How to make Object Texture Coordinate not to change along animation

Question

I'm now working on textures with Object Texture Coordinate on a model with animation. I've discovered that Blender may use real-time coordinates for texture mapping, which makes the texture slide along the surface of the model.

My question is that, how can I use the static original Object Texture Coordinate at the first time step, rather than the dynamic real-time ones, for mapping, in order to make the texture sticking on the model during the animation.

In this question, the answers suggested to use Generated and UV Texture Coordinates. But for there's something different about what I want to paint on the model, so any other Texture Coordinates, especially Generated and UV Texture Coordinates, are not expected, if possible.

(Anyway, here's what I want to do with the static coordinates I asked for above. I'm modifying a model for MikuMikuDance in blender. With Object Texture Coordinates and 'constant' color ramp, I want to divide several rectangular areas on the character for future texturing. Of course, UV Texture Coordinates can also do this, but the area will be only rectangular on uv, but not on Cartisian coordinate. That's why I insist about Object Texture Coordinates. )

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Thanks to @MarkusvonBroady and @RobinBetts 's answer. I've met a defect of baking method: cracks may occurs between adjacent meshes due to the inaccuracy of baking:

However @MarkusvonBroady 's method of geometry node can avoid such cracks, for which this method is more recommended:

Answer 1

Similarly to Robin Betts' solution, you can 'bake' dynamically by storing data such as Position at any step in the modifier stack:

Geometry Nodes tree:

Consider switching the Point domain to Face Corner when you e.g. split edges and move the split vertices apart; or when you store some other data like normals (but then remember the normals would be stored in object space, not tangent space).

Shading tree:

Modifier stack:

Result:

Answer 2

One option would be to bake the Object-Space of the surface your undeformed, subdivided mesh into a UV Mapped image:

For the resulting image, choose a file-format that can accept negative values, (here, Blender-generated, '32-bit Float') and bake into Non-Color. From the above setup, you would just bake 'Emit'. (You don't need denoising or a high sample-rate)

Once baked, the image can be used as the texture-coordinate for whatever manipulations of 'Object' you would normally have made, and will stick to the surface when the object is deformed: