Arrugator

A tool for subdividing triangular meshes for GIS reprojection purposes.

See https://ivan.sanchezortega.es/development/2021/03/08/introducing-arrugator.html

Usage

The inputs are:

• A projector function (which takes an Array of 2 Numbers, and returns an Array of 2 Numbers). Typically this is meant to be a proj4js forward projection function, like proj4(srcCRS, destCRS).forward; however, arrugator has no hard dependency on proj4js, so other projection methods could be used.
• The unprojected coordinates (an Array of Arrays of 2 Numbers, typically NW-SW-NE-SE)
• The UV-mapping coordinates (an Array of Arrays of 2 Numbers, typically [[0,0],[0,1],[1,0],[1,1]])
• The vertex indices of the triangles composing the initial mesh (an Array of Arrays of 3 Numbers, typically [[0,1,3],[0,3,2]]).

Note that the typical input is four vertices, but there's no hard requirement on that. Any triangular mesh should do (and maybe there are edge cases I haven't think of where it's required so things work for weird projections like polyhedral ones).

And the ouputs are:

• The unprojected vertex coordinates (an Array of Arrays of 2 Numbers)
• The projected vertex coordinates (an Array of Arrays of 2 Numbers)
• The UV-mapping coordinates (an Array of Arrays of 2 Numbers)
• The vertex indices of the triangles composing the mesh (an Array of Arrays of 3 Numbers).

Usage example

Initialize some data (assuming proj4 has already been set up):

// These are the corner coordinates of a Spanish 1:2.000.000 overview map in ETRS89+UTM30N:
let epsg25830coords = [
	[-368027.127, 4880336.821], // top-left
	[-368027.127, 3859764.821], // bottom-left
	[1152416.873, 4880336.821], // top-right
	[1152416.873, 3859764.821], // bottom-right
];

let sourceUV = [
	[0, 0], // top-left
	[0, 1], // bottom-left
	[1, 0], // top-right
	[1, 1], // bottom-right
];

let arruga = new Arrugator(
	proj4("EPSG:25830", "EPSG:3034").forward,
	epsg25830coords,
	sourceUV,
	[
		[0, 1, 3],
		[0, 3, 2],
	] // topleft-bottomleft-bottomright ; topleft-bottomright-topright
);

Then, subdivide once:

arruga.step();

Or subdivide several times:

for (let i = 0; i < 10; i++) {
	arruga.step();
}

Or subdivide until epsilon is lower than a given number (square of distance in map units of the projected CRS - in this example, EPSG:3034 map units):

arruga.lowerEpsilon(1000000); // 1000 "meter"s, squared

If there are antimeridian artefacts, or an "epsilon stall" warning appears on your console, you might want to "force" subdividing every segment before running the default subdivisions:

arruga.force();

Once you're happy with the subdivisions, fetch the mesh state:

let arrugado = arruga.output();

let unprojectedCoords = arrugado.unprojected;
let projectedCoords = arrugado.projected;
let uvCoords = arrugado.uv;
let trigs = arrugado.trigs;

The output are Arrays of Arrays, so the use case of dumping the data into a TypedArray to use it in a WebGL buffer needs them to be .flat()tened before.

How to do this depends on how you're usign WebGL (or what WebGL framework you're using). For example, my glii examples work like:

const pos = new glii.SingleAttribute({ glslType: "vec2", growFactor: 2 });
const uv = new glii.SingleAttribute({ glslType: "vec2", growFactor: 2 });
const indices = new glii.TriangleIndices({ growFactor: 2 });

pos.setBytes(0, 0, Float32Array.from(arrugado.projected.flat()));
uv.setBytes(0, 0, Float32Array.from(arrugado.uv.flat()));
solidIndices.allocateSlots(arrugado.trigs.length * 3);
solidIndices.set(0, arrugado.trigs.flat());
wireIndices.allocateSlots(arrugado.trigs.length * 3);
wireIndices.set(0, arrugado.trigs.flat());

Demos

See the demo branch of this git repository; there are some glii-powered examples there, including demo raster data.

LineArrugator

There is also LineArrugator, a lightweight form of Arrugator designed to work on segment lists ("polylines") instead of working on triangle meshes.

The input is just a list of [x,y] coordinates, and the output is another list of [x,y] coordinates, projected.

let arruga = new LineArrugator(
	proj4('EPSG:4326','EPSG:25830').forward,
	[[-50, 0], [40, 25]]
);

arruga.lowerEpsilon(10000);

console.log(arruga.output());

Legalese

Released under the General Public License, v3. See the LICENSE file for details.