/internal/eigen.h" |
| #include "ceres/internal/euler_angles.h" |
| #include "ceres/internal/export.h" |
| #include "ceres/is_close.h" |
| #include "ceres/jet.h" |
| #include "ceres/stringprintf.h" |
| #include "ceres/test_util.h" |
| #include "gmock/gmock.h" |
| #include "gtest/gtest.h" |
| |
| namespace ceres { |
| namespace internal { |
| |
| inline constexpr double kPi = constants::pi; |
| const double kHalfSqrt2 = 0.707106781186547524401; |
| |
| // A tolerance value for floating-point comparisons. |
| static double const kTolerance = std::numeric_limits<double>::epsilon() * 10; |
| |
| // Looser tolerance used for numerically unstable conversions. |
| static double const kLooseTolerance = 1e-9; |
| |
| // Use as: |
| // double quaternion[4]; |
| // EXPECT_THAT(quaternion, IsNormalizedQuaternion()); |
| MATCHER(IsNormalizedQuaternion, "") { |
| double norm2 = |
| arg[0] * arg[0] + arg[1] * arg[1] + arg[2] * arg[2] + arg[3] * arg[3]; |
| if (fabs(norm2 - 1.0) > kTolerance) { |
| *result_listener << "squared norm is " << norm2; |
| return false; |
| } |
| |
| return true; |
| } |
| |
| // Use as: |
| // double expected_quaternion[4]; |
| // double actual_quaternion[4]; |
| // EXPECT_THAT(actual_quaternion, IsNearQuaternion(expected_quaternion)); |
| MATCHER_P(IsNearQuaternion, expected, "") { |
| // Quaternions are equivalent upto a sign change. So we will compare |
| // both signs before declaring failure. |
| bool is_near = true; |
| // NOTE: near (and far) can be defined as macros on the Windows platform (for |
| // ancient pascal calling convention). Do not use these identifiers. |
| for (int i = 0; i < 4; i++) { |
| if (fabs(arg[i] - expected[i]) > kTolerance) { |
| is_near = false; |
| break; |
| } |
| } |
| |
| if (is_near) { |
| return true; |
| } |
| |
| is_near = true; |
| for (int i = 0; i < 4; i++) { |
| if (fabs(arg[i] + expected[i]) > kTolerance) { |
| is_near = false; |
| break; |
| } |
| } |
| |
| if (is_near) { |
| return true; |
| } |
| |
| // clang-format off |
| *result_listener << "expected : " |
| << expected[0] << " " |
| << expected[1] << " " |
| << expected[2] << " " |
| << expected[3] << " " |
| << "actual : " |
| << arg[0] << " " |
| << arg[1] << " " |
| << arg[2] << " " |
| << arg[3]; |
| // clang-format on |
| return false; |
| } |
| |
| // Use as: |
| // double expected_axis_angle[3]; |
| // double actual_axis_angle[3]; |
| // EXPECT_THAT(actual_axis_angle, IsNearAngleAxis(expected_axis_angle)); |
| MATCHER_P(IsNearAngleAxis, expected, "") { |
| Eigen::Vector3d a(arg[0], arg[1], arg[2]); |
| Eigen::Vector3d e(expected[0], expected[1], expected[2]); |
| const double e_norm = e.norm(); |
| |
| double delta_norm = std::numeric_limits<double>::max(); |
| if (e_norm > 0) { |
| // Deal with the sign ambiguity near PI. Since the sign can flip, |
| // we take the smaller of the two differences. |
| if (fabs(e_norm - kPi) < kLooseTolerance) { |
| delta_norm = std::min((a - e).norm(), (a + e).norm()) / e_norm; |
| } else { |
| delta_norm = (a - e).norm() / e_norm; |
| } |
| } else { |
| delta_norm = a.norm(); |
| } |
| |
| if (delta_norm <= kLooseTolerance) { |
| return true; |
| } |
| |
| // clang-format off |
| *result_listener << " arg:" |
| << " " << arg[0] |
| << " " << arg[1] |
| << " " << arg[2] |
| << " was expected to be:" |
| << " " << expected[0] |
| << " " << expected[1] |
| << " " << expected[2]; |
| // clang-format on |
| return false; |
| } |
| |
| // Use as: |
| // double matrix[9]; |
| // EXPECT_THAT(matrix, IsOrthonormal()); |
| MATCHER(IsOrthonormal, "") { |
| for (int c1 = 0; c1 < 3; c1++) { |
| for (int c2 = 0; c2 < 3; c2++) { |
| double v = 0; |
| for (int i = 0; i < 3; i++) { |
| v += arg[i + 3 * c1] * arg[i + 3 * c2]; |
| } |
| double expected = (c1 == c2) ? 1 : 0; |
| if (fabs(expected - v) > kTolerance) { |
| *result_listener << "Columns " << c1 << " and " << c2 |
| << " should have dot product " << expected |
| << " but have " << v; |
| return false; |
| } |
| } |
| } |
| |
| return true; |
| } |
| |
| // Use as: |
| // double matrix1[9]; |
| // double matrix2[9]; |
| // EXPECT_THAT(matrix1, IsNear3x3Matrix(matrix2)); |
| MATCHER_P(IsNear3x3Matrix, expected, "") { |
| for (int i = 0; i < 9; i++) { |
| if (fabs(arg[i] - expected[i]) > kTolerance) { |
| *result_listener << "component " << i << " should be " << expected[i]; |
| return false; |
| } |
| } |
| |
| return true; |
| } |
| |
| // Transforms a zero axis/angle to a quaternion. |
| TEST(Rotation, ZeroAngleAxisToQuaternion) { |
| double axis_angle[3] = {0, 0, 0}; |
| double quaternion[4]; |
| double expected[4] = {1, 0, 0, 0}; |
| AngleAxisToQuaternion(axis_angle, quaternion); |
| EXPECT_THAT(quaternion, IsNormalizedQuaternion()); |
| EXPECT_THAT(quaternion, IsNearQuaternion(expected)); |
| } |
| |
| // Test that exact conversion works for small angles. |
| TEST(Rotation, SmallAngleAxisToQuaternion) { |
| // Small, finite value to test. |
| double theta = 1.0e-2; |
| double axis_angle[3] = {theta, 0, 0}; |
| double quaternion[4]; |
| double expected[4] = {cos(theta / 2), sin(theta / 2.0), 0, 0}; |
| AngleAxisToQuaternion(axis_angle, quaternion); |
| EXPECT_THAT(quaternion, IsNormalizedQuaternion()); |
| EXPECT_THAT(quaternion, IsNearQuaternion(expected)); |
| } |
| |
| // Test that approximate conversion works for very small angles. |
| TEST(Rotation, TinyAngleAxisToQuaternion) { |
| // Very small value that could potentially cause underflow. |
| double theta = pow(std::numeric_limits<double>::min(), 0.75); |
| double axis_angle[3] = {theta, 0, 0}; |
| double quaternion[4]; |
| double expected[4] = {cos(theta / 2), sin(theta / 2.0), 0, 0}; |
| AngleAxisToQuaternion(axis_angle, quaternion); |
| EXPECT_THAT(quaternion, IsNormalizedQuaternion()); |
| EXPECT_THAT(quaternion, IsNearQuaternion(expected)); |
| } |
| |
| // Transforms a rotation by pi/2 around X to a quaternion. |
| TEST(Rotation, XRotationToQuaternion) { |
| double axis_angle[3] = {kPi / 2, 0, 0}; |
| double quaternion[4]; |
| double expected[4] = {kHalfSqrt2, kHalfSqrt2, 0, 0}; |
| AngleAxisToQuaternion(axis_angle, quaternion); |
| EXPECT_THAT(quaternion, IsNormalizedQuaternion()); |
| EXPECT_THAT(quaternion, IsNearQuaternion(expected)); |
| } |
| |
| // Transforms a unit quaternion to an axis angle. |
| TEST(Rotation, UnitQuaternionToAngleAxis) { |
| double quaternion[4] = {1, 0, 0, 0}; |
| double axis_angle[3]; |
| double expected[3] = {0, 0, 0}; |
| QuaternionToAngleAxis(quaternion, axis_angle); |
| EXPECT_THAT(axis_angle, IsNearAngleAxis(expected)); |
| } |
| |
| // Transforms a quaternion that rotates by pi about the Y axis to an axis angle. |
| TEST(Rotation, YRotationQuaternionToAngleAxis) { |
| double quaternion[4] = {0, 0, 1, 0}; |
| double axis_angle[3]; |
| double expected[3] = {0, kPi, 0}; |
| QuaternionToAngleAxis(quaternion, axis_angle); |
| EXPECT_THAT(axis_angle, IsNearAngleAxis(expected)); |
| } |
| |
| // Transforms a quaternion that rotates by pi/3 about the Z axis to an axis |
| // angle. |
| TEST(Rotation, ZRotationQuaternionToAngleAxis) { |
| double quaternion[4] = {sqrt(3) / 2, 0, 0, 0.5}; |
| double axis_angle[3]; |
| double expected[3] = {0, 0, kPi / 3}; |
| QuaternionToAngleAxis(quaternion, axis_angle); |
| EXPECT_THAT(axis_angle, IsNearAngleAxis(expected)); |
| } |
| |
| // Test that exact conversion works for small angles. |
| TEST(Rotation, SmallQuaternionToAngleAxis) { |
| // Small, finite value to test. |
| double theta = 1.0e-2; |
| double quaternion[4] = {cos(theta / 2), sin(theta / 2.0), 0, 0}; |
| double axis_angle[3]; |
| double expected[3] = {theta, 0, 0}; |
| QuaternionToAngleAxis(quaternion, axis_angle); |
| EXPECT_THAT(axis_angle, IsNearAngleAxis(expected)); |
| } |
| |
| // Test that approximate conversion works for very small angles. |
| TEST(Rotation, TinyQuaternionToAngleAxis) { |
| // Very small value that could potentially cause underflow. |
| double theta = pow(std::numeric_limits<double>::min(), 0.75); |
| double quaternion[4] = {cos(theta / 2), sin(theta / 2.0), 0, 0}; |
| double axis_angle[3]; |
| double expected[3] = {theta, 0, 0}; |
| QuaternionToAngleAxis(quaternion, axis_angle); |
| EXPECT_THAT(axis_angle, IsNearAngleAxis(expected)); |
| } |
| |
| TEST(Rotation, QuaternionToAngleAxisAngleIsLessThanPi) { |
| double quaternion[4]; |
| double angle_axis[3]; |
| |
| const double half_theta = 0.75 * kPi; |
| |
| quaternion[0] = cos(half_theta); |
| quaternion[1] = 1.0 * sin(half_theta); |
| quaternion[2] = 0.0; |
| quaternion[3] = 0.0; |
| QuaternionToAngleAxis(quaternion, angle_axis); |
| const double angle = std::hypot(angle_axis[0], angle_axis[1], angle_axis[2]); |
| EXPECT_LE(angle, kPi); |
| } |
| |
| static constexpr int kNumTrials = 10000; |
| |
| // Takes a bunch of random axis/angle values, converts them to quaternions, |
| // and back again. |
| TEST(Rotation, AngleAxisToQuaterionAndBack) { |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0}; |
