Comparison of bisector-point and double-angle-bisect draw systems

From the triangle formed by C, P, and the perpendicular from P to OC,
tan( β)
βθd ,
( )
( )
R⋅sin θ
=
d − R⋅cos θ
( ) := atan2( d − R⋅cos( θ)
, R⋅sin( θ)
)
Applying the law of sines to triangle OGP gives:
⎡⎣ ( ) ⎤⎦
sin 180⋅deg − θ + β
φθ, d
2R ⋅
( ) ⎛
:= asin⎜ ⎝
=
sin θ β θ d , +
sin( φ + β)
R
( ( ) ) ⎞
2 ⎠
−
βθd ( , )
The double-angle-bisect system (see Bob Jewett's October, 1995 BD article) predicts:
φ ( dab θ)
θ
:=
2
Here's how the methods compare for two different CB-OB distances:
d1 := 1ft ⋅
d2 := 6ft ⋅
θ := 0⋅deg .. 60⋅deg φ
dab
( θ)
deg
( )
φθd ,
1
deg
( )
φθd ,
2
deg
30
20
10
0
0 20 40 60
So the two systems agree fairly well for small cut angle shots. There is more disagrement
at bigger cut angles, especially when the distance between the CB and OB is large.
θ
deg