double degrees_to_radians ( double degrees );
double *q8_conjugate ( double q[] );
double *q8_exponentiate ( double q[] );
double *q8_inverse ( double q[] );
double *q8_multiply ( double q1[], double q2[] );
double *q8_multiply2 ( double q1[], double q2[] );
double q8_norm ( double q[] );
double *q8_normal_01 ( int *seed );
void q8_transpose_print ( double q[], char *title );
double r8_acos ( double c );
double *r8mat_mv_new ( int m, int n, double a[], double x[] );
void r8mat_print ( int m, int n, double a[], char *title );
void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi,
  int jhi, char *title );
double *r8vec_copy_new ( int n, double a1[] );
double *r8vec_cross_product ( double v1[3], double v2[3] );
double r8vec_dot_product ( int n, double a1[], double a2[] );
double r8vec_norm ( int n, double a[] );
void r8vec_print ( int n, double a[], char *title );
double *r8vec_uniform_01_new ( int n, int *seed );
double *r8vec_zeros_new ( int n );
double radians_to_degrees ( double angle );
double *rotation_axis_vector ( double axis[3], double angle, double v[3] );
double *rotation_axis2mat ( double axis[3], double angle );
double *rotation_axis2quat ( double axis[3], double angle );
double *rotation_mat_vector ( double a[3*3], double v[3] );
void rotation_mat2axis ( double a[3*3], double axis[3], double *angle );
double *rotation_mat2quat ( double a[3*3] );
double *rotation_quat_vector ( double q[4], double v[3] );
void rotation_quat2axis ( double q[4], double axis[3], double *angle );
double *rotation_quat2mat ( double q[4]  );
void timestamp ( );