Planar two-point G1 Hermite interpolating log-aesthetic spirals

Log-aesthetic spirals are currently being studied as fair curves that can be used in computer aided design. A family of planar log-aesthetic spirals that include a point of zero curvature is used in this paper. The two-point G1 Hermite data that is considered has some restrictions on the angles. This paper proves that for any member of the family, a unique segment of that spiral can be found that matches given two-point G1 Hermite data.