CoinBLAS VS procedural-gl-js

When you consider that a graph and a matrix are isomorphic, doing vector matrix multiplication takes a vector with a set value, say row 4, and multiplies it by a matrix where row 4 has values present that represent edges to the nodes that are adjacent to it (ie "adjacency" matrix). The result is a vector with the next "step" in a BFS across the graph, do that in a loop and you step across the whole graph.

A cool result of this is, for example, taking an adjacency matrix and squaring it is the "Friend of a Friend" graph. It takes every node/row and multiplies it by itself, returning a matrix that are adjacent to the adjacencies of each node, ie, the friends (adjacencies of the adjacencies) of friends (adjacencies) of the nodes.

Deeper traversal are just higher nodes, a matrix cubed are the friends of the friends of the friends.

A picture is worth a thousand words, see figure 7 of this paper:

https://arxiv.org/pdf/1606.05790.pdf

Also check out figure 8, this shows how incidence matrices can work to represent hyper and multi graphs. An pair of incidence matrices reprsent two graphs, one from nodes to edges and the other from edges to nodes, these are n by m and m by n. When you multiply them, you get a square adjacency matrix that "projects" the incidence into an adjacency. This can be used to collapse hypergraphs into simple graphs that use different semirings to combine the multiple edges.

For some pretty pictures of this kind of stuff, check out CoinBLAS (note I am not a crypto-bro, it was just a very handy extremely large multi-graph that I could easily download in chunks to play with):

https://github.com/Graphegon/CoinBLAS/

Python wrapper around The GraphBLAS API:

https://github.com/michelp/pygraphblas

For an upcoming paper we've open sourced using pygraphblas to analyse the bitcoin graph using the GAP benchmarks on a server with 1TB of RAM:

https://github.com/Graphegon/CoinBLAS

Nice writeup, I always like it when the shaders are highlighted like this. I got started in a similar way 7 years ago and have been making 3D terrains with THREE.js & WebGL since.

The real fun begins when you need to implement some sort of Level-of-Detail system and streaming in data to give the illusion of high detail everywhere without sacrificing performance.

Last year I released an open-source framework (https://github.com/felixpalmer/procedural-gl-js) for creating 3D terrains for web applications, you can see Uluru here: https://www.procedural.eu/map/?longitude=131.036&latitude=-2... (unfortunately the aerial imagery from our default provider isn't as high resolution as other places in Europe)

Great visualization and approach with compressing the tile data. Do you have a comparison of how much smaller the payload ends up being compared to simply sending PNG files?

I use PNGs to encode elevation data in my 3D mapping library (https://github.com/felixpalmer/procedural-gl-js/) and this does a pretty good job of compressing the data, for example in the ocean the PNG files are also very small as the image is mostly black. Different use case I now as your data is much more sparse, but I wonder how close the PNG compression would be compared to your approach.

Yeah, the React parts of this are very minimal. I'm not really sure what using it gets you, since it just manages a single div.

The _actual_ library that does all the work is here: https://github.com/felixpalmer/procedural-gl-js

- Tiny filesize means library is parsed fast. Package size is less than THREE.js thanks to code stripping

Check it out on Github: https://github.com/felixpalmer/procedural-gl-js/

The imagery comes from the Orthofoto dataset on https://www.basemap.at/ - the actual texturing is done by the Procedural GL JS library https://github.com/felixpalmer/procedural-gl-js