mario::konrad
programming / C++ / sailing / nerd stuff
Miscellaneous
© 2003 / Mario Konrad

Newton-Raphson

xn+1=xnf(xn)f(xn)x_{n+1} = x_{n} - \frac{f(x_{n})}{f'(x_{n})}

Sigmoid

f(x)=11+e(xa)*cf(x) = \frac{1}{1 + e^{-(x-a)*c}}

Slerp

Spherical Linear Interpolation:

slerp(p0,p1,t)=sin((1t)*ω)sin(ω)*p0+sin(t*ω)sin(ω)*p1\mathrm{slerp}(p_0, p_1, t) = \frac{\sin((1-t) * \omega)}{\sin(\omega)} * p_0 + \frac{\sin(t * \omega)}{\sin(\omega)} * p_1 withω=arccos(p0*p1)\mathrm{with}\quad \omega = \arccos(p_0 * p_1) andt=[0,1]\mathrm{and}\quad t = [ 0, 1 ]