Export model with Vertex Paint to .fbx I have a complex model saved from mayavi library in python and its colors are saved at Vertex paint.

My final goal is to import this model into Unity with textures.

And Only way I found is, import this model first into Blender, create a new image in UV/Image mode; select all vertices of model, Bake it; and I get that new image as the texture file.

Is there any simpler way? where I can export the model from blender with its Vertex paint (if possible as texture) as .fbx or .3ds or .obj

Thanks in advance.
If anyone stuck in the same dilemma; Here's a solution.

And @Firewall's comment showing the shader script can also be implemented.