mirror of
https://github.com/ceres-solver/ceres-solver.git
synced 2026-08-29 16:40:38 +08:00
Sameer Agarwal
2041 lines
83 KiB
C++
2041 lines
83 KiB
C++
// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2025 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
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#include "ceres/rotation.h"
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#include <algorithm>
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#include <array>
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#include <cmath>
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#include <limits>
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#include <random>
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#include <string>
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#include <utility>
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#include "Eigen/Core"
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#include "absl/log/log.h"
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#include "absl/strings/str_format.h"
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#include "ceres/constants.h"
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#include "ceres/internal/eigen.h"
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#include "ceres/internal/euler_angles.h"
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#include "ceres/internal/export.h"
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#include "ceres/is_close.h"
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#include "ceres/jet.h"
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#include "ceres/test_util.h"
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#include "gmock/gmock.h"
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#include "gtest/gtest.h"
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namespace ceres {
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namespace internal {
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inline constexpr double kPi = constants::pi;
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const double kHalfSqrt2 = 0.707106781186547524401;
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// A tolerance value for floating-point comparisons.
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static double const kTolerance = std::numeric_limits<double>::epsilon() * 10;
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// Looser tolerance used for numerically unstable conversions.
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static double const kLooseTolerance = 1e-9;
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// Use as:
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// double quaternion[4];
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// EXPECT_THAT(quaternion, IsNormalizedQuaternion());
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MATCHER(IsNormalizedQuaternion, "") {
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double norm2 =
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arg[0] * arg[0] + arg[1] * arg[1] + arg[2] * arg[2] + arg[3] * arg[3];
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if (fabs(norm2 - 1.0) > kTolerance) {
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*result_listener << "squared norm is " << norm2;
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return false;
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}
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return true;
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}
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// Use as:
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// double expected_quaternion[4];
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// double actual_quaternion[4];
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// EXPECT_THAT(actual_quaternion, IsNearQuaternion(expected_quaternion));
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MATCHER_P(IsNearQuaternion, expected, "") {
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// Quaternions are equivalent up to a sign change. So we will compare
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// both signs before declaring failure.
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bool is_near = true;
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// NOTE: near (and far) can be defined as macros on the Windows platform (for
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// ancient pascal calling convention). Do not use these identifiers.
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for (int i = 0; i < 4; i++) {
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if (fabs(arg[i] - expected[i]) > kTolerance) {
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is_near = false;
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break;
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}
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}
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if (is_near) {
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return true;
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}
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is_near = true;
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for (int i = 0; i < 4; i++) {
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if (fabs(arg[i] + expected[i]) > kTolerance) {
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is_near = false;
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break;
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}
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}
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if (is_near) {
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return true;
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}
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// clang-format off
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*result_listener << "expected : "
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<< expected[0] << " "
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<< expected[1] << " "
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<< expected[2] << " "
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<< expected[3] << " "
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<< "actual : "
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<< arg[0] << " "
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<< arg[1] << " "
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<< arg[2] << " "
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<< arg[3];
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// clang-format on
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return false;
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}
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// Use as:
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// double expected_axis_angle[3];
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// double actual_axis_angle[3];
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// EXPECT_THAT(actual_axis_angle, IsNearAngleAxis(expected_axis_angle));
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MATCHER_P(IsNearAngleAxis, expected, "") {
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Eigen::Vector3d a(arg[0], arg[1], arg[2]);
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Eigen::Vector3d e(expected[0], expected[1], expected[2]);
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const double e_norm = e.norm();
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double delta_norm = std::numeric_limits<double>::max();
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if (e_norm > 0) {
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// Deal with the sign ambiguity near PI. Since the sign can flip,
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// we take the smaller of the two differences.
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if (fabs(e_norm - kPi) < kLooseTolerance) {
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delta_norm = std::min((a - e).norm(), (a + e).norm()) / e_norm;
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} else {
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delta_norm = (a - e).norm() / e_norm;
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}
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} else {
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delta_norm = a.norm();
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}
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if (delta_norm <= kLooseTolerance) {
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return true;
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}
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// clang-format off
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*result_listener << " arg:"
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<< " " << arg[0]
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<< " " << arg[1]
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<< " " << arg[2]
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<< " was expected to be:"
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<< " " << expected[0]
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<< " " << expected[1]
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<< " " << expected[2];
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// clang-format on
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return false;
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}
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// Use as:
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// double matrix[9];
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// EXPECT_THAT(matrix, IsOrthonormal());
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MATCHER(IsOrthonormal, "") {
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for (int c1 = 0; c1 < 3; c1++) {
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for (int c2 = 0; c2 < 3; c2++) {
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double v = 0;
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for (int i = 0; i < 3; i++) {
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v += arg[i + 3 * c1] * arg[i + 3 * c2];
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}
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double expected = (c1 == c2) ? 1 : 0;
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if (fabs(expected - v) > kTolerance) {
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*result_listener << "Columns " << c1 << " and " << c2
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<< " should have dot product " << expected
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<< " but have " << v;
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return false;
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}
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}
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}
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return true;
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}
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// Use as:
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// double matrix1[9];
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// double matrix2[9];
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// EXPECT_THAT(matrix1, IsNear3x3Matrix(matrix2));
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MATCHER_P(IsNear3x3Matrix, expected, "") {
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for (int i = 0; i < 9; i++) {
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if (fabs(arg[i] - expected[i]) > kTolerance) {
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*result_listener << "component " << i << " should be " << expected[i];
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return false;
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}
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}
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return true;
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}
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template <typename T>
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class QuaternionTest : public testing::Test {};
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using QuaternionOrderTypes =
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testing::Types<ceres::CeresQuaternionOrder, ceres::EigenQuaternionOrder>;
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TYPED_TEST_SUITE(QuaternionTest, QuaternionOrderTypes);
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// Transforms a zero axis/angle to a quaternion.
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TYPED_TEST(QuaternionTest, ZeroAngleAxisToQuaternion) {
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using Order = TypeParam;
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double axis_angle[3] = {0, 0, 0};
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double quaternion[4];
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const std::array<double, 4> expected =
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MakeQuaternion<Order>(1.0, 0.0, 0.0, 0.0);
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AngleAxisToQuaternion<Order>(axis_angle, quaternion);
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EXPECT_THAT(quaternion, IsNormalizedQuaternion());
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EXPECT_THAT(quaternion, IsNearQuaternion(expected));
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}
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// Test that exact conversion works for small angles.
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TYPED_TEST(QuaternionTest, SmallAngleAxisToQuaternion) {
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using Order = TypeParam;
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// Small, finite value to test.
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double theta = 1.0e-2;
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double axis_angle[3] = {theta, 0, 0};
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double quaternion[4];
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const std::array<double, 4> expected =
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MakeQuaternion<Order>(cos(theta / 2.0), sin(theta / 2.0), 0.0, 0.0);
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AngleAxisToQuaternion<Order>(axis_angle, quaternion);
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EXPECT_THAT(quaternion, IsNormalizedQuaternion());
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EXPECT_THAT(quaternion, IsNearQuaternion(expected));
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}
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// Test that approximate conversion works for very small angles.
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TYPED_TEST(QuaternionTest, TinyAngleAxisToQuaternion) {
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using Order = TypeParam;
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// Very small value that could potentially cause underflow.
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double theta = pow(std::numeric_limits<double>::min(), 0.75);
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double axis_angle[3] = {theta, 0, 0};
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double quaternion[4];
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const std::array<double, 4> expected =
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MakeQuaternion<Order>(cos(theta / 2.0), sin(theta / 2.0), 0.0, 0.0);
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AngleAxisToQuaternion<Order>(axis_angle, quaternion);
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EXPECT_THAT(quaternion, IsNormalizedQuaternion());
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EXPECT_THAT(quaternion, IsNearQuaternion(expected));
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}
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// Transforms a rotation by pi/2 around X to a quaternion.
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TYPED_TEST(QuaternionTest, XRotationToQuaternion) {
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using Order = TypeParam;
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double axis_angle[3] = {kPi / 2, 0, 0};
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double quaternion[4];
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const std::array<double, 4> expected =
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MakeQuaternion<Order>(kHalfSqrt2, kHalfSqrt2, 0.0, 0.0);
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AngleAxisToQuaternion<Order>(axis_angle, quaternion);
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EXPECT_THAT(quaternion, IsNormalizedQuaternion());
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EXPECT_THAT(quaternion, IsNearQuaternion(expected));
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}
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// Transforms a unit quaternion to an axis angle.
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TYPED_TEST(QuaternionTest, UnitQuaternionToAngleAxis) {
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using Order = TypeParam;
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const std::array<double, 4> quaternion =
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MakeQuaternion<Order>(1.0, 0.0, 0.0, 0.0);
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double axis_angle[3];
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double expected[3] = {0, 0, 0};
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QuaternionToAngleAxis<Order>(quaternion.data(), axis_angle);
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EXPECT_THAT(axis_angle, IsNearAngleAxis(expected));
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}
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// Transforms a quaternion that rotates by pi about the Y axis to an axis angle.
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TYPED_TEST(QuaternionTest, YRotationQuaternionToAngleAxis) {
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using Order = TypeParam;
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const std::array<double, 4> quaternion =
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MakeQuaternion<Order>(0.0, 0.0, 1.0, 0.0);
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double axis_angle[3];
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double expected[3] = {0, kPi, 0};
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QuaternionToAngleAxis<Order>(quaternion.data(), axis_angle);
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EXPECT_THAT(axis_angle, IsNearAngleAxis(expected));
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}
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// Transforms a quaternion that rotates by pi/3 about the Z axis to an axis
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// angle.
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TYPED_TEST(QuaternionTest, ZRotationQuaternionToAngleAxis) {
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using Order = TypeParam;
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const std::array<double, 4> quaternion =
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MakeQuaternion<Order>(sqrt(3) / 2, 0.0, 0.0, 0.5);
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double axis_angle[3];
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double expected[3] = {0, 0, kPi / 3};
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QuaternionToAngleAxis<Order>(quaternion.data(), axis_angle);
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EXPECT_THAT(axis_angle, IsNearAngleAxis(expected));
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}
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// Test that exact conversion works for small angles.
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TYPED_TEST(QuaternionTest, SmallQuaternionToAngleAxis) {
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using Order = TypeParam;
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// Small, finite value to test.
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double theta = 1.0e-2;
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const std::array<double, 4> quaternion =
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MakeQuaternion<Order>(cos(theta / 2.0), sin(theta / 2.0), 0.0, 0.0);
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double axis_angle[3];
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double expected[3] = {theta, 0, 0};
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QuaternionToAngleAxis<Order>(quaternion.data(), axis_angle);
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EXPECT_THAT(axis_angle, IsNearAngleAxis(expected));
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}
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// Test that approximate conversion works for very small angles.
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TYPED_TEST(QuaternionTest, TinyQuaternionToAngleAxis) {
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using Order = TypeParam;
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// Very small value that could potentially cause underflow.
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double theta = pow(std::numeric_limits<double>::min(), 0.75);
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const std::array<double, 4> quaternion =
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MakeQuaternion<Order>(cos(theta / 2.0), sin(theta / 2.0), 0.0, 0.0);
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double axis_angle[3];
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double expected[3] = {theta, 0, 0};
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QuaternionToAngleAxis<Order>(quaternion.data(), axis_angle);
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EXPECT_THAT(axis_angle, IsNearAngleAxis(expected));
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}
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TYPED_TEST(QuaternionTest, QuaternionToAngleAxisAngleIsLessThanPi) {
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using Order = TypeParam;
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double angle_axis[3];
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const double half_theta = 0.75 * kPi;
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const std::array<double, 4> quaternion =
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MakeQuaternion<Order>(cos(half_theta), 1.0 * sin(half_theta), 0.0, 0.0);
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QuaternionToAngleAxis<Order>(quaternion.data(), angle_axis);
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const double angle = std::hypot(angle_axis[0], angle_axis[1], angle_axis[2]);
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EXPECT_LE(angle, kPi);
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}
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static constexpr int kNumTrials = 10000;
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// Takes a bunch of random axis/angle values, converts them to quaternions,
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// and back again.
