// // Lol Engine // // Copyright: (c) 2010-2012 Sam Hocevar // This program is free software; you can redistribute it and/or // modify it under the terms of the Do What The Fuck You Want To // Public License, Version 2, as published by Sam Hocevar. See // http://sam.zoy.org/projects/COPYING.WTFPL for more details. // #if defined HAVE_CONFIG_H # include "config.h" #endif #include "core.h" #include "lol/unit.h" namespace lol { LOLUNIT_FIXTURE(RotationTest) { void SetUp() {} void TearDown() {} LOLUNIT_TEST(Rotate2D) { /* Rotations must be CCW */ mat2 m90 = mat2::rotate(90.f); vec2 a(2.f, 3.f); vec2 b = m90 * a; LOLUNIT_ASSERT_DOUBLES_EQUAL(b.x, -a.y, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(b.y, a.x, 1e-5); float d = determinant(m90); LOLUNIT_ASSERT_DOUBLES_EQUAL(d, 1.0, 1e-5); } LOLUNIT_TEST(Compose2D) { /* Rotating 20 degrees twice must equal rotating 40 degrees */ mat2 m20 = mat2::rotate(20.f); mat2 m40 = mat2::rotate(40.f); mat2 m20x20 = m20 * m20; LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[0][0], m40[0][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[1][0], m40[1][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[0][1], m40[0][1], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[1][1], m40[1][1], 1e-5); } LOLUNIT_TEST(Rotate3D) { /* Rotations must be CCW along each axis */ mat3 m90x = mat3::rotate(90.f, 1.f, 0.f, 0.f); mat3 m90y = mat3::rotate(90.f, 0.f, 1.f, 0.f); mat3 m90z = mat3::rotate(90.f, 0.f, 0.f, 1.f); vec3 a(2.f, 3.f, 4.f); vec3 b = m90x * a; vec3 c = m90y * a; vec3 d = m90z * a; LOLUNIT_ASSERT_DOUBLES_EQUAL(b.x, a.x, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(b.y, -a.z, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(b.z, a.y, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(c.x, a.z, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(c.y, a.y, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(c.z, -a.x, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(d.x, -a.y, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(d.y, a.x, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(d.z, a.z, 1e-5); float dx = determinant(m90x); float dy = determinant(m90y); float dz = determinant(m90z); LOLUNIT_ASSERT_DOUBLES_EQUAL(dx, 1.0, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(dy, 1.0, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(dz, 1.0, 1e-5); } LOLUNIT_TEST(Compose3D) { /* Rotating 20 degrees twice must equal rotating 40 degrees */ mat3 m20 = mat3::rotate(20.f, 1.f, 2.f, 3.f); mat3 m40 = mat3::rotate(40.f, 1.f, 2.f, 3.f); mat3 m20x20 = m20 * m20; LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[0][0], m40[0][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[1][0], m40[1][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[2][0], m40[2][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[0][1], m40[0][1], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[1][1], m40[1][1], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[2][1], m40[2][1], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[0][2], m40[0][2], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[1][2], m40[1][2], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[2][2], m40[2][2], 1e-5); } LOLUNIT_TEST(QuaternionTransform) { /* Rotating using a quaternion must equal rotating using a matrix */ mat3 m20 = mat3::rotate(20.f, 1.f, 2.f, 3.f); quat q20 = quat::rotate(20.f, 1.f, 2.f, 3.f); vec3 a(-2.f, 4.f, 3.f); vec3 b = m20 * a; vec3 c = q20.transform(a); LOLUNIT_ASSERT_DOUBLES_EQUAL(c.x, b.x, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(c.y, b.y, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(c.z, b.z, 1e-5); float n = norm(q20); LOLUNIT_ASSERT_DOUBLES_EQUAL(n, 1.0, 1e-5); } LOLUNIT_TEST(QuaternionFromMatrix) { /* A rotation matrix converted to a quaternion should match the * quaternion built with the same parameters */ quat q1 = quat::rotate(20.f, 1.f, 2.f, 3.f); quat q2 = quat(mat3::rotate(20.f, 1.f, 2.f, 3.f)); LOLUNIT_ASSERT_DOUBLES_EQUAL(q2.w, q1.w, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(q2.x, q1.x, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(q2.y, q1.y, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(q2.z, q1.z, 1e-5); float n1 = norm(q1); float n2 = norm(q2); LOLUNIT_ASSERT_DOUBLES_EQUAL(n1, 1.0, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(n2, 1.0, 1e-5); } LOLUNIT_TEST(MatrixFromQuaternion) { /* A quaternion converted to a rotation matrix should match the * rotation matrix built with the same parameters */ mat3 m1 = mat3::rotate(60.f, 1.f, -2.f, 3.f); mat3 m2 = mat3(quat::rotate(60.f, 1.f, -2.f, 3.f)); LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[0][0], m1[0][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[1][0], m1[1][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[2][0], m1[2][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[0][1], m1[0][1], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[1][1], m1[1][1], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[2][1], m1[2][1], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[0][2], m1[0][2], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[1][2], m1[1][2], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[2][2], m1[2][2], 1e-5); float d1 = determinant(m1); float d2 = determinant(m2); LOLUNIT_ASSERT_DOUBLES_EQUAL(d1, 1.0, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(d2, 1.0, 1e-5); } LOLUNIT_TEST(MatrixCompositionThroughQuaternions) { /* Combining two rotation matrices should match the matrix created * from the combination of the two equivalent quaternions */ mat3 m1 = mat3::rotate(60.f, 1.f, -2.f, 3.f); mat3 m2 = mat3::rotate(20.f, -3.f, 1.f, -3.f); mat3 m3 = m2 * m1; mat3 m4(quat(m2) * quat(m1)); LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[0][0], m3[0][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[1][0], m3[1][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[2][0], m3[2][0], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[0][1], m3[0][1], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[1][1], m3[1][1], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[2][1], m3[2][1], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[0][2], m3[0][2], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[1][2], m3[1][2], 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[2][2], m3[2][2], 1e-5); } LOLUNIT_TEST(QuaternionCompositionThroughMatrices) { /* Combining two quaternions should match the quaternion created * from the combination of the two equivalent rotation matrices */ quat q1 = quat::rotate(60.f, 1.f, -2.f, 3.f); quat q2 = quat::rotate(20.f, -3.f, 1.f, -2.f); quat q3 = q2 * q1; quat q4(mat3(q2) * mat3(q1)); LOLUNIT_ASSERT_DOUBLES_EQUAL(q4.w, q3.w, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(q4.x, q3.x, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(q4.y, q3.y, 1e-5); LOLUNIT_ASSERT_DOUBLES_EQUAL(q4.z, q3.z, 1e-5); } }; } /* namespace lol */