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collision_point_depth.cpp

collision_point_depth.cpp 14 KB
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  1. #include <UnitTest++.h>
    2. 

  2. #include <ode/ode.h>
    3. 

  3. #include "common.h"
    4. 

  4. 

  5. TEST(test_collision_sphere_point_depth)
    6. 

  6. {
    7. 

  7.     // Test case: sphere at the origin.
    8. 

  8.     {
    9. 

  9.         const dReal radius = 1;
    10. 

  10.         dGeomID sphere = dCreateSphere(0, radius);
    11. 

  11. 

  12.         dGeomSetPosition(sphere, 0,0,0);
    13. 

  13. 

  14.         // depth at center should equal radius
    15. 

  15.         CHECK_EQUAL(radius, dGeomSpherePointDepth(sphere, 0,0,0));
    16. 

  16. 

  17.         // half-radius depth
    18. 

  18.         CHECK_EQUAL(0.5 * radius, dGeomSpherePointDepth(sphere, 0.5,   0,   0));
    19. 

  19.         CHECK_EQUAL(0.5 * radius, dGeomSpherePointDepth(sphere,   0, 0.5,   0));
    20. 

  20.         CHECK_EQUAL(0.5 * radius, dGeomSpherePointDepth(sphere,   0,   0, 0.5));
    21. 

  21.         CHECK_EQUAL(0.5 * radius, dGeomSpherePointDepth(sphere, -0.5,    0,    0));
    22. 

  22.         CHECK_EQUAL(0.5 * radius, dGeomSpherePointDepth(sphere,    0, -0.5,    0));
    23. 

  23.         CHECK_EQUAL(0.5 * radius, dGeomSpherePointDepth(sphere,    0,    0, -0.5));
    24. 

  24.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere, 0.3, 0.4,   0), 1e-12);
    25. 

  25.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere,   0, 0.3, 0.4), 1e-12);
    26. 

  26.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere, 0.4,   0, 0.3), 1e-12);
    27. 

  27.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere, -0.3,  0.4,    0), 1e-12);
    28. 

  28.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere,    0, -0.3,  0.4), 1e-12);
    29. 

  29.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere,  0.4,    0, -0.3), 1e-12);
    30. 

  30.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere,  0.3, -0.4,    0), 1e-12);
    31. 

  31.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere,    0,  0.3, -0.4), 1e-12);
    32. 

  32.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere, -0.4,    0,  0.3), 1e-12);
    33. 

  33.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere, -0.3, -0.4,    0), 1e-12);
    34. 

  34.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere,    0, -0.3, -0.4), 1e-12);
    35. 

  35.         CHECK_CLOSE(0.5 * radius, dGeomSpherePointDepth(sphere, -0.4,    0, -0.3), 1e-12);
    36. 

  36. 

  37.         // 0.1 radius depth
    38. 

  38.         CHECK_CLOSE(0.1 * radius, dGeomSpherePointDepth(sphere, 0.9,   0,   0), 1e-12);
    39. 

  39.         CHECK_CLOSE(0.1 * radius, dGeomSpherePointDepth(sphere,   0, 0.9,   0), 1e-12);
    40. 

  40.         CHECK_CLOSE(0.1 * radius, dGeomSpherePointDepth(sphere,   0,   0, 0.9), 1e-12);
    41. 

  41.         CHECK_CLOSE(0.1 * radius, dGeomSpherePointDepth(sphere, -0.9,    0,    0), 1e-12);
    42. 

  42.         CHECK_CLOSE(0.1 * radius, dGeomSpherePointDepth(sphere,    0, -0.9,    0), 1e-12);
    43. 

  43.         CHECK_CLOSE(0.1 * radius, dGeomSpherePointDepth(sphere,    0,    0, -0.9), 1e-12);
    44. 

  44. 

  45.         // on surface (zero depth)
    46. 

  46.         CHECK_EQUAL(0, dGeomSpherePointDepth(sphere, 1.0,   0,   0));
    47. 

  47.         CHECK_EQUAL(0, dGeomSpherePointDepth(sphere,   0, 1.0,   0));
    48. 

  48.         CHECK_EQUAL(0, dGeomSpherePointDepth(sphere,   0,   0, 1.0));
    49. 

  49.         CHECK_EQUAL(0, dGeomSpherePointDepth(sphere, -1.0,    0,    0));
    50. 

  50.         CHECK_EQUAL(0, dGeomSpherePointDepth(sphere,    0, -1.0,    0));
    51. 

  51.         CHECK_EQUAL(0, dGeomSpherePointDepth(sphere,    0,    0, -1.0));
    52. 

  52.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere, 0.6, 0.8,   0), 1e-12);
    53. 

  53.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere,   0, 0.6, 0.8), 1e-12);
    54. 

  54.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere, 0.8,   0, 0.6), 1e-12);
    55. 

  55.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere, -0.6,  0.8,    0), 1e-12);
    56. 

  56.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere,    0, -0.6,  0.8), 1e-12);
    57. 

  57.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere,  0.8,    0, -0.6), 1e-12);
    58. 

  58.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere,  0.6, -0.8,    0), 1e-12);
    59. 

  59.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere,    0,  0.6, -0.8), 1e-12);
    60. 

  60.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere, -0.8,    0,  0.6), 1e-12);
    61. 

  61.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere, -0.6, -0.8,    0), 1e-12);
    62. 

  62.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere,    0, -0.6, -0.8), 1e-12);
    63. 

  63.         CHECK_CLOSE(0, dGeomSpherePointDepth(sphere, -0.8,    0, -0.6), 1e-12);
    64. 

  64. 

  65.         // 0.1 radius from surface (negative depth)
    66. 

  66.         CHECK_CLOSE(-0.1 * radius, dGeomSpherePointDepth(sphere, 1.1,   0,   0), 1e-12);
    67. 

  67.         CHECK_CLOSE(-0.1 * radius, dGeomSpherePointDepth(sphere,   0, 1.1,   0), 1e-12);
    68. 

  68.         CHECK_CLOSE(-0.1 * radius, dGeomSpherePointDepth(sphere,   0,   0, 1.1), 1e-12);
    69. 

  69.         CHECK_CLOSE(-0.1 * radius, dGeomSpherePointDepth(sphere, -1.1,    0,    0), 1e-12);
    70. 

  70.         CHECK_CLOSE(-0.1 * radius, dGeomSpherePointDepth(sphere,    0, -1.1,    0), 1e-12);
    71. 

  71.         CHECK_CLOSE(-0.1 * radius, dGeomSpherePointDepth(sphere,    0,    0, -1.1), 1e-12);
    72. 

  72. 

  73.         // half-radius from surface (negative depth)
    74. 

  74.         CHECK_EQUAL(-0.5 * radius, dGeomSpherePointDepth(sphere, 1.5,   0,   0));
    75. 

  75.         CHECK_EQUAL(-0.5 * radius, dGeomSpherePointDepth(sphere,   0, 1.5,   0));
    76. 

  76.         CHECK_EQUAL(-0.5 * radius, dGeomSpherePointDepth(sphere,   0,   0, 1.5));
    77. 

  77.         CHECK_EQUAL(-0.5 * radius, dGeomSpherePointDepth(sphere, -1.5,    0,    0));
    78. 

  78.         CHECK_EQUAL(-0.5 * radius, dGeomSpherePointDepth(sphere,    0, -1.5,    0));
    79. 

  79.         CHECK_EQUAL(-0.5 * radius, dGeomSpherePointDepth(sphere,    0,    0, -1.5));
    80. 

  80.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere, 0.9, 1.2,   0), 1e-12);
    81. 

  81.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere,   0, 0.9, 1.2), 1e-12);
    82. 

  82.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere, 1.2,   0, 0.9), 1e-12);
    83. 

  83.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere, -0.9,  1.2,    0), 1e-12);
    84. 

  84.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere,    0, -0.9,  1.2), 1e-12);
    85. 

  85.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere,  1.2,    0, -0.9), 1e-12);
    86. 

  86.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere,  0.9, -1.2,    0), 1e-12);
    87. 

  87.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere,    0,  0.9, -1.2), 1e-12);
    88. 

  88.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere, -1.2,    0,  0.9), 1e-12);
    89. 

  89.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere, -0.9, -1.2,    0), 1e-12);
    90. 

  90.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere,    0, -0.9, -1.2), 1e-12);
    91. 

  91.         CHECK_CLOSE(-0.5, dGeomSpherePointDepth(sphere, -1.2,    0, -0.9), 1e-12);
    92. 

  92.     }
    93. 

  93. }
    94. 

  94. 

  95. TEST(test_collision_box_point_depth)
    96. 

  96. {
    97. 

  97.     // Test case: cube at the origin.
    98. 

  98.     {
    99. 

  99.         const dReal length = 1;
    100. 

  100.         dGeomID cube = dCreateBox(0, 2*length, 2*length, 2*length);
    101. 

  101. 