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TYPED_TEST(QuaternionTest, AngleAxisToQuaterionAndBack) {
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using Order = TypeParam;
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std::mt19937 prng;
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std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0};
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for (int i = 0; i < kNumTrials; i++) {
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double axis_angle[3];
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// Make an axis by choosing three random numbers in [-1, 1) and
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// normalizing.
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double norm = 0;
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for (double& coeff : axis_angle) {
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coeff = uniform_distribution(prng);
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norm += coeff * coeff;
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}
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norm = sqrt(norm);
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// Angle in [-pi, pi).
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double theta = uniform_distribution(
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prng, std::uniform_real_distribution<double>::param_type{-kPi, kPi});
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for (double& coeff : axis_angle) {
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coeff = coeff * theta / norm;
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}
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double quaternion[4];
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double round_trip[3];
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// We use ASSERTs here because if there's one failure, there are
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// probably many and spewing a million failures doesn't make anyone's
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// day.
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AngleAxisToQuaternion<Order>(axis_angle, quaternion);
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ASSERT_THAT(quaternion, IsNormalizedQuaternion());
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QuaternionToAngleAxis<Order>(quaternion, round_trip);
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ASSERT_THAT(round_trip, IsNearAngleAxis(axis_angle));
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}
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}
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// Takes a bunch of random quaternions, converts them to axis/angle,
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// and back again.
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TYPED_TEST(QuaternionTest, QuaterionToAngleAxisAndBack) {
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using Order = TypeParam;
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std::mt19937 prng;
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std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0};
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for (int i = 0; i < kNumTrials; i++) {
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double quaternion[4];
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// Choose four random numbers in [-1, 1) and normalize.
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double norm = 0;
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for (double& coeff : quaternion) {
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coeff = uniform_distribution(prng);
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norm += coeff * coeff;
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}
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norm = sqrt(norm);
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for (double& coeff : quaternion) {
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coeff = coeff / norm;
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}
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double axis_angle[3];
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double round_trip[4];
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QuaternionToAngleAxis<Order>(quaternion, axis_angle);
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AngleAxisToQuaternion<Order>(axis_angle, round_trip);
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ASSERT_THAT(round_trip, IsNormalizedQuaternion());
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ASSERT_THAT(round_trip, IsNearQuaternion(quaternion));
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}
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}
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// Transforms a zero axis/angle to a rotation matrix.
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TEST(Rotation, ZeroAngleAxisToRotationMatrix) {
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double axis_angle[3] = {0, 0, 0};
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double matrix[9];
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double expected[9] = {1, 0, 0, 0, 1, 0, 0, 0, 1};
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AngleAxisToRotationMatrix(axis_angle, matrix);
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EXPECT_THAT(matrix, IsOrthonormal());
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EXPECT_THAT(matrix, IsNear3x3Matrix(expected));
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}
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TEST(Rotation, NearZeroAngleAxisToRotationMatrix) {
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double axis_angle[3] = {1e-24, 2e-24, 3e-24};
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double matrix[9];
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double expected[9] = {1, 0, 0, 0, 1, 0, 0, 0, 1};
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AngleAxisToRotationMatrix(axis_angle, matrix);
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EXPECT_THAT(matrix, IsOrthonormal());
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EXPECT_THAT(matrix, IsNear3x3Matrix(expected));
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}
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// Transforms a rotation by pi/2 around X to a rotation matrix and back.