| for (int i = 0; i < kNumTrials; i++) { |
| double axis_angle[3]; |
| // Make an axis by choosing three random numbers in [-1, 1) and |
| // normalizing. |
| double norm = 0; |
| for (double& coeff : axis_angle) { |
| coeff = uniform_distribution(prng); |
| norm += coeff * coeff; |
| } |
| norm = sqrt(norm); |
| |
| // Angle in [-pi, pi). |
| double theta = uniform_distribution( |
| prng, std::uniform_real_distribution<double>::param_type{-kPi, kPi}); |
| for (double& coeff : axis_angle) { |
| coeff = coeff * theta / norm; |
| } |
| |
| double quaternion[4]; |
| double round_trip[3]; |
| // We use ASSERTs here because if there's one failure, there are |
| // probably many and spewing a million failures doesn't make anyone's |
| // day. |
| AngleAxisToQuaternion(axis_angle, quaternion); |
| ASSERT_THAT(quaternion, IsNormalizedQuaternion()); |
| QuaternionToAngleAxis(quaternion, round_trip); |
| ASSERT_THAT(round_trip, IsNearAngleAxis(axis_angle)); |
| } |
| } |
| |
| // Takes a bunch of random quaternions, converts them to axis/angle, |
| // and back again. |
| TEST(Rotation, QuaterionToAngleAxisAndBack) { |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0}; |
| for (int i = 0; i < kNumTrials; i++) { |
| double quaternion[4]; |
| // Choose four random numbers in [-1, 1) and normalize. |
| double norm = 0; |
| for (double& coeff : quaternion) { |
| coeff = uniform_distribution(prng); |
| norm += coeff * coeff; |
| } |
| norm = sqrt(norm); |
| |
| for (double& coeff : quaternion) { |
| coeff = coeff / norm; |
| } |
| |
| double axis_angle[3]; |
| double round_trip[4]; |
| QuaternionToAngleAxis(quaternion, axis_angle); |
| AngleAxisToQuaternion(axis_angle, round_trip); |
| ASSERT_THAT(round_trip, IsNormalizedQuaternion()); |
| ASSERT_THAT(round_trip, IsNearQuaternion(quaternion)); |
| } |
| } |
| |
| // Transforms a zero axis/angle to a rotation matrix. |
| TEST(Rotation, ZeroAngleAxisToRotationMatrix) { |
| double axis_angle[3] = {0, 0, 0}; |
| double matrix[9]; |
| double expected[9] = {1, 0, 0, 0, 1, 0, 0, 0, 1}; |
| AngleAxisToRotationMatrix(axis_angle, matrix); |
| EXPECT_THAT(matrix, IsOrthonormal()); |
| EXPECT_THAT(matrix, IsNear3x3Matrix(expected)); |
| } |
| |
| TEST(Rotation, NearZeroAngleAxisToRotationMatrix) { |
| double axis_angle[3] = {1e-24, 2e-24, 3e-24}; |
| double matrix[9]; |
| double expected[9] = {1, 0, 0, 0, 1, 0, 0, 0, 1}; |
| AngleAxisToRotationMatrix(axis_angle, matrix); |
| EXPECT_THAT(matrix, IsOrthonormal()); |
| EXPECT_THAT(matrix, IsNear3x3Matrix(expected)); |
| } |
| |
| // Transforms a rotation by pi/2 around X to a rotation matrix and back. |
| TEST(Rotation, XRotationToRotationMatrix) { |
| double axis_angle[3] = {kPi / 2, 0, 0}; |
| double matrix[9]; |
| // The rotation matrices are stored column-major. |
| double expected[9] = {1, 0, 0, 0, 0, 1, 0, -1, 0}; |
| AngleAxisToRotationMatrix(axis_angle, matrix); |
| EXPECT_THAT(matrix, IsOrthonormal()); |
| EXPECT_THAT(matrix, IsNear3x3Matrix(expected)); |
| double round_trip[3]; |
| RotationMatrixToAngleAxis(matrix, round_trip); |
| EXPECT_THAT(round_trip, IsNearAngleAxis(axis_angle)); |
| } |
| |
| // Transforms an axis angle that rotates by pi about the Y axis to a |
| // rotation matrix and back. |
| TEST(Rotation, YRotationToRotationMatrix) { |
| double axis_angle[3] = {0, kPi, 0}; |
| double matrix[9]; |
| double expected[9] = {-1, 0, 0, 0, 1, 0, 0, 0, -1}; |
| AngleAxisToRotationMatrix(axis_angle, matrix); |
| EXPECT_THAT(matrix, IsOrthonormal()); |
| EXPECT_THAT(matrix, IsNear3x3Matrix(expected)); |
| |
| double round_trip[3]; |
| RotationMatrixToAngleAxis(matrix, round_trip); |
| EXPECT_THAT(round_trip, IsNearAngleAxis(axis_angle)); |
| } |
| |
| TEST(Rotation, NearPiAngleAxisRoundTrip) { |
| double in_axis_angle[3]; |
| double matrix[9]; |
| double out_axis_angle[3]; |
| |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0}; |
| for (int i = 0; i < kNumTrials; i++) { |
| // Make an axis by choosing three random numbers in [-1, 1) and |
| // normalizing. |
| double norm = 0; |
| for (double& coeff : in_axis_angle) { |
| coeff = uniform_distribution(prng); |
| norm += coeff * coeff; |
| } |
| norm = sqrt(norm); |
| |
| // Angle in [pi - kMaxSmallAngle, pi). |
| constexpr double kMaxSmallAngle = 1e-8; |
| double theta = |
| uniform_distribution(prng, |
| std::uniform_real_distribution<double>::param_type{ |
| kPi - kMaxSmallAngle, kPi}); |
| |
| for (double& coeff : in_axis_angle) { |
| coeff *= (theta / norm); |
| } |
| AngleAxisToRotationMatrix(in_axis_angle, matrix); |
| RotationMatrixToAngleAxis(matrix, out_axis_angle); |
| EXPECT_THAT(in_axis_angle, IsNearAngleAxis(out_axis_angle)); |
| } |
| } |
| |
| TEST(Rotation, AtPiAngleAxisRoundTrip) { |
| // A rotation of kPi about the X axis; |
| // clang-format off |
| static constexpr double kMatrix[3][3] = { |
| {1.0, 0.0, 0.0}, |
| {0.0, -1.0, 0.0}, |
| {0.0, 0.0, -1.0} |
| }; |
| // clang-format on |
| |
| double in_matrix[9]; |
| // Fill it from kMatrix in col-major order. |
| for (int j = 0, k = 0; j < 3; ++j) { |
| for (int i = 0; i < 3; ++i, ++k) { |
| in_matrix[k] = kMatrix[i][j]; |
| } |
| } |
| |
| const double expected_axis_angle[3] = {kPi, 0, 0}; |
| |
| double out_matrix[9]; |
| double axis_angle[3]; |
| RotationMatrixToAngleAxis(in_matrix, axis_angle); |
| AngleAxisToRotationMatrix(axis_angle, out_matrix); |
| |
| LOG(INFO) << "AngleAxis = " << axis_angle[0] << " " << axis_angle[1] << " " |
| << axis_angle[2]; |
| LOG(INFO) << "Expected AngleAxis = " << kPi << " 0 0"; |
| double out_rowmajor[3][3]; |
| for (int j = 0, k = 0; j < 3; ++j) { |
| for (int i = 0; i < 3; ++i, ++k) { |
| out_rowmajor[i][j] = out_matrix[k]; |
| } |
| } |
| LOG(INFO) << "Rotation:"; |
| LOG(INFO) << "EXPECTED | ACTUAL"; |
| for (int i = 0; i < 3; ++i) { |
| std::string line; |
| for (int j = 0; j < 3; ++j) { |
| StringAppendF(&line, "%g ", kMatrix[i][j]); |
| } |
| line += " | "; |
| for (int j = 0; j < 3; ++j) { |
| StringAppendF(&line, "%g ", out_rowmajor[i][j]); |
| } |
| LOG(INFO) << line; |
| } |
| |
| EXPECT_THAT(axis_angle, IsNearAngleAxis(expected_axis_angle)); |
| EXPECT_THAT(out_matrix, IsNear3x3Matrix(in_matrix)); |
| } |
| |
| // Transforms an axis angle that rotates by pi/3 about the Z axis to a |
| // rotation matrix. |
| TEST(Rotation, ZRotationToRotationMatrix) { |
| double axis_angle[3] = {0, 0, kPi / 3}; |
| double matrix[9]; |
| // This is laid-out row-major on the screen but is actually stored |
| // column-major. |
| // clang-format off |
| double expected[9] = { 0.5, sqrt(3) / 2, 0, // Column 1 |
| -sqrt(3) / 2, 0.5, 0, // Column 2 |
| 0, 0, 1 }; // Column 3 |
| // clang-format on |
| AngleAxisToRotationMatrix(axis_angle, matrix); |
| EXPECT_THAT(matrix, IsOrthonormal()); |
| EXPECT_THAT(matrix, IsNear3x3Matrix(expected)); |
| double round_trip[3]; |
| RotationMatrixToAngleAxis(matrix, round_trip); |
| EXPECT_THAT(round_trip, IsNearAngleAxis(axis_angle)); |
| } |
| |
| // Takes a bunch of random axis/angle values, converts them to rotation |
| // matrices, and back again. |
| TEST(Rotation, AngleAxisToRotationMatrixAndBack) { |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0}; |
| for (int i = 0; i < kNumTrials; i++) { |
| double axis_angle[3]; |
| // Make an axis by choosing three random numbers in [-1, 1) and |
| // normalizing. |
| double norm = 0; |
| for (double& i : axis_angle) { |
| i = uniform_distribution(prng); |
| norm += i * i; |
| } |
| norm = sqrt(norm); |
| |
| // Angle in [-pi, pi). |
| double theta = uniform_distribution( |
| prng, std::uniform_real_distribution<double>::param_type{-kPi, kPi}); |
| for (double& i : axis_angle) { |
| i = i * theta / norm; |
| } |
| |
| double matrix[9]; |
| double round_trip[3]; |
| AngleAxisToRotationMatrix(axis_angle, matrix); |
| ASSERT_THAT(matrix, IsOrthonormal()); |
| RotationMatrixToAngleAxis(matrix, round_trip); |
| |
| for (int i = 0; i < 3; ++i) { |
| EXPECT_NEAR(round_trip[i], axis_angle[i], kLooseTolerance); |
| } |
| } |
| } |
| |
| // Takes a bunch of random axis/angle values near zero, converts them |
| // to rotation matrices, and back again. |
| TEST(Rotation, AngleAxisToRotationMatrixAndBackNearZero) { |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0}; |
| for (int i = 0; i < kNumTrials; i++) { |
| double axis_angle[3]; |
| // Make an axis by choosing three random numbers in [-1, 1) and |
| // normalizing. |
| double norm = 0; |
| for (double& i : axis_angle) { |
| i = uniform_distribution(prng); |
| norm += i * i; |
| } |
| norm = sqrt(norm); |
| |
| // Tiny theta. |
| constexpr double kScale = 1e-16; |
| double theta = |
| uniform_distribution(prng, |
| std::uniform_real_distribution<double>::param_type{ |
| -kScale * kPi, kScale * kPi}); |
| for (double& i : axis_angle) { |
| i = i * theta / norm; |
| } |
| |
| double matrix[9]; |
| double round_trip[3]; |
| AngleAxisToRotationMatrix(axis_angle, matrix); |