  102.         dGeomSetPosition(cube, 0,0,0);
    103. 

  103. 

  104.         // depth at center should equal half length
    105. 

  105.         CHECK_EQUAL(length, dGeomBoxPointDepth(cube, 0,0,0));
    106. 

  106. 

  107.         // half-length depth
    108. 

  108.         CHECK_EQUAL(0.5 * length, dGeomBoxPointDepth(cube, 0.5,   0,   0));
    109. 

  109.         CHECK_EQUAL(0.5 * length, dGeomBoxPointDepth(cube,   0, 0.5,   0));
    110. 

  110.         CHECK_EQUAL(0.5 * length, dGeomBoxPointDepth(cube,   0,   0, 0.5));
    111. 

  111.         CHECK_EQUAL(0.5 * length, dGeomBoxPointDepth(cube, -0.5,    0,    0));
    112. 

  112.         CHECK_EQUAL(0.5 * length, dGeomBoxPointDepth(cube,    0, -0.5,    0));
    113. 

  113.         CHECK_EQUAL(0.5 * length, dGeomBoxPointDepth(cube,    0,    0, -0.5));
    114. 

  114. 

  115.         // closest point 0.6 * length
    116. 

  116.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube, 0.3, 0.4,   0), 1e-12);
    117. 

  117.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube,   0, 0.3, 0.4), 1e-12);
    118. 

  118.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube, 0.4,   0, 0.3), 1e-12);
    119. 

  119.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube, -0.3,  0.4,    0), 1e-12);
    120. 

  120.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube,    0, -0.3,  0.4), 1e-12);
    121. 

  121.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube,  0.4,    0, -0.3), 1e-12);
    122. 

  122.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube,  0.3, -0.4,    0), 1e-12);
    123. 

  123.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube,    0,  0.3, -0.4), 1e-12);
    124. 

  124.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube, -0.4,    0,  0.3), 1e-12);
    125. 

  125.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube, -0.3, -0.4,    0), 1e-12);
    126. 

  126.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube,    0, -0.3, -0.4), 1e-12);
    127. 

  127.         CHECK_CLOSE(0.6 * length, dGeomBoxPointDepth(cube, -0.4,    0, -0.3), 1e-12);
    128. 

  128. 

  129.         // 0.1 length depth
    130. 

  130.         CHECK_CLOSE(0.1 * length, dGeomBoxPointDepth(cube, 0.9,   0,   0), 1e-12);
    131. 

  131.         CHECK_CLOSE(0.1 * length, dGeomBoxPointDepth(cube,   0, 0.9,   0), 1e-12);
    132. 

  132.         CHECK_CLOSE(0.1 * length, dGeomBoxPointDepth(cube,   0,   0, 0.9), 1e-12);
    133. 

  133.         CHECK_CLOSE(0.1 * length, dGeomBoxPointDepth(cube, -0.9,    0,    0), 1e-12);
    134. 

  134.         CHECK_CLOSE(0.1 * length, dGeomBoxPointDepth(cube,    0, -0.9,    0), 1e-12);
    135. 

  135.         CHECK_CLOSE(0.1 * length, dGeomBoxPointDepth(cube,    0,    0, -0.9), 1e-12);
    136. 

  136. 

  137.         // on surface (zero depth)
    138. 

  138.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube, 1.0,   0,   0));
    139. 

  139.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube,   0, 1.0,   0));
    140. 

  140.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube,   0,   0, 1.0));
    141. 

  141.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube, -1.0,    0,    0));
    142. 

  142.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube,    0, -1.0,    0));
    143. 

  143.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube,    0,    0, -1.0));
    144. 

  144.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube, 0.3, 1.0,   0));
    145. 

  145.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube,   0, 0.3, 1.0));
    146. 

  146.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube, 1.0,   0, 0.3));
    147. 

  147.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube, -0.3,  1.0,    0));
    148. 

  148.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube,    0, -0.3,  1.0));
    149. 

  149.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube,  1.0,    0, -0.3));
    150. 

  150.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube,  0.3, -1.0,    0));
    151. 

  151.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube,    0,  0.3, -1.0));
    152. 

  152.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube, -1.0,    0,  0.3));
    153. 

  153.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube, -0.3, -1.0,    0));
    154. 

  154.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube,    0, -0.3, -1.0));
    155. 

  155.         CHECK_EQUAL(0, dGeomBoxPointDepth(cube, -1.0,    0, -0.3));
    156. 

  156. 

  157.         // 0.1 length from surface (negative depth)
    158. 

