Drawable Region of the Generalized Log Aesthetic Curves

Algorithm 1

Remark: Control points 𝑃₀,𝑃₂ are given with a preferred 𝛼. Via GLAC function, second

control point is determined. New points are transformed to the originals and plotted. 𝑠 is modified

from 0 to a large number such that 𝜃_𝑑 is in range of 0<𝜃_𝑑<𝜋 to get the complete drawable boundary.

Input: 𝑃₀(−1,0),𝑃₂(1,0),𝛼,𝜈,𝑠.

Output: Complete drawable boundary of interactive GLAC.

Begin

Step 1. If −1<𝜈<0 then

       if 𝛼=0 then

            []Λ←−log−𝜈𝑠.

       else

            ()Λ←−𝜈^−𝛼−1𝑠𝛼.

    else if 𝜈>0 and 𝛼<0 then

            Λ←−1𝑠𝛼.

Step 2. Determine 𝑆𝑃𝑥₀,𝑦₀ and 𝐸𝑃𝑥₂,𝑦₂ using (3).

Step 3. Determine scaling factor 𝑃𝑟←²𝑃₀𝑆𝑃𝐸𝑃 and angle 𝜃_𝑒←cos⁻¹𝑥₂𝑥₂²+𝑦₂².

Step 4. Determine 𝑃₁ using the tangent line of both end points.

Step 5. Scale points to 𝑟, reflect through 𝑥-axis, rotate to −𝜃_𝑒 and translate to 𝑃₀,𝑃₂.

Step 6. Plot point 𝑃₁.

Step 7. Modify 𝑠 from 0 to a large number and repeat Step 1. to 6.

Step 8. Reflect points via 𝑥-axis and𝑦-axis.

Step 9. Output.

End.