URL: https://svn.lrde.epita.fr/svn/oln/trunk/milena ChangeLog: 2007-09-25 Simon Nivault <simon.nivault@lrde.epita.fr> Add interpolation features for quaternions. * mln/value/quat.hh: Update. --- quat.hh | 85 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 84 insertions(+), 1 deletion(-) Index: trunk/milena/mln/value/quat.hh =================================================================== --- trunk/milena/mln/value/quat.hh (revision 1167) +++ trunk/milena/mln/value/quat.hh (revision 1168) @@ -112,8 +112,25 @@ bool about_equal(const T& f, const T& q); bool about_equal(const quat& p, const quat& q); + // Misc. - // meths and procs bodies... + bool interpol_ok(const quat& p, const quat& q, float h); + + // Linear Quaternion Interpolation. + + quat lerp(const quat& p, const quat& q, float h); + + // Spherical Linear Quaternion Interpolation. + + quat slerp(const quat& p, const quat& q, float h); + + quat slerp_2(const quat& p, const quat& q, float h); + + quat slerp_3(const quat& p, const quat& q, float h); + + quat slerp_4(const quat& p, const quat& q, float h); + + quat slerp_5(const quat& p, const quat& q, float h); # ifndef MLN_INCLUDE_ONLY @@ -337,6 +354,72 @@ return about_equal<float>(norm::l2(p - q), 0); } + // Misc. + + bool interpol_ok(const quat& p, const quat& q, float h) + { + return + p.is_unit() && + q.is_unit() && + h >= 0 && + h <= 1; + } + + + // Linear Quaternion Interpolation. + + quat lerp(const quat& p, const quat& q, float h) + { + assert(interpol_ok(p, q, h)); + return (1 - h) * p + h * q; + } + + + // Spherical Linear Quaternion Interpolation. + + quat slerp(const quat& p, const quat& q, float h) + { + assert(interpol_ok(p, q, h)); + float omega = acos(p.sprod(q)); + return + about_equal(omega, 0.f) ? + lerp(p, q, h) : + quat((sin((1-h)*omega) * p + sin(h*omega) * q) / sin(omega)); + } + + quat slerp_2(const quat& p, const quat& q, float h) + { + assert(interpol_ok(p, q, h)); + quat tmp = p * pow(p.conj() * q, h); + assert(about_equal(tmp, slerp(p, q, h))); + return tmp; + } + + quat slerp_3(const quat& p, const quat& q, float h) + { + assert(interpol_ok(p, q, h)); + quat tmp = pow(p * q.conj(), 1 - h) * q; + assert(about_equal(tmp, slerp(p, q, h))); + return tmp; + } + + quat slerp_4(const quat& p, const quat& q, float h) + { + assert(interpol_ok(p, q, h)); + quat tmp = pow(q * p.conj(), h) * p; + assert(about_equal(tmp, slerp(p, q, h))); + return tmp; + } + + quat slerp_5(const quat& p, const quat& q, float h) + { + assert(interpol_ok(p, q, h)); + quat tmp = q * pow(q.conj() * p, 1 - h); + assert(about_equal(tmp, slerp(p, q, h))); + return tmp; + } + + # endif // ! MLN_INCLUDE_ONLY } // end of namespace mln::value