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-// Ceres Solver - A fast non-linear least squares minimizer
-// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
-// http://code.google.com/p/ceres-solver/
-//
-// Redistribution and use in source and binary forms, with or without
-// modification, are permitted provided that the following conditions are met:
-//
-// * Redistributions of source code must retain the above copyright notice,
-// this list of conditions and the following disclaimer.
-// * Redistributions in binary form must reproduce the above copyright notice,
-// this list of conditions and the following disclaimer in the documentation
-// and/or other materials provided with the distribution.
-// * Neither the name of Google Inc. nor the names of its contributors may be
-// used to endorse or promote products derived from this software without
-// specific prior written permission.
-//
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
-// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
-// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
-// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
-// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
-// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
-// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
-// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
-// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
-// POSSIBILITY OF SUCH DAMAGE.
-//
-// Author: keir@google.com (Keir Mierle)
-//
-// Tests the use of Cere's Jet type with the quaternions found in util/math/. In
-// theory, the unittests for the quaternion class should be type parameterized
-// to make for easier testing of instantiations of the quaternion class, but it
-// is not so, and not obviously worth the work to make the switch at this time.
-
-#include "base/stringprintf.h"
-#include "gtest/gtest.h"
-#include "util/math/mathlimits.h"
-#include "util/math/matrix3x3.h"
-#include "util/math/quaternion.h"
-#include "util/math/vector3.h"
-#include "ceres/test_util.h"
-#include "ceres/jet.h"
-#include "ceres/jet_traits.h"
-
-namespace ceres {
-namespace internal {
-
-// Use a 4-element derivative to simulate the case where each of the
-// quaternion elements are derivative parameters.
-typedef Jet<double, 4> J;
-
-struct JetTraitsTest : public ::testing::Test {
- protected:
- JetTraitsTest()
- : a(J(1.1, 0), J(2.1, 1), J(3.1, 2), J(4.1, 3)),
- b(J(0.1, 0), J(1.1, 1), J(2.1, 2), J(5.0, 3)),
- double_a(a[0].a, a[1].a, a[2].a, a[3].a),
- double_b(b[0].a, b[1].a, b[2].a, b[3].a) {
- // The quaternions should be valid rotations, so normalize them.
- a.Normalize();
- b.Normalize();
- double_a.Normalize();
- double_b.Normalize();
- }
-
- virtual ~JetTraitsTest() {}
-
- // A couple of arbitrary normalized quaternions.
- Quaternion<J> a, b;
-
- // The equivalent of a, b but in scalar form.
- Quaternion<double> double_a, double_b;
-};
-
-// Compare scalar multiplication to jet multiplication. Ignores derivatives.
-TEST_F(JetTraitsTest, QuaternionScalarMultiplicationWorks) {
- Quaternion<J> c = a * b;
- Quaternion<double> double_c = double_a * double_b;
-
- for (int i = 0; i < 4; ++i) {
- EXPECT_EQ(double_c[i], c[i].a);
- }
-}
-
-// Compare scalar slerp to jet slerp. Ignores derivatives.
-TEST_F(JetTraitsTest, QuaternionScalarSlerpWorks) {
- const J fraction(0.1);
- Quaternion<J> c = Quaternion<J>::Slerp(a, b, fraction);
- Quaternion<double> double_c =
- Quaternion<double>::Slerp(double_a, double_b, fraction.a);
-
- for (int i = 0; i < 4; ++i) {
- EXPECT_EQ(double_c[i], c[i].a);
- }
-}
-
-// On a 32-bit optimized build, the mismatch is about 1.4e-14.
-double const kTolerance = 1e-13;
-
-void ExpectJetsClose(const J &x, const J &y) {
- ExpectClose(x.a, y.a, kTolerance);
- ExpectClose(x.v[0], y.v[0], kTolerance);
- ExpectClose(x.v[1], y.v[1], kTolerance);
- ExpectClose(x.v[2], y.v[2], kTolerance);
- ExpectClose(x.v[3], y.v[3], kTolerance);
-}
-
-void ExpectQuaternionsClose(const Quaternion<J>& x, const Quaternion<J>& y) {
- for (int i = 0; i < 4; ++i) {
- ExpectJetsClose(x[i], y[i]);
- }
-}
-
-// Compare jet slurp to jet slerp using identies, checking derivatives.
-TEST_F(JetTraitsTest, CheckSlerpIdentitiesWithNontrivialDerivatives) {
- // Do a slerp to 0.75 directly.
- Quaternion<J> direct = Quaternion<J>::Slerp(a, b, J(0.75));
-
- // Now go part way twice, in theory ending at the same place.
- Quaternion<J> intermediate = Quaternion<J>::Slerp(a, b, J(0.5));
- Quaternion<J> indirect = Quaternion<J>::Slerp(intermediate, b, J(0.5));
-
- // Check that the destination is the same, including derivatives.
- ExpectQuaternionsClose(direct, indirect);
-}
-
-TEST_F(JetTraitsTest, CheckAxisAngleIsInvertibleWithNontrivialDerivatives) {
- Vector3<J> axis;
- J angle;
- a.GetAxisAngle(&axis, &angle);
- b.SetFromAxisAngle(axis, angle);
-
- ExpectQuaternionsClose(a, b);
-}
-
-TEST_F(JetTraitsTest,
- CheckRotationMatrixIsInvertibleWithNontrivialDerivatives) {
- Vector3<J> axis;
- J angle;
- Matrix3x3<J> R;
- a.ToRotationMatrix(&R);
- b.SetFromRotationMatrix(R);
-
- ExpectQuaternionsClose(a, b);
-}
-
-// This doesn't check correctnenss, only that the instantiation compiles.
-TEST_F(JetTraitsTest, CheckRotationBetweenIsCompilable) {
- // Get two arbitrary vectors x and y.
- Vector3<J> x, y;
- J ignored_angle;
- a.GetAxisAngle(&x, &ignored_angle);
- b.GetAxisAngle(&y, &ignored_angle);
-
- Quaternion<J> between_x_and_y = Quaternion<J>::RotationBetween(x, y);
-
- // Prevent optimizing this away.
- EXPECT_NE(between_x_and_y[0].a, 0.0);
-}
-
-TEST_F(JetTraitsTest, CheckRotatedWorksAsExpected) {
- // Get two arbitrary vectors x and y.
- Vector3<J> x;
- J ignored_angle;
- a.GetAxisAngle(&x, &ignored_angle);
-
- // Rotate via a quaternion.
- Vector3<J> y = b.Rotated(x);
-
- // Rotate via a rotation matrix.
- Matrix3x3<J> R;
- b.ToRotationMatrix(&R);
- Vector3<J> yp = R * x;
-
- ExpectJetsClose(yp[0], y[0]);
- ExpectJetsClose(yp[1], y[1]);
- ExpectJetsClose(yp[2], y[2]);
-}
-
-TEST_F(JetTraitsTest, CheckRotatedWorksAsExpectedWithDoubles) {
- // Get two arbitrary vectors x and y.
- Vector3<double> x;
- double ignored_angle;
- double_a.GetAxisAngle(&x, &ignored_angle);
-
- // Rotate via a quaternion.
- Vector3<double> y = double_b.Rotated(x);
-
- // Rotate via a rotation matrix.
- Matrix3x3<double> R;
- double_b.ToRotationMatrix(&R);
- Vector3<double> yp = R * x;
-
- ExpectClose(yp[0], y[0], kTolerance);
- ExpectClose(yp[1], y[1], kTolerance);
- ExpectClose(yp[2], y[2], kTolerance);
-}
-
-} // namespace internal
-} // namespace ceres