| ASSERT_THAT(matrix, IsOrthonormal()); |
| RotationMatrixToAngleAxis(matrix, round_trip); |
| |
| for (int i = 0; i < 3; ++i) { |
| EXPECT_NEAR( |
| round_trip[i], axis_angle[i], std::numeric_limits<double>::epsilon()); |
| } |
| } |
| } |
| |
| // Transposes a 3x3 matrix. |
| static void Transpose3x3(double m[9]) { |
| std::swap(m[1], m[3]); |
| std::swap(m[2], m[6]); |
| std::swap(m[5], m[7]); |
| } |
| |
| // Convert Euler angles from radians to degrees. |
| static void ToDegrees(double euler_angles[3]) { |
| for (int i = 0; i < 3; ++i) { |
| euler_angles[i] *= 180.0 / kPi; |
| } |
| } |
| |
| // Compare the 3x3 rotation matrices produced by the axis-angle |
| // rotation 'aa' and the Euler angle rotation 'ea' (in radians). |
| static void CompareEulerToAngleAxis(double aa[3], double ea[3]) { |
| double aa_matrix[9]; |
| AngleAxisToRotationMatrix(aa, aa_matrix); |
| Transpose3x3(aa_matrix); // Column to row major order. |
| |
| double ea_matrix[9]; |
| ToDegrees(ea); // Radians to degrees. |
| const int kRowStride = 3; |
| EulerAnglesToRotationMatrix(ea, kRowStride, ea_matrix); |
| |
| EXPECT_THAT(aa_matrix, IsOrthonormal()); |
| EXPECT_THAT(ea_matrix, IsOrthonormal()); |
| EXPECT_THAT(ea_matrix, IsNear3x3Matrix(aa_matrix)); |
| } |
| |
| // Test with rotation axis along the x/y/z axes. |
| // Also test zero rotation. |
| TEST(EulerAnglesToRotationMatrix, OnAxis) { |
| int n_tests = 0; |
| for (double x = -1.0; x <= 1.0; x += 1.0) { |
| for (double y = -1.0; y <= 1.0; y += 1.0) { |
| for (double z = -1.0; z <= 1.0; z += 1.0) { |
| if ((x != 0) + (y != 0) + (z != 0) > 1) continue; |
| double axis_angle[3] = {x, y, z}; |
| double euler_angles[3] = {x, y, z}; |
| CompareEulerToAngleAxis(axis_angle, euler_angles); |
| ++n_tests; |
| } |
| } |
| } |
| ASSERT_EQ(7, n_tests); |
| } |
| |
| // Test that a random rotation produces an orthonormal rotation |
| // matrix. |
| TEST(EulerAnglesToRotationMatrix, IsOrthonormal) { |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution{-180.0, 180.0}; |
| for (int trial = 0; trial < kNumTrials; ++trial) { |
| double euler_angles_degrees[3]; |
| for (double& euler_angles_degree : euler_angles_degrees) { |
| euler_angles_degree = uniform_distribution(prng); |
| } |
| double rotation_matrix[9]; |
| EulerAnglesToRotationMatrix(euler_angles_degrees, 3, rotation_matrix); |
| EXPECT_THAT(rotation_matrix, IsOrthonormal()); |
| } |
| } |
| |
| static double sample_euler[][3] = {{0.5235988, 1.047198, 0.7853982}, |
| {0.5235988, 1.047198, 0.5235988}, |
| {0.7853982, 0.5235988, 1.047198}}; |
| |
| // ZXY Intrinsic Euler Angle to rotation matrix conversion test from |
| // scipy/spatial/transform/test/test_rotation.py |
| TEST(EulerAngles, IntrinsicEulerSequence312ToRotationMatrixCanned) { |
| // clang-format off |
| double const expected[][9] = |
| {{0.306186083320088, -0.249999816228639, 0.918558748402491, |
| 0.883883627842492, 0.433012359189203, -0.176776777947208, |
| -0.353553128699351, 0.866025628186053, 0.353553102817459}, |
| { 0.533493553519713, -0.249999816228639, 0.808012821828067, |
| 0.808012821828067, 0.433012359189203, -0.399519181705765, |
| -0.249999816228639, 0.866025628186053, 0.433012359189203}, |
| { 0.047366781483451, -0.612372449482883, 0.789149143778432, |
| 0.659739427618959, 0.612372404654096, 0.435596057905909, |
| -0.750000183771249, 0.500000021132493, 0.433012359189203}}; |
| // clang-format on |
| |
| for (int i = 0; i < 3; ++i) { |
| double results[9]; |
| EulerAnglesToRotation<IntrinsicZXY>(sample_euler[i], results); |
| ASSERT_THAT(results, IsNear3x3Matrix(expected[i])); |
| } |
| } |
| |
| // ZXY Extrinsic Euler Angle to rotation matrix conversion test from |
| // scipy/spatial/transform/test/test_rotation.py |
| TEST(EulerAngles, ExtrinsicEulerSequence312ToRotationMatrix) { |
| // clang-format off |
| double const expected[][9] = |
| {{0.918558725988105, 0.176776842651999, 0.353553128699352, |
| 0.249999816228639, 0.433012359189203, -0.866025628186053, |
| -0.306186150563275, 0.883883614901527, 0.353553102817459}, |
| { 0.966506404215301, -0.058012606358071, 0.249999816228639, |
| 0.249999816228639, 0.433012359189203, -0.866025628186053, |
| -0.058012606358071, 0.899519223970752, 0.433012359189203}, |
| { 0.659739424151467, -0.047366829779744, 0.750000183771249, |
| 0.612372449482883, 0.612372404654096, -0.500000021132493, |
| -0.435596000136163, 0.789149175666285, 0.433012359189203}}; |
| // clang-format on |
| |
| for (int i = 0; i < 3; ++i) { |
| double results[9]; |
| EulerAnglesToRotation<ExtrinsicZXY>(sample_euler[i], results); |
| ASSERT_THAT(results, IsNear3x3Matrix(expected[i])); |
| } |
| } |
| |
| // ZXZ Intrinsic Euler Angle to rotation matrix conversion test from |
| // scipy/spatial/transform/test/test_rotation.py |
| TEST(EulerAngles, IntrinsicEulerSequence313ToRotationMatrix) { |
| // clang-format off |
| double expected[][9] = |
| {{0.435595832832961, -0.789149008363071, 0.433012832394307, |
| 0.659739379322704, -0.047367454164077, -0.750000183771249, |
| 0.612372616786097, 0.612372571957297, 0.499999611324802}, |
| { 0.625000065470068, -0.649518902838302, 0.433012832394307, |
| 0.649518902838302, 0.124999676794869, -0.750000183771249, |
| 0.433012832394307, 0.750000183771249, 0.499999611324802}, |
| {-0.176777132429787, -0.918558558684756, 0.353553418477159, |
| 0.883883325123719, -0.306186652473014, -0.353553392595246, |
| 0.433012832394307, 0.249999816228639, 0.866025391583588}}; |
| // clang-format on |
| for (int i = 0; i < 3; ++i) { |
| double results[9]; |
| EulerAnglesToRotation<IntrinsicZXZ>(sample_euler[i], results); |
| ASSERT_THAT(results, IsNear3x3Matrix(expected[i])); |
| } |
| } |
| |
| // ZXZ Extrinsic Euler Angle to rotation matrix conversion test from |
| // scipy/spatial/transform/test/test_rotation.py |
| TEST(EulerAngles, ExtrinsicEulerSequence313ToRotationMatrix) { |
| // clang-format off |
| double expected[][9] = |
| {{0.435595832832961, -0.659739379322704, 0.612372616786097, |
| 0.789149008363071, -0.047367454164077, -0.612372571957297, |
| 0.433012832394307, 0.750000183771249, 0.499999611324802}, |
| { 0.625000065470068, -0.649518902838302, 0.433012832394307, |
| 0.649518902838302, 0.124999676794869, -0.750000183771249, |
| 0.433012832394307, 0.750000183771249, 0.499999611324802}, |
| {-0.176777132429787, -0.883883325123719, 0.433012832394307, |
| 0.918558558684756, -0.306186652473014, -0.249999816228639, |
| 0.353553418477159, 0.353553392595246, 0.866025391583588}}; |
| // clang-format on |
| for (int i = 0; i < 3; ++i) { |
| double results[9]; |
| EulerAnglesToRotation<ExtrinsicZXZ>(sample_euler[i], results); |
| ASSERT_THAT(results, IsNear3x3Matrix(expected[i])); |
| } |
| } |
| |
| template <typename T> |
| struct GeneralEulerAngles : public ::testing::Test { |
| public: |
| static constexpr bool kIsParityOdd = T::kIsParityOdd; |
| static constexpr bool kIsProperEuler = T::kIsProperEuler; |
| static constexpr bool kIsIntrinsic = T::kIsIntrinsic; |
| |
| template <typename URBG> |
| static void RandomEulerAngles(double* euler, URBG& prng) { |
| using ParamType = std::uniform_real_distribution<double>::param_type; |
| std::uniform_real_distribution<double> uniform_distribution{-kPi, kPi}; |
| // Euler angles should be in |
| // [-pi,pi) x [0,pi) x [-pi,pi]) |
| // if the outer axes are repeated and |
| // [-pi,pi) x [-pi/2,pi/2) x [-pi,pi]) |
| // otherwise |
| euler[0] = uniform_distribution(prng); |
| euler[2] = uniform_distribution(prng); |
| if constexpr (kIsProperEuler) { |
| euler[1] = uniform_distribution(prng, ParamType{0, kPi}); |
| } else { |
| euler[1] = uniform_distribution(prng, ParamType{-kPi / 2, kPi / 2}); |
| } |
| } |
| |
| static void CheckPrincipalRotationMatrixProduct(double angles[3]) { |
| // Convert Shoemake's Euler angle convention into 'apparent' rotation axes |
| // sequences, i.e. the alphabetic code (ZYX, ZYZ, etc.) indicates in what |
| // sequence rotations about different axes are applied |
| constexpr int i = T::kAxes[0]; |
| constexpr int j = (3 + (kIsParityOdd ? (i - 1) % 3 : (i + 1) % 3)) % 3; |
| constexpr int k = kIsProperEuler ? i : 3 ^ i ^ j; |
| constexpr auto kSeq = |
| kIsIntrinsic ? std::array{k, j, i} : std::array{i, j, k}; |
| |
| double aa_matrix[9]; |
| Eigen::Map<Eigen::Matrix3d, 0, Eigen::Stride<1, 3>> aa(aa_matrix); |
| aa.setIdentity(); |
| for (int i = 0; i < 3; ++i) { |
| Eigen::Vector3d angle_axis; |
| if constexpr (kIsIntrinsic) { |
| angle_axis = -angles[i] * Eigen::Vector3d::Unit(kSeq[i]); |
| } else { |
| angle_axis = angles[i] * Eigen::Vector3d::Unit(kSeq[i]); |
| } |
| Eigen::Matrix3d m; |
| AngleAxisToRotationMatrix(angle_axis.data(), m.data()); |
| aa = m * aa; |
| } |
| if constexpr (kIsIntrinsic) { |
| aa.transposeInPlace(); |
| } |
| |
| double ea_matrix[9]; |
| EulerAnglesToRotation<T>(angles, ea_matrix); |
| |
| EXPECT_THAT(aa_matrix, IsOrthonormal()); |
