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lol/test/unit/rotation.cpp

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  1. //

  2. // Lol Engine

  3. //

  4. // Copyright: (c) 2010-2012 Sam Hocevar <sam@hocevar.net>

  5. //   This program is free software; you can redistribute it and/or

  6. //   modify it under the terms of the Do What The Fuck You Want To

  7. //   Public License, Version 2, as published by Sam Hocevar. See

  8. //   http://sam.zoy.org/projects/COPYING.WTFPL for more details.

  9. //

  10. 

  11. #if defined HAVE_CONFIG_H

  12. #   include "config.h"

  13. #endif

  14. 

  15. #include "core.h"

  16. #include "lol/unit.h"

  17. 

  18. namespace lol

  19. {

  20. 

  21. LOLUNIT_FIXTURE(RotationTest)

  22. {

  23.     void SetUp() {}

  24. 

  25.     void TearDown() {}

  26. 

  27.     LOLUNIT_TEST(Rotate2D)

  28.     {

  29.         /* Rotations must be CCW */

  30.         mat2 m90 = mat2::rotate(90.f);

  31. 

  32.         vec2 a(2.f, 3.f);

  33.         vec2 b = m90 * a;

  34. 

  35.         LOLUNIT_ASSERT_DOUBLES_EQUAL(b.x, -a.y, 1e-5);

  36.         LOLUNIT_ASSERT_DOUBLES_EQUAL(b.y,  a.x, 1e-5);

  37. 

  38.         float d = determinant(m90);

  39. 

  40.         LOLUNIT_ASSERT_DOUBLES_EQUAL(d, 1.0, 1e-5);

  41.     }

  42. 

  43.     LOLUNIT_TEST(Compose2D)

  44.     {

  45.         /* Rotating 20 degrees twice must equal rotating 40 degrees */

  46.         mat2 m20 = mat2::rotate(20.f);

  47.         mat2 m40 = mat2::rotate(40.f);

  48.         mat2 m20x20 = m20 * m20;

  49. 

  50.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[0][0], m40[0][0], 1e-5);

  51.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[1][0], m40[1][0], 1e-5);

  52. 

  53.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[0][1], m40[0][1], 1e-5);

  54.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[1][1], m40[1][1], 1e-5);

  55.     }

  56. 

  57.     LOLUNIT_TEST(Rotate3D)

  58.     {

  59.         /* Rotations must be CCW along each axis */

  60.         mat3 m90x = mat3::rotate(90.f, 1.f, 0.f, 0.f);

  61.         mat3 m90y = mat3::rotate(90.f, 0.f, 1.f, 0.f);

  62.         mat3 m90z = mat3::rotate(90.f, 0.f, 0.f, 1.f);

  63. 

  64.         vec3 a(2.f, 3.f, 4.f);

  65.         vec3 b = m90x * a;

  66.         vec3 c = m90y * a;

  67.         vec3 d = m90z * a;

  68. 

  69.         LOLUNIT_ASSERT_DOUBLES_EQUAL(b.x,  a.x, 1e-5);

  70.         LOLUNIT_ASSERT_DOUBLES_EQUAL(b.y, -a.z, 1e-5);

  71.         LOLUNIT_ASSERT_DOUBLES_EQUAL(b.z,  a.y, 1e-5);

  72. 

  73.         LOLUNIT_ASSERT_DOUBLES_EQUAL(c.x,  a.z, 1e-5);

  74.         LOLUNIT_ASSERT_DOUBLES_EQUAL(c.y,  a.y, 1e-5);

  75.         LOLUNIT_ASSERT_DOUBLES_EQUAL(c.z, -a.x, 1e-5);

  76. 

  77.         LOLUNIT_ASSERT_DOUBLES_EQUAL(d.x, -a.y, 1e-5);

  78.         LOLUNIT_ASSERT_DOUBLES_EQUAL(d.y,  a.x, 1e-5);

  79.         LOLUNIT_ASSERT_DOUBLES_EQUAL(d.z,  a.z, 1e-5);

  80. 

  81.         float dx = determinant(m90x);

  82.         float dy = determinant(m90y);

  83.         float dz = determinant(m90z);

  84. 

  85.         LOLUNIT_ASSERT_DOUBLES_EQUAL(dx, 1.0, 1e-5);

  86.         LOLUNIT_ASSERT_DOUBLES_EQUAL(dy, 1.0, 1e-5);

  87.         LOLUNIT_ASSERT_DOUBLES_EQUAL(dz, 1.0, 1e-5);

  88.     }

  89. 

  90.     LOLUNIT_TEST(Compose3D)

  91.     {

  92.         /* Rotating 20 degrees twice must equal rotating 40 degrees */

  93.         mat3 m20 = mat3::rotate(20.f, 1.f, 2.f, 3.f);

  94.         mat3 m40 = mat3::rotate(40.f, 1.f, 2.f, 3.f);

  95.         mat3 m20x20 = m20 * m20;

  96. 

  97.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[0][0], m40[0][0], 1e-5);

  98.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[1][0], m40[1][0], 1e-5);

  99.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[2][0], m40[2][0], 1e-5);

  100. 

  101.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[0][1], m40[0][1], 1e-5);

  102.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[1][1], m40[1][1], 1e-5);

  103.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[2][1], m40[2][1], 1e-5);

  104. 

  105.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[0][2], m40[0][2], 1e-5);

  106.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[1][2], m40[1][2], 1e-5);

  107.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m20x20[2][2], m40[2][2], 1e-5);

  108.     }

  109. 

  110.     LOLUNIT_TEST(QuaternionTransform)

  111.     {

  112.         /* Rotating using a quaternion must equal rotating using a matrix */

  113.         mat3 m20 = mat3::rotate(20.f, 1.f, 2.f, 3.f);

  114.         quat q20 = quat::rotate(20.f, 1.f, 2.f, 3.f);

  115.         vec3 a(-2.f, 4.f, 3.f);

  116. 

