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  1. #include <bits/stdc++.h>
  2.  
  3. using namespace std;
  4.  
  5. typedef double ftype;
  6. typedef complex<ftype> point;
  7. typedef complex<point> quater;
  8. #define qA real()
  9. #define qB imag()
  10. #define qs qA.real()
  11. #define qx qA.imag()
  12. #define qy qB.real()
  13. #define qz qB.imag()
  14.  
  15. quater operator * (quater a, quater b)
  16. {
  17.     return {{a.qA * b.qA - a.qB * conj(b.qB)},
  18.             {a.qA * b.qB + a.qB * conj(b.qA)}};
  19. }
  20.  
  21. quater conj(quater a)
  22. {
  23.     return {conj(a.qA), - a.qB};
  24. }
  25.  
  26. ftype norm(quater a)
  27. {
  28.     return (a * conj(a)).qs;
  29. }
  30.  
  31. ftype abs(quater a)
  32. {
  33.     return sqrt(norm(a));
  34. }
  35.  
  36. quater operator / (quater a, quater b)
  37. {
  38.     return a * conj(b) / point(norm(b));
  39. }
  40.  
  41. quater vec(ftype x, ftype y, ftype z)
  42. {
  43.     return {{0, x}, {y, z}};
  44. }
  45.  
  46. quater vec(quater a)
  47. {
  48.     return a -= a.qs;
  49. }
  50.  
  51. ftype dot(quater a, quater b)
  52. {
  53.     return -(a * b).qs;
  54. }
  55.  
  56. quater cross(quater a, quater b)
  57. {
  58.     return vec(a * b);
  59. }
  60.  
  61. ftype mix(quater a, quater b, quater c)
  62. {
  63.     return dot(a, cross(b, c));
  64. }
  65.  
  66. quater conj(quater a, quater g)
  67. {
  68.     return g * a / g;
  69. }
  70.  
  71. quater rotation(quater i, ftype phi)
  72. {
  73.     return point(cos(phi / 2)) + i * point(sin(phi / 2));
  74. }
  75.  
  76. quater rotate(quater a, quater i, ftype phi)
  77. {
  78.     return conj(a, rotation(i, phi));
  79. }
  80.  
  81. signed main()
  82. {
  83.     ios::sync_with_stdio(0);
  84.     cin.tie(0);
  85.     const double pi = acos(-1.);
  86.     quater A = vec(0, 0, 1);
  87.     quater B = vec(1, 0, 0);
  88.     double phi = pi / 4;
  89.     cout << rotate(B, A, phi) << "\n";
  90.     return 0;
  91. }
  92.  
Success #stdin #stdout 0s 3472KB
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Standard input is empty
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((0,0.707107),(0.707107,0))
https://ideone.com/BBOx9H
quaternions
language:
C++14 (gcc 8.3)
created:
8 years ago
visibility:
secret

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