| EXPECT_THAT(ea_matrix, IsOrthonormal()); |
| EXPECT_THAT(ea_matrix, IsNear3x3Matrix(aa_matrix)); |
| } |
| }; |
| |
| using EulerSystemList = ::testing::Types<ExtrinsicXYZ, |
| ExtrinsicXYX, |
| ExtrinsicXZY, |
| ExtrinsicXZX, |
| ExtrinsicYZX, |
| ExtrinsicYZY, |
| ExtrinsicYXZ, |
| ExtrinsicYXY, |
| ExtrinsicZXY, |
| ExtrinsicZXZ, |
| ExtrinsicZYX, |
| ExtrinsicZYZ, |
| IntrinsicZYX, |
| IntrinsicXYX, |
| IntrinsicYZX, |
| IntrinsicXZX, |
| IntrinsicXZY, |
| IntrinsicYZY, |
| IntrinsicZXY, |
| IntrinsicYXY, |
| IntrinsicYXZ, |
| IntrinsicZXZ, |
| IntrinsicXYZ, |
| IntrinsicZYZ>; |
| TYPED_TEST_SUITE(GeneralEulerAngles, EulerSystemList); |
| |
| TYPED_TEST(GeneralEulerAngles, EulerAnglesToRotationMatrixAndBack) { |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0}; |
| for (int i = 0; i < kNumTrials; ++i) { |
| double euler[3]; |
| TestFixture::RandomEulerAngles(euler, prng); |
| |
| double matrix[9]; |
| double round_trip[3]; |
| EulerAnglesToRotation<TypeParam>(euler, matrix); |
| ASSERT_THAT(matrix, IsOrthonormal()); |
| RotationMatrixToEulerAngles<TypeParam>(matrix, round_trip); |
| for (int j = 0; j < 3; ++j) |
| ASSERT_NEAR(euler[j], round_trip[j], 128.0 * kLooseTolerance); |
| } |
| } |
| |
| // Check that the rotation matrix converted from euler angles is equivalent to |
| // product of three principal axis rotation matrices |
| // R_euler = R_a2(euler_2) * R_a1(euler_1) * R_a0(euler_0) |
| TYPED_TEST(GeneralEulerAngles, PrincipalRotationMatrixProduct) { |
| std::mt19937 prng; |
| double euler[3]; |
| for (int i = 0; i < kNumTrials; ++i) { |
| TestFixture::RandomEulerAngles(euler, prng); |
| TestFixture::CheckPrincipalRotationMatrixProduct(euler); |
| } |
| } |
| |
| // Gimbal lock (euler[1] == +/-pi) handling test. If a rotation matrix |
| // represents a gimbal-locked configuration, then converting this rotation |
| // matrix to euler angles and back must produce the same rotation matrix. |
| // |
| // From scipy/spatial/transform/test/test_rotation.py, but additionally covers |
| // gimbal lock handling for proper euler angles, which scipy appears to fail to |
| // do properly. |
| TYPED_TEST(GeneralEulerAngles, GimbalLocked) { |
| constexpr auto kBoundaryAngles = TestFixture::kIsProperEuler |
| ? std::array{0.0, kPi} |
| : std::array{-kPi / 2, kPi / 2}; |
| constexpr double gimbal_locked_configurations[4][3] = { |
| {0.78539816, kBoundaryAngles[1], 0.61086524}, |
| {0.61086524, kBoundaryAngles[0], 0.34906585}, |
| {0.61086524, kBoundaryAngles[1], 0.43633231}, |
| {0.43633231, kBoundaryAngles[0], 0.26179939}}; |
| double angle_estimates[3]; |
| double mat_expected[9]; |
| double mat_estimated[9]; |
| for (const auto& euler_angles : gimbal_locked_configurations) { |
| EulerAnglesToRotation<TypeParam>(euler_angles, mat_expected); |
| RotationMatrixToEulerAngles<TypeParam>(mat_expected, angle_estimates); |
| EulerAnglesToRotation<TypeParam>(angle_estimates, mat_estimated); |
| ASSERT_THAT(mat_expected, IsNear3x3Matrix(mat_estimated)); |
| } |
| } |
| |
| // Tests using Jets for specific behavior involving auto differentiation |
| // near singularity points. |
| |
| using J3 = Jet<double, 3>; |
| using J4 = Jet<double, 4>; |
| |
| namespace { |
| |
| // Converts an array of N real numbers (doubles) to an array of jets |
| template <int N> |
| void ArrayToArrayOfJets(double const* const src, Jet<double, N>* dst) { |
| for (int i = 0; i < N; ++i) { |
| dst[i] = Jet<double, N>(src[i], i); |
| } |
| } |
| |
| // Generically initializes a Jet with type T and a N-dimensional dual part |
| // N is explicitly given (instead of inferred from sizeof...(Ts)) so that the |
| // dual part can be initialized from Eigen expressions |
| template <int N, typename T, typename... Ts> |
| Jet<T, N> MakeJet(T a, const T& v0, Ts&&... v) { |
| Jet<T, N> j; |
| j.a = a; // Real part |
| ((j.v << v0), ..., std::forward<Ts>(v)); // Fill dual part with N components |
| return j; |
| } |
| |
| J3 MakeJ3(double a, double v0, double v1, double v2) { |
| J3 j; |
| j.a = a; |
| j.v[0] = v0; |
| j.v[1] = v1; |
| j.v[2] = v2; |
| return j; |
| } |
| |
| J4 MakeJ4(double a, double v0, double v1, double v2, double v3) { |
| J4 j; |
| j.a = a; |
| j.v[0] = v0; |
| j.v[1] = v1; |
| j.v[2] = v2; |
| j.v[3] = v3; |
| return j; |
| } |
| |
| } // namespace |
| |
| // Use EXPECT_THAT(x, testing::PointWise(JetClose(prec), y); to achieve Jet |
| // array comparison |
| MATCHER_P(JetClose, relative_precision, "") { |
| using internal::IsClose; |
| using LHSJetType = std::remove_reference_t<std::tuple_element_t<0, arg_type>>; |
| using RHSJetType = std::remove_reference_t<std::tuple_element_t<1, arg_type>>; |
| |
| constexpr int kDualPartDimension = LHSJetType::DIMENSION; |
| static_assert( |
| kDualPartDimension == RHSJetType::DIMENSION, |
| "Can only compare Jets with dual parts having equal dimensions"); |
| auto&& [x, y] = arg; |
| double relative_error; |
| double absolute_error; |
| if (!IsClose( |
| x.a, y.a, relative_precision, &relative_error, &absolute_error)) { |
| *result_listener << "Real part mismatch: x.a = " << x.a |
| << " and y.a = " << y.a |
| << " where the relative error between them is " |
| << relative_error |
| << " and the absolute error between them is " |
| << absolute_error; |
| return false; |
| } |
| for (int i = 0; i < kDualPartDimension; i++) { |
| if (!IsClose(x.v[i], |
| y.v[i], |
| relative_precision, |
| &relative_error, |
| &absolute_error)) { |
| *result_listener << "Dual part mismatch: x.v[" << i << "] = " << x.v[i] |
| << " and y.v[" << i << "] = " << y.v[i] |
| << " where the relative error between them is " |
| << relative_error |
| << " and the absolute error between them is " |
| << absolute_error; |
| return false; |
| } |
| } |
| return true; |
| } |
| |
| // Log-10 of a value well below machine precision. |
| static const int kSmallTinyCutoff = static_cast<int>( |
| 2 * log(std::numeric_limits<double>::epsilon()) / log(10.0)); |
| |
| // Log-10 of a value just below values representable by double. |
| static const int kTinyZeroLimit = |
| static_cast<int>(1 + log(std::numeric_limits<double>::min()) / log(10.0)); |
| |
| // Test that exact conversion works for small angles when jets are used. |
| TEST(Rotation, SmallAngleAxisToQuaternionForJets) { |
| // Examine small x rotations that are still large enough |
| // to be well within the range represented by doubles. |
| for (int i = -2; i >= kSmallTinyCutoff; i--) { |
| double theta = pow(10.0, i); |
| J3 axis_angle[3] = {J3(theta, 0), J3(0, 1), J3(0, 2)}; |
| J3 quaternion[4]; |
| J3 expected[4] = { |
| MakeJ3(cos(theta / 2), -sin(theta / 2) / 2, 0, 0), |
| MakeJ3(sin(theta / 2), cos(theta / 2) / 2, 0, 0), |
| MakeJ3(0, 0, sin(theta / 2) / theta, 0), |
| MakeJ3(0, 0, 0, sin(theta / 2) / theta), |
| }; |
| AngleAxisToQuaternion(axis_angle, quaternion); |
| EXPECT_THAT(quaternion, testing::Pointwise(JetClose(kTolerance), expected)); |
| } |
| } |
| |
| // Test that conversion works for very small angles when jets are used. |
| TEST(Rotation, TinyAngleAxisToQuaternionForJets) { |
| // Examine tiny x rotations that extend all the way to where |
| // underflow occurs. |
| for (int i = kSmallTinyCutoff; i >= kTinyZeroLimit; i--) { |
| double theta = pow(10.0, i); |
| J3 axis_angle[3] = {J3(theta, 0), J3(0, 1), J3(0, 2)}; |
| J3 quaternion[4]; |
| // To avoid loss of precision in the test itself, |
| // a finite expansion is used here, which will |
| // be exact up to machine precision for the test values used. |
| J3 expected[4] = { |
| MakeJ3(1.0, 0, 0, 0), |
| MakeJ3(0, 0.5, 0, 0), |
| MakeJ3(0, 0, 0.5, 0), |
| MakeJ3(0, 0, 0, 0.5), |
| }; |
| AngleAxisToQuaternion(axis_angle, quaternion); |
| EXPECT_THAT(quaternion, testing::Pointwise(JetClose(kTolerance), expected)); |
| } |
| } |
| |
| // Test that derivatives are correct for zero rotation. |
| TEST(Rotation, ZeroAngleAxisToQuaternionForJets) { |
| J3 axis_angle[3] = {J3(0, 0), J3(0, 1), J3(0, 2)}; |
| J3 quaternion[4]; |
| J3 expected[4] = { |
| MakeJ3(1.0, 0, 0, 0), |
| MakeJ3(0, 0.5, 0, 0), |
| MakeJ3(0, 0, 0.5, 0), |
| MakeJ3(0, 0, 0, 0.5), |
| }; |
| AngleAxisToQuaternion(axis_angle, quaternion); |
| EXPECT_THAT(quaternion, testing::Pointwise(JetClose(kTolerance), expected)); |
| } |
| |
| // Test that exact conversion works for small angles. |
| TEST(Rotation, SmallQuaternionToAngleAxisForJets) { |
| // Examine small x rotations that are still large enough |
| // to be well within the range represented by doubles. |
| for (int i = -2; i >= kSmallTinyCutoff; i--) { |
| double theta = pow(10.0, i); |
| double s = sin(theta); |
| double c = cos(theta); |
| J4 quaternion[4] = {J4(c, 0), J4(s, 1), J4(0, 2), J4(0, 3)}; |
| J4 axis_angle[3]; |
| // clang-format off |
| J4 expected[3] = { |
| MakeJ4(2*theta, -2*s, 2*c, 0, 0), |
| MakeJ4(0, 0, 0, 2*theta/s, 0), |
| MakeJ4(0, 0, 0, 0, 2*theta/s), |
| }; |
| // clang-format on |