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TEST(Rotation, XRotationToRotationMatrix) {
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double axis_angle[3] = {kPi / 2, 0, 0};
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double matrix[9];
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// The rotation matrices are stored column-major.
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double expected[9] = {1, 0, 0, 0, 0, 1, 0, -1, 0};
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AngleAxisToRotationMatrix(axis_angle, matrix);
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EXPECT_THAT(matrix, IsOrthonormal());
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EXPECT_THAT(matrix, IsNear3x3Matrix(expected));
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double round_trip[3];
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RotationMatrixToAngleAxis(matrix, round_trip);
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EXPECT_THAT(round_trip, IsNearAngleAxis(axis_angle));
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}
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// Transforms an axis angle that rotates by pi about the Y axis to a
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// rotation matrix and back.
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TEST(Rotation, YRotationToRotationMatrix) {
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double axis_angle[3] = {0, kPi, 0};
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double matrix[9];
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double expected[9] = {-1, 0, 0, 0, 1, 0, 0, 0, -1};
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AngleAxisToRotationMatrix(axis_angle, matrix);
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EXPECT_THAT(matrix, IsOrthonormal());
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EXPECT_THAT(matrix, IsNear3x3Matrix(expected));
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double round_trip[3];
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RotationMatrixToAngleAxis(matrix, round_trip);
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EXPECT_THAT(round_trip, IsNearAngleAxis(axis_angle));
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}
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TEST(Rotation, NearPiAngleAxisRoundTrip) {
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double in_axis_angle[3];
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double matrix[9];
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double out_axis_angle[3];
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std::mt19937 prng;
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std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0};
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|
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) {
|
|
absl::StrAppendFormat(&line, "%g ", kMatrix[i][j]);
|
|
}
|
|
line += " | ";
|
|
for (int j = 0; j < 3; ++j) {
|
|
absl::StrAppendFormat(&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.
|
|
TYPED_TEST(QuaternionTest, SmallAngleAxisToQuaternionForJets) {
|
|
using Order = TypeParam;
|
|
// 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];
|
|
const std::array<J3, 4> expected =
|
|
MakeQuaternion<Order>(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<Order>(axis_angle, quaternion);
|
|
EXPECT_THAT(quaternion, testing::Pointwise(JetClose(kTolerance), expected));
|
|
}
|
|
}
|
|
|
|
// Test that conversion works for very small angles when jets are used.
|
|
TYPED_TEST(QuaternionTest, TinyAngleAxisToQuaternionForJets) {
|
|
using Order = TypeParam;
|
|
// 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.
|
|
const std::array<J3, 4> expected =
|
|
MakeQuaternion<Order>(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<Order>(axis_angle, quaternion);
|
|
EXPECT_THAT(quaternion, testing::Pointwise(JetClose(kTolerance), expected));
|
|
}
|
|
}
|
|
|
|
// Test that derivatives are correct for zero rotation.
|
|
TYPED_TEST(QuaternionTest, ZeroAngleAxisToQuaternionForJets) {
|
|
using Order = TypeParam;
|
|
J3 axis_angle[3] = {J3(0, 0), J3(0, 1), J3(0, 2)};
|
|
J3 quaternion[4];
|
|
const std::array<J3, 4> expected =
|
|
MakeQuaternion<Order>(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<Order>(axis_angle, quaternion);
|
|
EXPECT_THAT(quaternion, testing::Pointwise(JetClose(kTolerance), expected));
|
|
}
|
|
|
|
// Test that exact conversion works for small angles.
|
|
TYPED_TEST(QuaternionTest, SmallQuaternionToAngleAxisForJets) {
|
|
using Order = TypeParam;
|
|
// 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);
|
|
const std::array<J4, 4> quaternion =
|
|
MakeQuaternion<Order>(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<Order>(quaternion.data(), axis_angle);
|
|
EXPECT_THAT(axis_angle, testing::Pointwise(JetClose(kTolerance), expected));
|
|
}
|
|
}
|
|
|
|
// Test that conversion works for very small angles.
