Remaining algorithms

[DanielVandH]

Would still like to eventually implement the following algorithms; chapter numbers refer to pages in Bobach's thesis here.

• Farin's $C^1$ interpolant (Chapter 3.2.7.2)
• Hiyoshi's $C^2$ interpolant (Chapter 3.2.7.3)
• Hioyshi's coordinates (Chapter 3.2.5.5, Chapter 5.5)
• Ghost point extrapolation (Chapter 8)

The main issues being I'm not 100% sure I understand the splines yet for the first two methods, and Bobach's description of Hiyoshi's coordinates confuses me.

[DanielVandH]

I have a working version of Farin's $C^1$ interpolant in https://github.com/DanielVandH/NaturalNeighbours.jl/tree/farin. Just needs to be properly tested.

[DanielVandH]

Good references for Farin and Hiyoshi's smooth coordinates:

https://link.springer.com/chapter/10.1007/978-3-540-24767-8_8
https://theses.hal.science/tel-00832487/PDF/these-flototto.pdf

Also, for Hiyoshi's $C^k$ interpolant, https://www.sciencedirect.com/science/article/pii/S0925772101000529 is the initial reference (but Bobach's discussion of the implementation in his thesis and here https://link.springer.com/content/pdf/10.1007/11919629_20.pdf?pdf=inline%20link will be the main reference).

The reference for ghost point extrapolation is Bobach's thesis and https://www.sciencedirect.com/science/article/pii/S001044850800167X.

[DanielVandH]

https://dl.acm.org/doi/abs/10.1504/IJCSE.2007.014460 another reference for Hiyoshi's $C^2$