| QuaternionToAngleAxis(quaternion, axis_angle); |
| EXPECT_THAT(axis_angle, testing::Pointwise(JetClose(kTolerance), expected)); |
| } |
| } |
| |
| // Test that conversion works for very small angles. |
| TEST(Rotation, TinyQuaternionToAngleAxisForJets) { |
| // Examine tiny x rotations that extend all the way to where |
| // underflow occurs. |
| for (int i = kSmallTinyCutoff; i >= kTinyZeroLimit; i--) { |
| double theta = pow(10.0, i); |
| double s = sin(theta); |
| double c = cos(theta); |
| J4 quaternion[4] = {J4(c, 0), J4(s, 1), J4(0, 2), J4(0, 3)}; |
| J4 axis_angle[3]; |
| // To avoid loss of precision in the test itself, |
| // a finite expansion is used here, which will |
| // be exact up to machine precision for the test values used. |
| // clang-format off |
| J4 expected[3] = { |
| MakeJ4(2*theta, -2*s, 2.0, 0, 0), |
| MakeJ4(0, 0, 0, 2.0, 0), |
| MakeJ4(0, 0, 0, 0, 2.0), |
| }; |
| // clang-format on |
| QuaternionToAngleAxis(quaternion, axis_angle); |
| EXPECT_THAT(axis_angle, testing::Pointwise(JetClose(kTolerance), expected)); |
| } |
| } |
| |
| // Test that conversion works for no rotation. |
| TEST(Rotation, ZeroQuaternionToAngleAxisForJets) { |
| J4 quaternion[4] = {J4(1, 0), J4(0, 1), J4(0, 2), J4(0, 3)}; |
| J4 axis_angle[3]; |
| J4 expected[3] = { |
| MakeJ4(0, 0, 2.0, 0, 0), |
| MakeJ4(0, 0, 0, 2.0, 0), |
| MakeJ4(0, 0, 0, 0, 2.0), |
| }; |
| QuaternionToAngleAxis(quaternion, axis_angle); |
| EXPECT_THAT(axis_angle, testing::Pointwise(JetClose(kTolerance), expected)); |
| } |
| |
| // The following 4 test cases cover the conversion of Euler Angles to rotation |
| // matrices for Jets |
| // |
| // The dual parts (with dimension 3) of the resultant matrix of Jets contain the |
| // derivative of each matrix element w.r.t. the input Euler Angles. In other |
| // words, for each element in R = EulerAnglesToRotationMatrix(angles), we have |
| // R_ij.v = jacobian(R_ij, angles) |
| // |
| // The test data (dual parts of the Jets) is generated by analytically |
| // differentiating the formulas for Euler Angle to Rotation Matrix conversion |
| |
| // Test ZXY/312 Intrinsic Euler Angles to rotation matrix conversion using Jets |
| // The two ZXY test cases specifically cover handling of Tait-Bryan angles |
| // i.e. last axis of rotation is different from the first |
| TEST(EulerAngles, Intrinsic312EulerSequenceToRotationMatrixForJets) { |
| J3 euler_angles[3]; |
| J3 rotation_matrix[9]; |
| |
| ArrayToArrayOfJets(sample_euler[0], euler_angles); |
| EulerAnglesToRotation<IntrinsicZXY>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3( 0.306186083320, -0.883883627842, -0.176776571821, -0.918558748402), // NOLINT |
| MakeJ3(-0.249999816229, -0.433012359189, 0.433012832394, 0.000000000000), // NOLINT |
| MakeJ3( 0.918558748402, 0.176776777947, 0.176776558880, 0.306186083320), // NOLINT |
| MakeJ3( 0.883883627842, 0.306186083320, 0.306185986727, 0.176776777947), // NOLINT |
| MakeJ3( 0.433012359189, -0.249999816229, -0.750000183771, 0.000000000000), // NOLINT |
| MakeJ3(-0.176776777947, 0.918558748402, -0.306185964313, 0.883883627842), // NOLINT |
| MakeJ3(-0.353553128699, 0.000000000000, 0.612372616786, -0.353553102817), // NOLINT |
| MakeJ3( 0.866025628186, 0.000000000000, 0.499999611325, 0.000000000000), // NOLINT |
| MakeJ3( 0.353553102817, 0.000000000000, -0.612372571957, -0.353553128699) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_euler[1], euler_angles); |
| EulerAnglesToRotation<IntrinsicZXY>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3( 0.533493553520, -0.808012821828, -0.124999913397, -0.808012821828), // NOLINT |
| MakeJ3(-0.249999816229, -0.433012359189, 0.433012832394, 0.000000000000), // NOLINT |
| MakeJ3( 0.808012821828, 0.399519181706, 0.216506188745, 0.533493553520), // NOLINT |
| MakeJ3( 0.808012821828, 0.533493553520, 0.216506188745, 0.399519181706), // NOLINT |
| MakeJ3( 0.433012359189, -0.249999816229, -0.750000183771, 0.000000000000), // NOLINT |
| MakeJ3(-0.399519181706, 0.808012821828, -0.374999697927, 0.808012821828), // NOLINT |
| MakeJ3(-0.249999816229, 0.000000000000, 0.433012832394, -0.433012359189), // NOLINT |
| MakeJ3( 0.866025628186, 0.000000000000, 0.499999611325, 0.000000000000), // NOLINT |
| MakeJ3( 0.433012359189, 0.000000000000, -0.750000183771, -0.249999816229) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_euler[2], euler_angles); |
| EulerAnglesToRotation<IntrinsicZXY>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3( 0.047366781483, -0.659739427619, -0.530330235247, -0.789149143778), // NOLINT |
| MakeJ3(-0.612372449483, -0.612372404654, 0.353553418477, 0.000000000000), // NOLINT |
| MakeJ3( 0.789149143778, -0.435596057906, 0.306185986727, 0.047366781483), // NOLINT |
| MakeJ3( 0.659739427619, 0.047366781483, 0.530330196424, -0.435596057906), // NOLINT |
| MakeJ3( 0.612372404654, -0.612372449483, -0.353553392595, 0.000000000000), // NOLINT |
| MakeJ3( 0.435596057906, 0.789149143778, -0.306185964313, 0.659739427619), // NOLINT |
| MakeJ3(-0.750000183771, 0.000000000000, 0.433012832394, -0.433012359189), // NOLINT |
| MakeJ3( 0.500000021132, 0.000000000000, 0.866025391584, 0.000000000000), // NOLINT |
| MakeJ3( 0.433012359189, 0.000000000000, -0.249999816229, -0.750000183771) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| } |
| |
| // Test ZXY/312 Extrinsic Euler Angles to rotation matrix conversion using Jets |
| TEST(EulerAngles, Extrinsic312EulerSequenceToRotationMatrixForJets) { |
| J3 euler_angles[3]; |
| J3 rotation_matrix[9]; |
| |
| ArrayToArrayOfJets(sample_euler[0], euler_angles); |
| EulerAnglesToRotation<ExtrinsicZXY>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3( 0.918558725988, 0.176776842652, 0.176776571821, -0.306186150563), // NOLINT |
| MakeJ3( 0.176776842652, -0.918558725988, 0.306185986727, 0.883883614902), // NOLINT |
| MakeJ3( 0.353553128699, 0.000000000000, -0.612372616786, 0.353553102817), // NOLINT |
| MakeJ3( 0.249999816229, 0.433012359189, -0.433012832394, 0.000000000000), // NOLINT |
| MakeJ3( 0.433012359189, -0.249999816229, -0.750000183771, 0.000000000000), // NOLINT |
| MakeJ3(-0.866025628186, 0.000000000000, -0.499999611325, 0.000000000000), // NOLINT |
| MakeJ3(-0.306186150563, 0.883883614902, 0.176776558880, -0.918558725988), // NOLINT |
| MakeJ3( 0.883883614902, 0.306186150563, 0.306185964313, -0.176776842652), // NOLINT |
| MakeJ3( 0.353553102817, 0.000000000000, -0.612372571957, -0.353553128699) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_euler[1], euler_angles); |
| EulerAnglesToRotation<ExtrinsicZXY>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3( 0.966506404215, -0.058012606358, 0.124999913397, -0.058012606358), // NOLINT |
| MakeJ3(-0.058012606358, -0.966506404215, 0.216506188745, 0.899519223971), // NOLINT |
| MakeJ3( 0.249999816229, 0.000000000000, -0.433012832394, 0.433012359189), // NOLINT |
| MakeJ3( 0.249999816229, 0.433012359189, -0.433012832394, 0.000000000000), // NOLINT |
| MakeJ3( 0.433012359189, -0.249999816229, -0.750000183771, 0.000000000000), // NOLINT |
| MakeJ3(-0.866025628186, 0.000000000000, -0.499999611325, 0.000000000000), // NOLINT |
| MakeJ3(-0.058012606358, 0.899519223971, 0.216506188745, -0.966506404215), // NOLINT |
| MakeJ3( 0.899519223971, 0.058012606358, 0.374999697927, 0.058012606358), // NOLINT |
| MakeJ3( 0.433012359189, 0.000000000000, -0.750000183771, -0.249999816229) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_euler[2], euler_angles); |
| EulerAnglesToRotation<ExtrinsicZXY>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3( 0.659739424151, -0.047366829780, 0.530330235247, -0.435596000136), // NOLINT |
| MakeJ3(-0.047366829780, -0.659739424151, 0.530330196424, 0.789149175666), // NOLINT |
| MakeJ3( 0.750000183771, 0.000000000000, -0.433012832394, 0.433012359189), // NOLINT |
| MakeJ3( 0.612372449483, 0.612372404654, -0.353553418477, 0.000000000000), // NOLINT |
| MakeJ3( 0.612372404654, -0.612372449483, -0.353553392595, 0.000000000000), // NOLINT |
| MakeJ3(-0.500000021132, 0.000000000000, -0.866025391584, 0.000000000000), // NOLINT |
| MakeJ3(-0.435596000136, 0.789149175666, 0.306185986727, -0.659739424151), // NOLINT |
| MakeJ3( 0.789149175666, 0.435596000136, 0.306185964313, 0.047366829780), // NOLINT |
| MakeJ3( 0.433012359189, 0.000000000000, -0.249999816229, -0.750000183771) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| } |
| |
| // Test ZXZ/313 Intrinsic Euler Angles to rotation matrix conversion using Jets |
| // The two ZXZ test cases specifically cover handling of proper Euler Sequences |
| // i.e. last axis of rotation is same as the first |
| TEST(EulerAngles, Intrinsic313EulerSequenceToRotationMatrixForJets) { |
| J3 euler_angles[3]; |
| J3 rotation_matrix[9]; |
| |
| ArrayToArrayOfJets(sample_euler[0], euler_angles); |
| EulerAnglesToRotation<IntrinsicZXZ>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3( 0.435595832833, -0.659739379323, 0.306186321334, -0.789149008363), // NOLINT |
