Recommended and mentioned products
OpenSCAD is a software for creating solid 3D CAD objects.
No scanner used on this one. I used openSCAD for this one. It's interface is more related to programming, compared to a 3d modeling or CAD interface.
Blender is the open source, cross platform suite of tools for 3D creation.
If you're looking for something a bit more freeform/artistic, Blender is a fantastic place to start, in my opinion. It's a little tougher to get exact measurements for some things (mostly due to it being for modeling and animation, not engineering, so internal units and scaling can throw things off) but it can be done.