Lamp design including following parts.
Reflector basically from 2 theory
Parabola formula Y^2=4*F*X
(X,Y) are coordinate position.
However the focus filament is not a spot. it is a pieces of bar. The filament for H3 is length of 5.0X1mm, The H4 is length of 5.5mmX1mm.
So use computer to analysis the output light beam direction. Make it parallel to X axis. The more horizontalized will make the curve more accurated.
That's for projector light.
Lens Fluting Design-
Lens maker's law 1/f=(n-1)(1/c1+1/c2)
C2=Cr=negative------ Get the focus.