js-spline | Package provides javascript implementation of algorithms

I'm trying to create a textured surface along a path in three.js. I want the texture to tile/repeat along the direction of the path, like this example created in blender:

One way to accomplish this is to create each of the faces "by hand" and to apply a material/texture to each. That works out fine for simple paths (e.g. straight lines) but gets complicated for more elaborate paths.

One of the tools three.js provides is ExtrudeGeometry. Applying a texture to a mesh created this way looks like this with the default UV mapping:

So clearly I need to write a custom UVGenerator function to pass to ExtrudeGeometry. Unfortunately, this doesn't appear to be something for which there is documentation, and previous questions that show up in search results are either out of date (the most complete answers involve a different API for the UVGenerator functions: example) or have no answers (an example).

Here's a jsFiddle example that illustrates the undesired/default behavior. The code is reproduced below. The uvGenerator() function in it is functionally identical to the default three.js uvGenerator, THREE.WorldUVGenerator. It's in the example just to make it easier to fiddle with.