++ on the mountains.

Here is a link to paper "Euler Spiral for Shape Completion" dated 2001. Uses "biarcs" also.
http://www.lems.brown.edu/vision/publications/Kimia's_Publication/Journals/Euler_spiral-IJCV.pdf

Another paper "3D Euler Spirals for 3D curve Completion," 2010:
http://webee.technion.ac.il/~ayellet/Ps/10-HT.pdf