Consider alternatives to standard cubic splines for width and height interpolation #108

Closed stfnp closed 5 years ago

In GitLab by spfeifer on Apr 18, 2018, 16:41

A method with a more 'local' character compared to the standard cubic splines used currently would be good. I.e. changing single data points should ideally only alter the curve in the neighborhood of those points. This should solve or improve problems like this one mentioned in issue #88:

When defining the thickness and width, the auto-curving makes extreme stuff (which caused a negative thickness for me), I had to define the same w/h for several points around to "straighten it out"

Optionally, a monotonicity preserving method would make it even easier to stay in the valid domain: If all supplied widths/heights are positive, the resulting interpolated values will be as well.

Akima Interpolation

Advantages: Apparently computationally efficient and doesn't tend to oscillate as much as standard splines, because it only uses a few local points for determining each cubic section. See example 2 on this website: http://valdivia.staff.jade-hs.de/akima.html

http://www.iue.tuwien.ac.at/phd/rottinger/node60.html

http://200.17.213.49/lib/exe/fetch.php/wiki:internas:biblioteca:akima.pdf

Variant for preserving the monotonicity of the data points:

https://www.osti.gov/servlets/purl/5328033