Drawable Region of the Generalized Log Aesthetic Curves

Table 2

The lower bound and upper bound for 𝜃.

Tangential angle
	𝜈<0 (𝜈≠−1)		𝜈>0		𝜈=−1
	LB	UB	LB	UB	LB	UB
𝛼<0	—	A	—	B	—	0
𝛼=0	—	1Λ1+𝜈−𝜈log[−𝜈]	—	—	—	0
0<𝛼<1	—	A	—	—	—	0
𝛼=1	—	−1Λ1+𝜈+log[−𝜈]	—	—	—	0
𝛼>1	B	A	B	—	1Λ𝛼(1−𝛼)	0

A and B represent1Λ(𝛼−1)((−𝜈)^1−𝛼𝜈−1)+Λ𝛼((−𝜈)^−𝛼−1) and1Λ1−𝜈1−𝛼𝛼.