How to add text (or texturize it) on a curve?

Question

I'm trying to add a simple text to an Archemedean curve spiral, just like I did with this similar shape, which is a mesh

Mesh

However I need to animate this to do a simple squash and stretch, which could be done with shape keys but using a curve (apart from it's efficiency, the spring wasn't deformed when resized on Z axis)

Curve

I'm trying to add that same text into such curve, have tried generated texture coordinates, aswell as UV, changing the image texture projection, interpolation, extension, none have worked properly, it's been a real nightmare, and I would infinitely appreciate any guidance.

Answer 1

If you set the spiral path's Twist Method to 'Z-Up', you can use its native Round Bevel, and its native UV Map.

Shape keys of the spiral in a couple of Edit-Mode Z-scales will map without distortion:

If the mapping in the material is the problem, then here's an example of the way the native UV can be used to map the text once in the profile circumference, and at intervals along the length of the spring:

Answer 2

New Mesh with Existing Curve, UV coordinates, Curve Modifier

The cylinder mesh can be UV Mapped in the standard fashion. The Curve modifier beforms the cylinder into a spiral in a second step. Shader Nodes allow the user to specify UV coordinates in nodes. This allows image placement in UV directions and animation of location. This flexibility may be important because the original question has spiral and the long cylinder. Blender has many options for manipulating UV Coordinates.

Please consider the following steps. The steps are abbreviated and can be more detailed according to comments.

• Use your existing spiral
• Add cylinder mesh. Mesh length will probably much longer than diameter. In edit mode add seams. UV Unwrap.
• Align mesh origin and curve origin. Add Curve Modifier to mesh and adjust to suit your tastes. You many need to adjust cylinder length and position and rotation about long dimension.

Image Above. High Level. A Spiral Curve exists similar to yours. A Separate UV Mapped Cylinder mesh with UV Seams. Mesh was UV Mapped in its original state in edit mode. The Cylinder was quite long to occupy the Curve. The circumference is much smaller than length. Please see the Curve Modifier which allows mesh to follow spiral. Curve Modifiers works best when the origin of mesh and curve coincide. Please see other educational content on Curve Modifier if that suits you. Zoomed out view to show some texture on a restricted part of mesh. Zoomed in view to show texture detail.

Image above. Shader Nodes. Please inspect and improve. Other approaches are possible. Upper Right Frame designates the UV coordinates of the texture to be placed ... and remaps to [0,1]. Note the reader uses the numerical coordinates to place the final image. Thus you can slide the image around the length and around the shorter diameter. An image derived from OP question image was used.

Image Above. Cylinder in edit mode for UV Unwrap respecting seams. Seams are visible and rather difficult to see in the image. Partial selection of faces and thus partial appearance in UV editor area. Please Click to zoom.