Wrapping 3d models - question

Chester7vp

Hello. I'm learning 3D modeling. Unfortunately, I have a problem and I don't know how to fix it. Designs a mug. If I have a flat object, I project it onto surfaces and I extrude it.

 Example:

 

But if I have a 3d object I can't do that. How can I bend an object on a cylinder.

Thingiverse example:

 

Can it be done in some program or do I have to carve it in for example zbrush?

PS: sorry for my english too. I'm still learning.

Ghogiel

 If you just need to deform it to a simple cylinder shape, Model the detail flat, then use a bend modifier/deformer.

gnoop

In Blender it could be curve or bend modifier to bend  the thing  around barrel,  then shrinkwrap modifier to lay /project bottom vertexes perfectly  on the barrel surface  and data transfer modifier in case you need to project / grab UV from the  barrel to the thing .

Chester7vp

It looks very simple. I'm starting to play in the blender. 
Unfortunately, this option cannot be found in DesignSprark Mechanical. 
Thank you very much for help.