| MakeJ3(-0.789149008363, 0.047367454164, 0.306186298920, -0.435595832833), // NOLINT |
| MakeJ3( 0.433012832394, 0.750000183771, 0.249999816229, 0.000000000000), // NOLINT |
| MakeJ3( 0.659739379323, 0.435595832833, -0.530330235247, -0.047367454164), // NOLINT |
| MakeJ3(-0.047367454164, -0.789149008363, -0.530330196424, -0.659739379323), // NOLINT |
| MakeJ3(-0.750000183771, 0.433012832394, -0.433012359189, 0.000000000000), // NOLINT |
| MakeJ3( 0.612372616786, 0.000000000000, 0.353553128699, 0.612372571957), // NOLINT |
| MakeJ3( 0.612372571957, 0.000000000000, 0.353553102817, -0.612372616786), // NOLINT |
| MakeJ3( 0.499999611325, 0.000000000000, -0.866025628186, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_euler[1], euler_angles); |
| EulerAnglesToRotation<IntrinsicZXZ>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3( 0.625000065470, -0.649518902838, 0.216506425348, -0.649518902838), // NOLINT |
| MakeJ3(-0.649518902838, -0.124999676795, 0.375000107735, -0.625000065470), // NOLINT |
| MakeJ3( 0.433012832394, 0.750000183771, 0.249999816229, 0.000000000000), // NOLINT |
| MakeJ3( 0.649518902838, 0.625000065470, -0.375000107735, 0.124999676795), // NOLINT |
| MakeJ3( 0.124999676795, -0.649518902838, -0.649519202838, -0.649518902838), // NOLINT |
| MakeJ3(-0.750000183771, 0.433012832394, -0.433012359189, 0.000000000000), // NOLINT |
| MakeJ3( 0.433012832394, 0.000000000000, 0.249999816229, 0.750000183771), // NOLINT |
| MakeJ3( 0.750000183771, 0.000000000000, 0.433012359189, -0.433012832394), // NOLINT |
| MakeJ3( 0.499999611325, 0.000000000000, -0.866025628186, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_euler[2], euler_angles); |
| EulerAnglesToRotation<IntrinsicZXZ>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3(-0.176777132430, -0.883883325124, 0.306186321334, -0.918558558685), // NOLINT |
| MakeJ3(-0.918558558685, 0.306186652473, 0.176776571821, 0.176777132430), // NOLINT |
| MakeJ3( 0.353553418477, 0.353553392595, 0.612372449483, 0.000000000000), // NOLINT |
| MakeJ3( 0.883883325124, -0.176777132430, -0.306186298920, -0.306186652473), // NOLINT |
| MakeJ3(-0.306186652473, -0.918558558685, -0.176776558880, -0.883883325124), // NOLINT |
| MakeJ3(-0.353553392595, 0.353553418477, -0.612372404654, 0.000000000000), // NOLINT |
| MakeJ3( 0.433012832394, 0.000000000000, 0.750000183771, 0.249999816229), // NOLINT |
| MakeJ3( 0.249999816229, 0.000000000000, 0.433012359189, -0.433012832394), // NOLINT |
| MakeJ3( 0.866025391584, 0.000000000000, -0.500000021132, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| } |
| |
| // Test ZXZ/313 Extrinsic Euler Angles to rotation matrix conversion using Jets |
| TEST(EulerAngles, Extrinsic313EulerSequenceToRotationMatrixForJets) { |
| J3 euler_angles[3]; |
| J3 rotation_matrix[9]; |
| |
| ArrayToArrayOfJets(sample_euler[0], euler_angles); |
| EulerAnglesToRotation<ExtrinsicZXZ>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3( 0.435595832833, -0.659739379323, 0.306186321334, -0.789149008363), // NOLINT |
| MakeJ3(-0.659739379323, -0.435595832833, 0.530330235247, 0.047367454164), // NOLINT |
| MakeJ3( 0.612372616786, 0.000000000000, 0.353553128699, 0.612372571957), // NOLINT |
| MakeJ3( 0.789149008363, -0.047367454164, -0.306186298920, 0.435595832833), // NOLINT |
| MakeJ3(-0.047367454164, -0.789149008363, -0.530330196424, -0.659739379323), // NOLINT |
| MakeJ3(-0.612372571957, 0.000000000000, -0.353553102817, 0.612372616786), // NOLINT |
| MakeJ3( 0.433012832394, 0.750000183771, 0.249999816229, 0.000000000000), // NOLINT |
| MakeJ3( 0.750000183771, -0.433012832394, 0.433012359189, 0.000000000000), // NOLINT |
| MakeJ3( 0.499999611325, 0.000000000000, -0.866025628186, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_euler[1], euler_angles); |
| EulerAnglesToRotation<ExtrinsicZXZ>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3( 0.625000065470, -0.649518902838, 0.216506425348, -0.649518902838), // NOLINT |
| MakeJ3(-0.649518902838, -0.625000065470, 0.375000107735, -0.124999676795), // NOLINT |
| MakeJ3( 0.433012832394, 0.000000000000, 0.249999816229, 0.750000183771), // NOLINT |
| MakeJ3( 0.649518902838, 0.124999676795, -0.375000107735, 0.625000065470), // NOLINT |
| MakeJ3( 0.124999676795, -0.649518902838, -0.649519202838, -0.649518902838), // NOLINT |
| MakeJ3(-0.750000183771, 0.000000000000, -0.433012359189, 0.433012832394), // NOLINT |
| MakeJ3( 0.433012832394, 0.750000183771, 0.249999816229, 0.000000000000), // NOLINT |
| MakeJ3( 0.750000183771, -0.433012832394, 0.433012359189, 0.000000000000), // NOLINT |
| MakeJ3( 0.499999611325, 0.000000000000, -0.866025628186, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_euler[2], euler_angles); |
| EulerAnglesToRotation<ExtrinsicZXZ>(euler_angles, rotation_matrix); |
| { |
| // clang-format off |
| const J3 expected[] = { |
| MakeJ3(-0.176777132430, -0.883883325124, 0.306186321334, -0.918558558685), // NOLINT |
| MakeJ3(-0.883883325124, 0.176777132430, 0.306186298920, 0.306186652473), // NOLINT |
| MakeJ3( 0.433012832394, 0.000000000000, 0.750000183771, 0.249999816229), // NOLINT |
| MakeJ3( 0.918558558685, -0.306186652473, -0.176776571821, -0.176777132430), // NOLINT |
| MakeJ3(-0.306186652473, -0.918558558685, -0.176776558880, -0.883883325124), // NOLINT |
| MakeJ3(-0.249999816229, 0.000000000000, -0.433012359189, 0.433012832394), // NOLINT |
| MakeJ3( 0.353553418477, 0.353553392595, 0.612372449483, 0.000000000000), // NOLINT |
| MakeJ3( 0.353553392595, -0.353553418477, 0.612372404654, 0.000000000000), // NOLINT |
| MakeJ3( 0.866025391584, 0.000000000000, -0.500000021132, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(rotation_matrix, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| } |
| |
| using J9 = Jet<double, 9>; |
| |
| // The following 4 tests Tests the conversion of rotation matrices to Euler |
| // Angles for Jets. |
| // |
| // The dual parts (with dimension 9) of the resultant array of Jets contain the |
| // derivative of each Euler angle w.r.t. each of the 9 elements of the rotation |
| // matrix, or a 9-by-1 array formed from flattening the rotation matrix. In |
| // other words, for each element in angles = RotationMatrixToEulerAngles(R), we |
| // have angles.v = jacobian(angles, [R11 R12 R13 R21 ... R32 R33]); |
| // |
| // Note: the order of elements in v depend on row/column-wise flattening of |
| // the rotation matrix |
| // |
| // The test data (dual parts of the Jets) is generated by analytically |
| // differentiating the formulas for Rotation Matrix to Euler Angle conversion |
| |
| // clang-format off |
| static double sample_matrices[][9] = { |
| { 0.433012359189, 0.176776842652, 0.883883614902, 0.249999816229, 0.918558725988, -0.306186150563, -0.866025628186, 0.353553128699, 0.353553102817}, // NOLINT |
| { 0.433012359189, -0.058012606358, 0.899519223971, 0.249999816229, 0.966506404215, -0.058012606358, -0.866025628186, 0.249999816229, 0.433012359189}, // NOLINT |
| { 0.612372404654, -0.047366829780, 0.789149175666, 0.612372449483, 0.659739424151, -0.435596000136, -0.500000021132, 0.750000183771, 0.433012359189} // NOLINT |
| }; |
| // clang-format on |
| |
| // Test rotation matrix to ZXY/312 Intrinsic Euler Angles conversion using Jets |
| // The two ZXY test cases specifically cover handling of Tait-Bryan angles |
| // i.e. last axis of rotation is different from the first |
| TEST(EulerAngles, RotationMatrixToIntrinsic312EulerSequenceForJets) { |
| J9 euler_angles[3]; |
| J9 rotation_matrix[9]; |
| |
| ArrayToArrayOfJets(sample_matrices[0], rotation_matrix); |
| RotationMatrixToEulerAngles<IntrinsicZXY>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>(-0.190125743401, 0.000000000000, -1.049781178951, 0.000000000000, 0.000000000000, 0.202030634558, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000), // NOLINT |
| MakeJet<9>( 0.361366843930, 0.000000000000, -0.066815309609, 0.000000000000, 0.000000000000, -0.347182270882, 0.000000000000, 0.000000000000, 0.935414445680, 0.000000000000), // NOLINT |
| MakeJet<9>( 1.183200015636, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.404060603418, 0.000000000000, -0.989743365598) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_matrices[1], rotation_matrix); |
| RotationMatrixToEulerAngles<IntrinsicZXY>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>( 0.059951064811, 0.000000000000, -1.030940063452, 0.000000000000, 0.000000000000, -0.061880107384, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000), // NOLINT |
| MakeJet<9>( 0.252680065344, 0.000000000000, 0.014978778808, 0.000000000000, 0.000000000000, -0.249550684831, 0.000000000000, 0.000000000000, 0.968245884001, 0.000000000000), // NOLINT |
| MakeJet<9>( 1.107149138016, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.461879804532, 0.000000000000, -0.923760579526) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_matrices[2], rotation_matrix); |