|
|
TYPED_TEST(QuaternionTest, TinyQuaternionToAngleAxisForJets) {
|
|
using Order = TypeParam;
|
|
// 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);
|
|
const std::array<J4, 4> quaternion =
|
|
MakeQuaternion<Order>(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<Order>(quaternion.data(), axis_angle);
|
|
EXPECT_THAT(axis_angle, testing::Pointwise(JetClose(kTolerance), expected));
|
|
}
|
|
}
|
|
|
|
// Test that conversion works for no rotation.
|
|
TYPED_TEST(QuaternionTest, ZeroQuaternionToAngleAxisForJets) {
|
|
using Order = TypeParam;
|
|
const std::array<J4, 4> quaternion =
|
|
MakeQuaternion<Order>(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<Order>(quaternion.data(), 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));
|
|
}
|
|
}
|
|
|
|
TYPED_TEST(QuaternionTest, RotatePointGivesSameAnswerAsRotationByMatrixCanned) {
|
|
using Order = TypeParam;
|
|
// Canned data generated in octave.
|
|
const std::array<double, 4> q = MakeQuaternion<Order>(+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<Order>(q.data(), Rq[0]);
|
|
ExpectArraysClose(9, Q[0], Rq[0], kTolerance);
|
|
|
|
// Now do the same but compute R with normalization.
|
|
QuaternionToRotation<Order>(q.data(), Rq[0]);
|
|
ExpectArraysClose(9, R[0], Rq[0], kTolerance);
|
|
}
|
|
|
|
TEST(Quaternion, RotatePointGivesSameAnswerForDifferentQuaternionOrders) {
|
|
// Rotation defined by a unit quaternion.
|
|
const std::array<double, 4> q1 =
|
|
MakeQuaternion<CeresQuaternionOrder>(+0.2318160216097109,
|
|
-0.0178430356832060,
|
|
+0.9044300776717159,
|
|
-0.3576998641394597);
|
|
const std::array<double, 4> q2 =
|
|
ConvertQuaternion<EigenQuaternionOrder, CeresQuaternionOrder>(q1);
|
|
|
|
constexpr double p[3] = {
|
|
+0.11,
|
|
-13.15,
|
|
1.17,
|
|
};
|
|
|
|
double result1[3];
|
|
QuaternionRotatePoint<CeresQuaternionOrder>(q1.data(), p, result1);
|
|
|
|
double result2[3];
|
|
QuaternionRotatePoint<EigenQuaternionOrder>(q2.data(), p, result2);
|
|
|
|
ExpectArraysClose(3, result1, result2, kTolerance);
|
|
}
|
|
|
|
TEST(Quaternion, RotatePointGivesSameAnswerForDifferentUnitQuaternionOrders) {
|
|
// Rotation defined by a unit quaternion.
|
|
const std::array<double, 4> q1 =
|
|
MakeQuaternion<CeresQuaternionOrder>(+0.2318160216097109,
|
|
-0.0178430356832060,
|
|
+0.9044300776717159,
|
|
-0.3576998641394597);
|
|
const std::array<double, 4> q2 =
|
|
ConvertQuaternion<EigenQuaternionOrder, CeresQuaternionOrder>(q1);
|
|
|
|
constexpr double p[3] = {
|
|
+0.11,
|
|
-13.15,
|
|
1.17,
|
|
};
|
|
|
|
double result1[3];
|
|
UnitQuaternionRotatePoint<CeresQuaternionOrder>(q1.data(), p, result1);
|
|
|
|
double result2[3];
|
|
UnitQuaternionRotatePoint<EigenQuaternionOrder>(q2.data(), p, result2);
|
|
|
|
ExpectArraysClose(3, result1, result2, kTolerance);
|
|
}
|
|
|
|
TYPED_TEST(QuaternionTest, RotatePointGivesSameAnswerAsRotationByMatrix) {
|
|
using Order = TypeParam;
|
|
// Rotation defined by a unit quaternion.
