Substance Designer "Arch Generator"

Hi all
This is my first time posting on the "merket" part of ArtStation.
During the lockdown this year I had some spare time to play with Substance Designer and I am happy to share the outcome here.
Specifically I kept hearing that the pixel processor is a really powerful node and I wondered what I could do with it and how much could I push it.
I really love those substances that reproduce building facades. I have seen some amazing work.
One thing I noticed though is that there is not really any easy way to create the main types of arches (excluding the 1 centered circular arch), especially when you have to show the voussoirs, or you want a texture (like a wood pattern) to follow its shape.
Therefore I decided to brush my high school trigonometry and give a read to a great book called "Practical geometry for builders and architects". 

The result of this exploration of the pixel processor was my "Arch Generator" node.
This is a node that can generate all the main types and sub-types of arches and that can map an image input along their length and width. It was a fascinating challenge to tackle and the result, while not 100% perfect, still does what is supposed to do in most of the cases.

For the most difficult cases (the true elliptical and parabolic arches) I had a LOT of help from the math geniuses at MathStackExchange and Inigo Quilez which involved getting around a nasty quartic equation which I would not wish it upon even my worst enemy. So a huge thank you guys!

My arch generator can simulate the following types of arches: 

Flat Arches
- Tapered
- Parallel 

1 Centered Arches
- Semicircular Arches (Roman Arches)
- Segmental Arches
- Horseshoe Arches

2 Centered Arches
- Pointed Lancet Arches
- Pointed Equilateral Arches
- Pointed Drop Arches
- Pointed Segmental Arches 

3 centered Arches
- Basket-Handle Arches
- Pseudo 3 centered Arches 

4 Centered Arches
- 4 centered Arches (Tudor Arches)
- Pseudo 4 centered Arches 

5 Centered Arches 

True Elliptical Arches
- Elliptical Arches with rays perpendicular to the ellipse
- Elliptical Arches with rays passing through the center

Parabolic Arches
- Parabolic Arches with rays perpendicular to the parabola
- Parabolic Arches with rays passing through the center 

Ogee Arches
- 3 centered Ogee Arches
- 4 centered Ogee Arches 

Reverse Ogee Arches
- 3 centered Reverse Ogee Arches
- 4 centered Reverse Ogee Arches 

Multifoil Arches
- With external arch
- Without external arch 

Pointed Multifoil Arches
- With external arch
- Without external arch