| RotationMatrixToEulerAngles<IntrinsicZXY>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>( 0.071673287221, 0.000000000000, -1.507976776767, 0.000000000000, 0.000000000000, -0.108267107713, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000), // NOLINT |
| MakeJet<9>( 0.848062356818, 0.000000000000, 0.053708966648, 0.000000000000, 0.000000000000, -0.748074610289, 0.000000000000, 0.000000000000, 0.661437619389, 0.000000000000), // NOLINT |
| MakeJet<9>( 0.857072360427, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.989743158900, 0.000000000000, -1.142857911244) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| } |
| |
| // Test rotation matrix to ZXY/312 Extrinsic Euler Angles conversion using Jets |
| TEST(EulerAngles, RotationMatrixToExtrinsic312EulerSequenceForJets) { |
| J9 euler_angles[3]; |
| J9 rotation_matrix[9]; |
| |
| ArrayToArrayOfJets(sample_matrices[0], rotation_matrix); |
| RotationMatrixToEulerAngles<ExtrinsicZXY>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>( 0.265728912717, 0.000000000000, 0.000000000000, 0.000000000000, 1.013581996386, -0.275861853641, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000), // NOLINT |
| MakeJet<9>( 0.311184173598, 0.000000000000, 0.000000000000, -0.284286741927, 0.000000000000, 0.000000000000, -0.951971659874, 0.000000000000, 0.000000000000, -0.113714586405), // NOLINT |
| MakeJet<9>( 1.190290284357, 0.000000000000, 0.000000000000, 0.390127543992, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.975319806582) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_matrices[1], rotation_matrix); |
| RotationMatrixToEulerAngles<ExtrinsicZXY>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>( 0.253115668605, 0.000000000000, 0.000000000000, 0.000000000000, 0.969770129215, -0.250844022378, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000), // NOLINT |
| MakeJet<9>( 0.058045195612, 0.000000000000, 0.000000000000, -0.052271487648, 0.000000000000, 0.000000000000, -0.998315850572, 0.000000000000, 0.000000000000, -0.025162553041), // NOLINT |
| MakeJet<9>( 1.122153748896, 0.000000000000, 0.000000000000, 0.434474567050, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.902556744846) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_matrices[2], rotation_matrix); |
| RotationMatrixToEulerAngles<ExtrinsicZXY>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>( 0.748180444286, 0.000000000000, 0.000000000000, 0.000000000000, 0.814235652244, -0.755776390750, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000), // NOLINT |
| MakeJet<9>( 0.450700288478, 0.000000000000, 0.000000000000, -0.381884322045, 0.000000000000, 0.000000000000, -0.900142280234, 0.000000000000, 0.000000000000, -0.209542930950), // NOLINT |
| MakeJet<9>( 1.068945699497, 0.000000000000, 0.000000000000, 0.534414175972, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.973950275281) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| } |
| |
| // Test rotation matrix to ZXZ/313 Intrinsic Euler Angles conversion using Jets |
| //// The two ZXZ test cases specifically cover handling of proper Euler |
| /// Sequences |
| // i.e. last axis of rotation is same as the first |
| TEST(EulerAngles, RotationMatrixToIntrinsic313EulerSequenceForJets) { |
| J9 euler_angles[3]; |
| J9 rotation_matrix[9]; |
| |
| ArrayToArrayOfJets(sample_matrices[0], rotation_matrix); |
| RotationMatrixToEulerAngles<IntrinsicZXZ>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>( 1.237323270947, 0.000000000000, 0.000000000000, 0.349926947837, 0.000000000000, 0.000000000000, 1.010152467826, 0.000000000000, 0.000000000000, 0.000000000000), // NOLINT |
| MakeJet<9>( 1.209429510533, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.327326615680, 0.133630397662, -0.935414455462), // NOLINT |
| MakeJet<9>(-1.183199990019, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.404060624546, 0.989743344897, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_matrices[1], rotation_matrix); |
| RotationMatrixToEulerAngles<IntrinsicZXZ>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>( 1.506392616830, 0.000000000000, 0.000000000000, 0.071400104821, 0.000000000000, 0.000000000000, 1.107100178948, 0.000000000000, 0.000000000000, 0.000000000000), // NOLINT |
| MakeJet<9>( 1.122964310061, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.416024849727, 0.120095910090, -0.901387983495), // NOLINT |
| MakeJet<9>(-1.289761690216, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.307691969119, 1.065877306886, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_matrices[2], rotation_matrix); |
| RotationMatrixToEulerAngles<IntrinsicZXZ>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>( 1.066432836578, 0.000000000000, 0.000000000000, 0.536117958181, 0.000000000000, 0.000000000000, 0.971260169116, 0.000000000000, 0.000000000000, 0.000000000000), // NOLINT |
| MakeJet<9>( 1.122964310061, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.240192006893, 0.360288083393, -0.901387983495), // NOLINT |
| MakeJet<9>(-0.588002509965, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.923076812076, 0.615384416607, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| } |
| |
| // Test rotation matrix to ZXZ/313 Extrinsic Euler Angles conversion using Jets |
| TEST(EulerAngles, RotationMatrixToExtrinsic313EulerSequenceForJets) { |
| J9 euler_angles[3]; |
| J9 rotation_matrix[9]; |
| |
| ArrayToArrayOfJets(sample_matrices[0], rotation_matrix); |
| RotationMatrixToEulerAngles<ExtrinsicZXZ>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>(-1.183199990019, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.404060624546, 0.989743344897, 0.000000000000), // NOLINT |
| MakeJet<9>( 1.209429510533, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.327326615680, 0.133630397662, -0.935414455462), // NOLINT |
| MakeJet<9>( 1.237323270947, 0.000000000000, 0.000000000000, 0.349926947837, 0.000000000000, 0.000000000000, 1.010152467826, 0.000000000000, 0.000000000000, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_matrices[1], rotation_matrix); |
| RotationMatrixToEulerAngles<ExtrinsicZXZ>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>(-1.289761690216, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.307691969119, 1.065877306886, 0.000000000000), // NOLINT |
| MakeJet<9>( 1.122964310061, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.416024849727, 0.120095910090, -0.901387983495), // NOLINT |
| MakeJet<9>( 1.506392616830, 0.000000000000, 0.000000000000, 0.071400104821, 0.000000000000, 0.000000000000, 1.107100178948, 0.000000000000, 0.000000000000, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| |
| ArrayToArrayOfJets(sample_matrices[2], rotation_matrix); |
| RotationMatrixToEulerAngles<ExtrinsicZXZ>(rotation_matrix, euler_angles); |
| { |
| // clang-format off |
| const J9 expected[] = { |
| MakeJet<9>(-0.588002509965, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.923076812076, 0.615384416607, 0.000000000000), // NOLINT |
| MakeJet<9>( 1.122964310061, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, 0.000000000000, -0.240192006893, 0.360288083393, -0.901387983495), // NOLINT |
| MakeJet<9>( 1.066432836578, 0.000000000000, 0.000000000000, 0.536117958181, 0.000000000000, 0.000000000000, 0.971260169116, 0.000000000000, 0.000000000000, 0.000000000000) // NOLINT |
| }; |
| // clang-format on |
| EXPECT_THAT(euler_angles, |
| testing::Pointwise(JetClose(kLooseTolerance), expected)); |
| } |
| } |
| |
| TEST(Quaternion, RotatePointGivesSameAnswerAsRotationByMatrixCanned) { |
| // Canned data generated in octave. |
| double const q[4] = { |
| +0.1956830471754074, |
| -0.0150618562474847, |
| +0.7634572982788086, |
| -0.3019454777240753, |
| }; |
| double const Q[3][3] = { |
| // Scaled rotation matrix. |
| {-0.6355194033477252, +0.0951730541682254, +0.3078870197911186}, |
| {-0.1411693904792992, +0.5297609702153905, -0.4551502574482019}, |
| {-0.2896955822708862, -0.4669396571547050, -0.4536309793389248}, |
| }; |
| double const R[3][3] = { |
| // With unit rows and columns. |
| {-0.8918859164053080, +0.1335655625725649, +0.4320876677394745}, |
| {-0.1981166751680096, +0.7434648665444399, -0.6387564287225856}, |
| {-0.4065578619806013, -0.6553016349046693, -0.6366242786393164}, |
| }; |
| |
| // Compute R from q and compare to known answer. |
| double Rq[3][3]; |
| QuaternionToScaledRotation<double>(q, Rq[0]); |
| ExpectArraysClose(9, Q[0], Rq[0], kTolerance); |
| |
| // Now do the same but compute R with normalization. |
| QuaternionToRotation<double>(q, Rq[0]); |
| ExpectArraysClose(9, R[0], Rq[0], kTolerance); |
| } |
| |
| TEST(Quaternion, RotatePointGivesSameAnswerAsRotationByMatrix) { |
| // Rotation defined by a unit quaternion. |
| double const q[4] = { |
| +0.2318160216097109, |
| -0.0178430356832060, |
| +0.9044300776717159, |