  117.         vec3 b = m20 * a;

  118.         vec3 c = q20.transform(a);

  119. 

  120.         LOLUNIT_ASSERT_DOUBLES_EQUAL(c.x, b.x, 1e-5);

  121.         LOLUNIT_ASSERT_DOUBLES_EQUAL(c.y, b.y, 1e-5);

  122.         LOLUNIT_ASSERT_DOUBLES_EQUAL(c.z, b.z, 1e-5);

  123. 

  124.         float n = norm(q20);

  125. 

  126.         LOLUNIT_ASSERT_DOUBLES_EQUAL(n, 1.0, 1e-5);

  127.     }

  128. 

  129.     LOLUNIT_TEST(QuaternionFromMatrix)

  130.     {

  131.         /* A rotation matrix converted to a quaternion should match the

  132.          * quaternion built with the same parameters */

  133.         quat q1 = quat::rotate(20.f, 1.f, 2.f, 3.f);

  134.         quat q2 = quat(mat3::rotate(20.f, 1.f, 2.f, 3.f));

  135. 

  136.         LOLUNIT_ASSERT_DOUBLES_EQUAL(q2.w, q1.w, 1e-5);

  137.         LOLUNIT_ASSERT_DOUBLES_EQUAL(q2.x, q1.x, 1e-5);

  138.         LOLUNIT_ASSERT_DOUBLES_EQUAL(q2.y, q1.y, 1e-5);

  139.         LOLUNIT_ASSERT_DOUBLES_EQUAL(q2.z, q1.z, 1e-5);

  140. 

  141.         float n1 = norm(q1);

  142.         float n2 = norm(q2);

  143. 

  144.         LOLUNIT_ASSERT_DOUBLES_EQUAL(n1, 1.0, 1e-5);

  145.         LOLUNIT_ASSERT_DOUBLES_EQUAL(n2, 1.0, 1e-5);

  146.     }

  147. 

  148.     LOLUNIT_TEST(MatrixFromQuaternion)

  149.     {

  150.         /* A quaternion converted to a rotation matrix should match the

  151.          * rotation matrix built with the same parameters */

  152.         mat3 m1 = mat3::rotate(60.f, 1.f, -2.f, 3.f);

  153.         mat3 m2 = mat3(quat::rotate(60.f, 1.f, -2.f, 3.f));

  154. 

  155.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[0][0], m1[0][0], 1e-5);

  156.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[1][0], m1[1][0], 1e-5);

  157.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[2][0], m1[2][0], 1e-5);

  158. 

  159.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[0][1], m1[0][1], 1e-5);

  160.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[1][1], m1[1][1], 1e-5);

  161.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[2][1], m1[2][1], 1e-5);

  162. 

  163.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[0][2], m1[0][2], 1e-5);

  164.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[1][2], m1[1][2], 1e-5);

  165.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m2[2][2], m1[2][2], 1e-5);

  166. 

  167.         float d1 = determinant(m1);

  168.         float d2 = determinant(m2);

  169. 

  170.         LOLUNIT_ASSERT_DOUBLES_EQUAL(d1, 1.0, 1e-5);

  171.         LOLUNIT_ASSERT_DOUBLES_EQUAL(d2, 1.0, 1e-5);

  172.     }

  173. 

  174.     LOLUNIT_TEST(MatrixCompositionThroughQuaternions)

  175.     {

  176.         /* Combining two rotation matrices should match the matrix created

  177.          * from the combination of the two equivalent quaternions */

  178.         mat3 m1 = mat3::rotate(60.f, 1.f, -2.f, 3.f);

  179.         mat3 m2 = mat3::rotate(20.f, -3.f, 1.f, -3.f);

  180. 

  181.         mat3 m3 = m2 * m1;

  182.         mat3 m4(quat(m2) * quat(m1));

  183. 

  184.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[0][0], m3[0][0], 1e-5);

  185.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[1][0], m3[1][0], 1e-5);

  186.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[2][0], m3[2][0], 1e-5);

  187. 

  188.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[0][1], m3[0][1], 1e-5);

  189.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[1][1], m3[1][1], 1e-5);

  190.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[2][1], m3[2][1], 1e-5);

  191. 

  192.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[0][2], m3[0][2], 1e-5);

  193.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[1][2], m3[1][2], 1e-5);

  194.         LOLUNIT_ASSERT_DOUBLES_EQUAL(m4[2][2], m3[2][2], 1e-5);

  195.     }

  196. 

  197.     LOLUNIT_TEST(QuaternionCompositionThroughMatrices)

  198.     {

  199.         /* Combining two quaternions should match the quaternion created

  200.          * from the combination of the two equivalent rotation matrices */

  201.         quat q1 = quat::rotate(60.f, 1.f, -2.f, 3.f);

  202.         quat q2 = quat::rotate(20.f, -3.f, 1.f, -2.f);

  203. 

  204.         quat q3 = q2 * q1;

  205.         quat q4(mat3(q2) * mat3(q1));

  206. 

  207.         LOLUNIT_ASSERT_DOUBLES_EQUAL(q4.w, q3.w, 1e-5);

  208.         LOLUNIT_ASSERT_DOUBLES_EQUAL(q4.x, q3.x, 1e-5);

  209.         LOLUNIT_ASSERT_DOUBLES_EQUAL(q4.y, q3.y, 1e-5);

  210.         LOLUNIT_ASSERT_DOUBLES_EQUAL(q4.z, q3.z, 1e-5);

  211.     }

  212. };

  213. 

  214. } /* namespace lol */