  158.         CHECK_CLOSE(-0.1 * length, dGeomBoxPointDepth(cube, 1.1,   0,   0), 1e-12);
    159. 

  159.         CHECK_CLOSE(-0.1 * length, dGeomBoxPointDepth(cube,   0, 1.1,   0), 1e-12);
    160. 

  160.         CHECK_CLOSE(-0.1 * length, dGeomBoxPointDepth(cube,   0,   0, 1.1), 1e-12);
    161. 

  161.         CHECK_CLOSE(-0.1 * length, dGeomBoxPointDepth(cube, -1.1,    0,    0), 1e-12);
    162. 

  162.         CHECK_CLOSE(-0.1 * length, dGeomBoxPointDepth(cube,    0, -1.1,    0), 1e-12);
    163. 

  163.         CHECK_CLOSE(-0.1 * length, dGeomBoxPointDepth(cube,    0,    0, -1.1), 1e-12);
    164. 

  164. 

  165.         // half-length from surface face (negative depth)
    166. 

  166.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube, 1.5,   0,   0));
    167. 

  167.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube,   0, 1.5,   0));
    168. 

  168.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube,   0,   0, 1.5));
    169. 

  169.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube, -1.5,    0,    0));
    170. 

  170.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube,    0, -1.5,    0));
    171. 

  171.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube,    0,    0, -1.5));
    172. 

  172.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube, 0.3, 1.5,   0));
    173. 

  173.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube,   0, 0.3, 1.5));
    174. 

  174.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube, 1.5,   0, 0.3));
    175. 

  175.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube, -0.3,  1.5,    0));
    176. 

  176.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube,    0, -0.3,  1.5));
    177. 

  177.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube,  1.5,    0, -0.3));
    178. 

  178.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube,  0.3, -1.5,    0));
    179. 

  179.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube,    0,  0.3, -1.5));
    180. 

  180.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube, -1.5,    0,  0.3));
    181. 

  181.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube, -0.3, -1.5,    0));
    182. 

  182.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube,    0, -0.3, -1.5));
    183. 

  183.         CHECK_EQUAL(-0.5 * length, dGeomBoxPointDepth(cube, -1.5,    0, -0.3));
    184. 

  184.         // half-length from surface edge (negative depth)
    185. 

  185.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube, 1.3, 1.4,   0), 1e-12);
    186. 

  186.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube,   0, 1.3, 1.4), 1e-12);
    187. 

  187.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube, 1.4,   0, 1.3), 1e-12);
    188. 

  188.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube, -1.3,  1.4,    0), 1e-12);
    189. 

  189.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube,    0, -1.3,  1.4), 1e-12);
    190. 

  190.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube,  1.4,    0, -1.3), 1e-12);
    191. 

  191.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube,  1.3, -1.4,    0), 1e-12);
    192. 

  192.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube,    0,  1.3, -1.4), 1e-12);
    193. 

  193.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube, -1.4,    0,  1.3), 1e-12);
    194. 

  194.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube, -1.3, -1.4,    0), 1e-12);
    195. 

  195.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube,    0, -1.3, -1.4), 1e-12);
    196. 

  196.         CHECK_CLOSE(-0.5 * length, dGeomBoxPointDepth(cube, -1.4,    0, -1.3), 1e-12);
    197. 

  197.         // 0.6 length from corner (negative depth)
    198. 

  198.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube, 1.2, 1.4, 1.4), 1e-12);
    199. 

  199.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube, 1.4, 1.2, 1.4), 1e-12);
    200. 

  200.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube, 1.4, 1.4, 1.2), 1e-12);
    201. 

  201.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube, -1.2,  1.4,  1.4), 1e-12);
    202. 

  202.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube,  1.4, -1.2,  1.4), 1e-12);
    203. 

  203.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube,  1.4,  1.4, -1.2), 1e-12);
    204. 

  204.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube,  1.2, -1.4,  1.4), 1e-12);
    205. 

  205.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube,  1.4,  1.2, -1.4), 1e-12);
    206. 

  206.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube, -1.4,  1.4,  1.2), 1e-12);
    207. 

  207.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube, -1.2, -1.4,  1.4), 1e-12);
    208. 

  208.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube,  1.4, -1.2, -1.4), 1e-12);
    209. 

  209.         CHECK_CLOSE(-0.6 * length, dGeomBoxPointDepth(cube, -1.4,  1.4, -1.2), 1e-12);
    210. 

  210.     }
    211. 

  211. }
    212.