| -0.3576998641394597, |
| }; |
| double const p[3] = { |
| +0.11, |
| -13.15, |
| 1.17, |
| }; |
| |
| double R[3 * 3]; |
| QuaternionToRotation(q, R); |
| |
| double result1[3]; |
| UnitQuaternionRotatePoint(q, p, result1); |
| |
| double result2[3]; |
| VectorRef(result2, 3) = ConstMatrixRef(R, 3, 3) * ConstVectorRef(p, 3); |
| ExpectArraysClose(3, result1, result2, kTolerance); |
| } |
| |
| // Verify that (a * b) * c == a * (b * c). |
| TEST(Quaternion, MultiplicationIsAssociative) { |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0}; |
| double a[4]; |
| double b[4]; |
| double c[4]; |
| for (int i = 0; i < 4; ++i) { |
| a[i] = uniform_distribution(prng); |
| b[i] = uniform_distribution(prng); |
| c[i] = uniform_distribution(prng); |
| } |
| |
| double ab[4]; |
| double ab_c[4]; |
| QuaternionProduct(a, b, ab); |
| QuaternionProduct(ab, c, ab_c); |
| |
| double bc[4]; |
| double a_bc[4]; |
| QuaternionProduct(b, c, bc); |
| QuaternionProduct(a, bc, a_bc); |
| |
| ASSERT_NEAR(ab_c[0], a_bc[0], kTolerance); |
| ASSERT_NEAR(ab_c[1], a_bc[1], kTolerance); |
| ASSERT_NEAR(ab_c[2], a_bc[2], kTolerance); |
| ASSERT_NEAR(ab_c[3], a_bc[3], kTolerance); |
| } |
| |
| TEST(AngleAxis, RotatePointGivesSameAnswerAsRotationMatrix) { |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0}; |
| double angle_axis[3]; |
| double R[9]; |
| double p[3]; |
| double angle_axis_rotated_p[3]; |
| double rotation_matrix_rotated_p[3]; |
| |
| for (int i = 0; i < 10000; ++i) { |
| double theta = (2.0 * i * 0.0011 - 1.0) * kPi; |
| for (int j = 0; j < 50; ++j) { |
| for (int k = 0; k < 3; ++k) { |
| angle_axis[k] = uniform_distribution(prng); |
| p[k] = uniform_distribution(prng); |
| } |
| |
| const double inv_norm = |
| theta / std::hypot(angle_axis[0], angle_axis[1], angle_axis[2]); |
| for (double& angle_axi : angle_axis) { |
| angle_axi *= inv_norm; |
| } |
| |
| AngleAxisToRotationMatrix(angle_axis, R); |
| rotation_matrix_rotated_p[0] = R[0] * p[0] + R[3] * p[1] + R[6] * p[2]; |
| rotation_matrix_rotated_p[1] = R[1] * p[0] + R[4] * p[1] + R[7] * p[2]; |
| rotation_matrix_rotated_p[2] = R[2] * p[0] + R[5] * p[1] + R[8] * p[2]; |
| |
| AngleAxisRotatePoint(angle_axis, p, angle_axis_rotated_p); |
| for (int k = 0; k < 3; ++k) { |
| // clang-format off |
| EXPECT_NEAR(rotation_matrix_rotated_p[k], |
| angle_axis_rotated_p[k], |
| kTolerance) << "p: " << p[0] |
| << " " << p[1] |
| << " " << p[2] |
| << " angle_axis: " << angle_axis[0] |
| << " " << angle_axis[1] |
| << " " << angle_axis[2]; |
| // clang-format on |
| } |
| } |
| } |
| } |
| |
| TEST(Quaternion, UnitQuaternion) { |
| using Jet = ceres::Jet<double, 4>; |
| std::array<Jet, 4> quaternion = { |
| Jet(1.0, 0), Jet(0.0, 1), Jet(0.0, 2), Jet(0.0, 3)}; |
| std::array<Jet, 3> point = {Jet(0.0), Jet(0.0), Jet(0.0)}; |
| std::array<Jet, 3> rotated_point; |
| QuaternionRotatePoint(quaternion.data(), point.data(), rotated_point.data()); |
| for (int i = 0; i < 3; ++i) { |
| EXPECT_EQ(rotated_point[i], point[i]); |
| EXPECT_FALSE(rotated_point[i].v.array().isNaN().any()); |
| } |
| } |
| |
| TEST(AngleAxis, NearZeroRotatePointGivesSameAnswerAsRotationMatrix) { |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0}; |
| double angle_axis[3]; |
| double R[9]; |
| double p[3]; |
| double angle_axis_rotated_p[3]; |
| double rotation_matrix_rotated_p[3]; |
| |
| for (int i = 0; i < 10000; ++i) { |
| double norm2 = 0.0; |
| for (int k = 0; k < 3; ++k) { |
| angle_axis[k] = uniform_distribution(prng); |
| p[k] = uniform_distribution(prng); |
| norm2 = angle_axis[k] * angle_axis[k]; |
| } |
| |
| double theta = (2.0 * i * 0.0001 - 1.0) * 1e-16; |
| const double inv_norm = theta / sqrt(norm2); |
| for (double& angle_axi : angle_axis) { |
| angle_axi *= inv_norm; |
| } |
| |
| AngleAxisToRotationMatrix(angle_axis, R); |
| rotation_matrix_rotated_p[0] = R[0] * p[0] + R[3] * p[1] + R[6] * p[2]; |
| rotation_matrix_rotated_p[1] = R[1] * p[0] + R[4] * p[1] + R[7] * p[2]; |
| rotation_matrix_rotated_p[2] = R[2] * p[0] + R[5] * p[1] + R[8] * p[2]; |
| |
| AngleAxisRotatePoint(angle_axis, p, angle_axis_rotated_p); |
| for (int k = 0; k < 3; ++k) { |
| // clang-format off |
| EXPECT_NEAR(rotation_matrix_rotated_p[k], |
| angle_axis_rotated_p[k], |
| kTolerance) << "p: " << p[0] |
| << " " << p[1] |
| << " " << p[2] |
| << " angle_axis: " << angle_axis[0] |
| << " " << angle_axis[1] |
| << " " << angle_axis[2]; |
| // clang-format on |
| } |
| } |
| } |
| |
| TEST(MatrixAdapter, RowMajor3x3ReturnTypeAndAccessIsCorrect) { |
| double array[9] = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}; |
| const float const_array[9] = { |
| 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f}; |
| MatrixAdapter<double, 3, 1> A = RowMajorAdapter3x3(array); |
| MatrixAdapter<const float, 3, 1> B = RowMajorAdapter3x3(const_array); |
| |
| for (int i = 0; i < 3; ++i) { |
| for (int j = 0; j < 3; ++j) { |
| // The values are integers from 1 to 9, so equality tests are appropriate |
| // even for float and double values. |
| EXPECT_EQ(A(i, j), array[3 * i + j]); |
| EXPECT_EQ(B(i, j), const_array[3 * i + j]); |
| } |
| } |
| } |
| |
| TEST(MatrixAdapter, ColumnMajor3x3ReturnTypeAndAccessIsCorrect) { |
| double array[9] = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}; |
| const float const_array[9] = { |
| 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f}; |
| MatrixAdapter<double, 1, 3> A = ColumnMajorAdapter3x3(array); |
| MatrixAdapter<const float, 1, 3> B = ColumnMajorAdapter3x3(const_array); |
| |
| for (int i = 0; i < 3; ++i) { |
| for (int j = 0; j < 3; ++j) { |
| // The values are integers from 1 to 9, so equality tests are |
| // appropriate even for float and double values. |
| EXPECT_EQ(A(i, j), array[3 * j + i]); |
| EXPECT_EQ(B(i, j), const_array[3 * j + i]); |
| } |
| } |
| } |
| |
| TEST(MatrixAdapter, RowMajor2x4IsCorrect) { |
| const int expected[8] = {1, 2, 3, 4, 5, 6, 7, 8}; |
| int array[8]; |
| MatrixAdapter<int, 4, 1> M(array); |
| // clang-format off |
| M(0, 0) = 1; M(0, 1) = 2; M(0, 2) = 3; M(0, 3) = 4; |
| M(1, 0) = 5; M(1, 1) = 6; M(1, 2) = 7; M(1, 3) = 8; |
| // clang-format on |
| for (int k = 0; k < 8; ++k) { |
| EXPECT_EQ(array[k], expected[k]); |
| } |
| } |
| |
| TEST(MatrixAdapter, ColumnMajor2x4IsCorrect) { |
| const int expected[8] = {1, 5, 2, 6, 3, 7, 4, 8}; |
| int array[8]; |
| MatrixAdapter<int, 1, 2> M(array); |
| // clang-format off |
| M(0, 0) = 1; M(0, 1) = 2; M(0, 2) = 3; M(0, 3) = 4; |
| M(1, 0) = 5; M(1, 1) = 6; M(1, 2) = 7; M(1, 3) = 8; |
| // clang-format on |
| for (int k = 0; k < 8; ++k) { |
| EXPECT_EQ(array[k], expected[k]); |
| } |
| } |
| |
| TEST(RotationMatrixToAngleAxis, NearPiExampleOneFromTobiasStrauss) { |
| // Example from Tobias Strauss |
| // clang-format off |
| const double rotation_matrix[] = { |
| -0.999807135425239, -0.0128154391194470, -0.0148814136745799, |
| -0.0128154391194470, -0.148441438622958, 0.988838158557669, |
| -0.0148814136745799, 0.988838158557669, 0.148248574048196 |
| }; |
| // clang-format on |
| |
| double angle_axis[3]; |
| RotationMatrixToAngleAxis(RowMajorAdapter3x3(rotation_matrix), angle_axis); |
| double round_trip[9]; |
| AngleAxisToRotationMatrix(angle_axis, RowMajorAdapter3x3(round_trip)); |
| EXPECT_THAT(rotation_matrix, IsNear3x3Matrix(round_trip)); |
| } |
| |
| static void CheckRotationMatrixToAngleAxisRoundTrip(const double theta, |
| const double phi, |
| const double angle) { |
| double angle_axis[3]; |
| angle_axis[0] = angle * sin(phi) * cos(theta); |
| angle_axis[1] = angle * sin(phi) * sin(theta); |
| angle_axis[2] = angle * cos(phi); |
| |
| double rotation_matrix[9]; |
| AngleAxisToRotationMatrix(angle_axis, rotation_matrix); |
| |
| double angle_axis_round_trip[3]; |
| RotationMatrixToAngleAxis(rotation_matrix, angle_axis_round_trip); |
| EXPECT_THAT(angle_axis_round_trip, IsNearAngleAxis(angle_axis)); |
| } |
| |
| TEST(RotationMatrixToAngleAxis, ExhaustiveRoundTrip) { |
| constexpr double kMaxSmallAngle = 1e-8; |
| std::mt19937 prng; |
| std::uniform_real_distribution<double> uniform_distribution1{ |
| kPi - kMaxSmallAngle, kPi}; |
| std::uniform_real_distribution<double> uniform_distribution2{ |
| -1.0, 2.0 * kMaxSmallAngle - 1.0}; |
| const int kNumSteps = 1000; |
| for (int i = 0; i < kNumSteps; ++i) { |
| const double theta = static_cast<double>(i) / kNumSteps * 2.0 * kPi; |
| for (int j = 0; j < kNumSteps; ++j) { |
| const double phi = static_cast<double>(j) / kNumSteps * kPi; |
| // Rotations of angle Pi. |
| CheckRotationMatrixToAngleAxisRoundTrip(theta, phi, kPi); |
| // Rotation of angle approximately Pi. |
| CheckRotationMatrixToAngleAxisRoundTrip( |
| theta, phi, uniform_distribution1(prng)); |
| // Rotations of angle approximately zero. |
| CheckRotationMatrixToAngleAxisRoundTrip( |
| theta, phi, uniform_distribution2(prng)); |
| } |
| } |
| } |
| |
| } // namespace internal |
| } // namespace ceres |
