如何将3D对象表面平坦化为2D阵列？

Question

I've got 3D objects which are represented as numpy arrays. How can I unfold the "surface" of such objects to get a 2D map of values (I don't care about inner values)?

It's similar to unwrapping globe surface, but the shape is varied from case to case.

Answer 1

This is a vertices problem. Each triangle on the model is a flat surface that can be mapped to a 2D plane. So the most naive solution without any assumed structure would be to:

for triangle in mesh:
    // project to plane defined by normal to avoid stretching

This solution is not ideal as it places all of the uv's on top of each other. The next step would be to spread out the triangles to fill a certain space. This is the layout stage that defines how the vertices are layed out in the 2D space.

Usually it is ideal to fit the UV's within a unit square. This allows for easy UV mapping from a single image.

Option: 2

You surround the object with a known 2D mapped shape and project each triangle onto the shape based on its normal. This provides a mechanism for unwrapping the uv's in a structured manor. An example object would be to project onto a cube.

Option: 3

consult academic papers and opensource libraries/tools like blender: https://wiki.blender.org/index.php/Doc:2.4/Manual/Textures/Mapping/UV/Unwrapping

blender uses methods as described above to unwrap arbitrary geometry. There are other methods to accomplish this as described on the blender unwrap page. The nice thing about blender is that you can consult the source code for the implementation of the uv unwrap methods.

Hope this is helpful.