Here are some papers connected to log-aesthetic curves and other inherently aesthetic curve and surface representations.

Connection with Archimedean spirals

Turns out that the radial curves of log-aesthetic curves are Archimedean spirals:

P. Salvi, Log-aesthetic curves and generalized Archimedean spirals. Computer Aided Geometric Design, Vol. 121, #102468, 2025. DOI • BibTeX

• Approximation of log-aesthetic curves with Archimedean spirals
• An extension of log-aesthetic curves based on Archimedean spirals

Trig-aesthetic curves

P. Salvi, Generalized catenaries and trig-aesthetic curves. Computer-Aided Design and Applications, Vol. 23(1), pp. 56-67, 2026. DOI • BibTeX

• A generalization of log-aesthetic curves that includes catenaries
• Trig-aesthetic curves:
  • A curve representation where the curvature is a trigonometric function of the arc length
  • Shape similar to elastica (also used for modeling curve meandering)

P. Salvi, Generalized catenaries and trig-aesthetic curves. Proceedings of the CAD Conference, pp. 6-11, 2025. DOI • BibTeX

• Conference version of the above

P. Salvi, The curves of Eduard Lehr. G - Slovak Journal for Geometry and Graphics, Vol. 22(43), pp. 5-23, 2025. Open Access • BibTeX

• A family of curves whose curvature is a periodic function of arc length
  • This contains trig-aesthetic curves
• Originally investigated in an obscure work by Eduard Lehr
• A description of the family with several corrections and amendments