|
|
const std::array<double, 4> q = MakeQuaternion<Order>(+0.2318160216097109,
|
|
-0.0178430356832060,
|
|
+0.9044300776717159,
|
|
-0.3576998641394597);
|
|
double const p[3] = {
|
|
+0.11,
|
|
-13.15,
|
|
1.17,
|
|
};
|
|
|
|
double R[3 * 3];
|
|
QuaternionToRotation<Order>(q.data(), R);
|
|
|
|
double result1[3];
|
|
UnitQuaternionRotatePoint<Order>(q.data(), 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).
|
|
TYPED_TEST(QuaternionTest, MultiplicationIsAssociative) {
|
|
using Order = TypeParam;
|
|
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<Order>(a, b, ab);
|
|
QuaternionProduct<Order>(ab, c, ab_c);
|
|
|
|
double bc[4];
|
|
double a_bc[4];
|
|
QuaternionProduct<Order>(b, c, bc);
|
|
QuaternionProduct<Order>(a, bc, a_bc);
|
|
|
|
ASSERT_NEAR(ab_c[Order::kW], a_bc[Order::kW], kTolerance);
|
|
ASSERT_NEAR(ab_c[Order::kX], a_bc[Order::kX], kTolerance);
|
|
ASSERT_NEAR(ab_c[Order::kY], a_bc[Order::kY], kTolerance);
|
|
ASSERT_NEAR(ab_c[Order::kZ], a_bc[Order::kZ], kTolerance);
|
|
}
|
|
|
|
TYPED_TEST(QuaternionTest, UnitConjugationIdentity) {
|
|
using Order = TypeParam;
|
|
std::mt19937 prng;
|
|
std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0};
|
|
double a[4];
|
|
for (int i = 0; i < 4; ++i) {
|
|
a[i] = uniform_distribution(prng);
|
|
}
|
|
Eigen::Map<Eigen::Vector4d>{a}.normalize();
|
|
double b[4];
|
|
QuaternionConjugate<Order>(a, b);
|
|
double c[4];
|
|
QuaternionProduct<Order>(a, b, c);
|
|
|
|
EXPECT_NEAR(c[Order::kW], 1, kTolerance);
|
|
EXPECT_NEAR(c[Order::kX], 0, kTolerance);
|
|
EXPECT_NEAR(c[Order::kY], 0, kTolerance);
|
|
EXPECT_NEAR(c[Order::kZ], 0, 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];
|
|
|
|
// Rotate point and write the result to a different and the same
|
|
// destination
|
|
for (double* const dst : {angle_axis_rotated_p, angle_axis}) {
|
|
AngleAxisRotatePoint(angle_axis, p, dst);
|
|
for (int k = 0; k < 3; ++k) {
|
|
// clang-format off
|
|
EXPECT_NEAR(rotation_matrix_rotated_p[k],
|
|
dst[k],
|
|
kTolerance) << "p: " << p[0]
|
|
<< " " << p[1]
|
|
<< " " << p[2]
|
|
<< " angle_axis: " << angle_axis[0]
|
|
<< " " << angle_axis[1]
|
|
<< " " << angle_axis[2];
|
|
// clang-format on
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
TYPED_TEST(QuaternionTest, UnitQuaternion) {
|
|
using Order = TypeParam;
|
|
using Jet = ceres::Jet<double, 4>;
|
|
const std::array<Jet, 4> quaternion =
|
|
MakeQuaternion<Order>(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<Order>(
|
|
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];
|
|
|
|
// Rotate point and write the result to a different and the same
|
|
// destination
|
|
for (double* const dst : {angle_axis_rotated_p, angle_axis}) {
|
|
AngleAxisRotatePoint(angle_axis, p, dst);
|
|
for (int k = 0; k < 3; ++k) {
|
|
// clang-format off
|
|
EXPECT_NEAR(rotation_matrix_rotated_p[k],
|
|
dst[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};
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|
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
|