libigl_Martin/canonical_quaternions.h

// Define some canonical quaternions for floats and doubles
// A Quaternion, q, is defined here as an arrays of four scalars (x,y,z,w),
// such that q = x*i + y*j + z*k + w
namespace igl
{
#  define SQRT_2_OVER_2 0.707106781f

  // Float versions
  // Identity
  const float IDENTITY_QUAT_F[4] = {0,0,0,1};
  // The following match the Matlab canonical views
  // X point right, Y pointing up and Z point out
  const float XY_PLANE_QUAT_F[4] = {0,0,0,1};
  // X points right, Y points *in* and Z points up
  const float XZ_PLANE_QUAT_F[4] = {-SQRT_2_OVER_2,0,0,SQRT_2_OVER_2};
  // X points out, Y points right, and Z points up
  const float YZ_PLANE_QUAT_F[4] = {-0.5,-0.5,-0.5,0.5};
  const float CANONICAL_VIEW_QUAT_F[][4] = 
    {
      {             0,             0,             0,             1},
      {             0,             0, SQRT_2_OVER_2, SQRT_2_OVER_2},
      {             0,             0,             1,             0},
      {             0,             0, SQRT_2_OVER_2,-SQRT_2_OVER_2},
  
      {             0,            -1,             0,             0},
      {-SQRT_2_OVER_2, SQRT_2_OVER_2,             0,             0},
      {            -1,             0,             0,             0},
      {-SQRT_2_OVER_2,-SQRT_2_OVER_2,             0,             0},
  
      {          -0.5,          -0.5,          -0.5,           0.5},
      {             0,-SQRT_2_OVER_2,             0, SQRT_2_OVER_2},
      {           0.5,          -0.5,           0.5,           0.5},
      { SQRT_2_OVER_2,             0, SQRT_2_OVER_2,             0},
  
      { SQRT_2_OVER_2,             0,-SQRT_2_OVER_2,             0},
      {           0.5,           0.5,          -0.5,           0.5},
      {             0, SQRT_2_OVER_2,             0, SQRT_2_OVER_2},
      {          -0.5,           0.5,           0.5,           0.5},
  
      {             0, SQRT_2_OVER_2, SQRT_2_OVER_2,             0},
      {          -0.5,           0.5,           0.5,          -0.5},
      {-SQRT_2_OVER_2,             0,             0,-SQRT_2_OVER_2},
      {          -0.5,          -0.5,          -0.5,          -0.5},
  
      {-SQRT_2_OVER_2,             0,             0, SQRT_2_OVER_2},
      {          -0.5,          -0.5,           0.5,           0.5},
      {             0,-SQRT_2_OVER_2, SQRT_2_OVER_2,             0},
      {           0.5,          -0.5,           0.5,          -0.5}
    };
  const size_t NUM_CANONICAL_VIEW_QUAT_F = 24;
#  undef SQRT_2_OVER_2

#  define SQRT_2_OVER_2 0.707106781186548f
  // Double versions
  // Identity
  const double IDENTITY_QUAT_D[4] = {0,0,0,1};
  // The following match the Matlab canonical views
  // X point right, Y pointing up and Z point out
  const double XY_PLANE_QUAT_D[4] = {0,0,0,1};
  // X points right, Y points *in* and Z points up
  const double XZ_PLANE_QUAT_D[4] = {-SQRT_2_OVER_2,0,0,SQRT_2_OVER_2};
  // X points out, Y points right, and Z points up
  const double YZ_PLANE_QUAT_D[4] = {-0.5,-0.5,-0.5,0.5};
  const double CANONICAL_VIEW_QUAT_D[][4] = 
    {
      {             0,             0,             0,             1},
      {             0,             0, SQRT_2_OVER_2, SQRT_2_OVER_2},
      {             0,             0,             1,             0},
      {             0,             0, SQRT_2_OVER_2,-SQRT_2_OVER_2},
  
      {             0,            -1,             0,             0},
      {-SQRT_2_OVER_2, SQRT_2_OVER_2,             0,             0},
      {            -1,             0,             0,             0},
      {-SQRT_2_OVER_2,-SQRT_2_OVER_2,             0,             0},
  
      {          -0.5,          -0.5,          -0.5,           0.5},
      {             0,-SQRT_2_OVER_2,             0, SQRT_2_OVER_2},
      {           0.5,          -0.5,           0.5,           0.5},
      { SQRT_2_OVER_2,             0, SQRT_2_OVER_2,             0},
  
      { SQRT_2_OVER_2,             0,-SQRT_2_OVER_2,             0},
      {           0.5,           0.5,          -0.5,           0.5},
      {             0, SQRT_2_OVER_2,             0, SQRT_2_OVER_2},
      {          -0.5,           0.5,           0.5,           0.5},
  
      {             0, SQRT_2_OVER_2, SQRT_2_OVER_2,             0},
      {          -0.5,           0.5,           0.5,          -0.5},
      {-SQRT_2_OVER_2,             0,             0,-SQRT_2_OVER_2},
      {          -0.5,          -0.5,          -0.5,          -0.5},
  
      {-SQRT_2_OVER_2,             0,             0, SQRT_2_OVER_2},
      {          -0.5,          -0.5,           0.5,           0.5},
      {             0,-SQRT_2_OVER_2, SQRT_2_OVER_2,             0},
      {           0.5,          -0.5,           0.5,          -0.5}
    };
  const size_t NUM_CANONICAL_VIEW_QUAT_D = 24;

#  undef SQRT_2_OVER_2
}