Calculating Reflection Vector

where L and N are unit length => projection of L on N is N cos [theta] S = N cos [theta] - L

R is L mirrored about N
R = N cos [theta] + S = 2N cos [theta] - L
= 2N (N^.L) - L => where I_spec = k_s I_l ( (2N (N^.L) - L )^.V )ⁿ
(2N (N^.L) - L )^.V = R^.V = cos [phi]

Alternatively: use halfway vector H
H = (L + V) / |L + V| = { direction of maximum highlights }

maximum highlight when H = N (because then R = V)
=> I_spec = k_s I_l (H^.N)ⁿ
H^.N = cos [alpha]