Quaternions

David Wagner 2010/01/13 19:16

Here are some quaternion functions.

Definitions

Mandelbulb Formulæ

For real p.

  • p alpha = delim{|}{ p arctan{{vert s_v vert}/s_w} }{|}
  • p beta= delim{|}{ p arctan{{vert t_v vert}/t_w} }{|}
  • q^{½p} = r^{½p} s^{½p} t^{½p}.

s^{½p}t^{½p} = {{vert s vert}^{½p}}  (cos {p alpha}/2 + {{s_v}/{vert s_v vert}} sin {p alpha}/2) {{vert t vert}^{½p}}  (cos {p beta }/2 + {{t_v}/{vert t_v vert}} sin {p beta }/2)

= ({vert s vert}{vert t vert})^{½p} (cos {p alpha}/2 + {{s_v}/{vert s_v vert}} sin {p alpha}/2) (cos {p beta }/2 + {{t_v}/{vert t_v vert}} sin {p beta }/2)


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