CGS stands for Constructive Solid Geometry and describes the most basic way to work with solid 3D geometry, which is creating complex objects by adding and removing pieces to/from solids by using Boolean operations such as union, subtraction or intersection.
As we saw earlier in this manual, FreeCAD can handle many types of geometry, but the preferred and most useful type for the kind of 3D objects that we want to design with FreeCAD, that is, real-world objects, is, without a doubt, solid, BREP geometry, that is mainly handled by the Part Workbench. Unlike polygon meshes, which are made only of points and triangles, BREP objects have their faces defined by mathematical curves, which permits abolute precision, no matter the scale.
The difference between the two can be compared to the difference between bitmap and vectorial images. As with bitmap images, polygon meshes have their curved surfaces divided into a series of points. If you look at it from very close, or print it very large, you will see not a curved but a faceted surface. In both vectorial images and BREP data, the position of any point on a curve is not stored in the geometry but calculated on the fly, with exact precision.
In FreeCAD, all BREP-based geometry is handled by another piece of open-source software, OpenCasCade. The main interface between FreeCAD and the OpenCasCade kernel is the Part Workbench. Most other workbenches build their functionality on top of the Part Workbench.
Although other workbenches often offer more advanced tools to build and manipulate geometry, since they all actually manipulate Part objects, it is very useful to know how these objects work internally, and be able to use the Part tools since, being more simple, they can very often help you to work around problems that the more intelligent tools fail to solve properly.
To illustrate the working of the Part Workbench, we will model this table, using only CSG operations (except the screws, for which we will use one of the addons, and the dimensions, which will see in the next chapter):
Let's create a new document (Ctrl+N or menu File -> New Document), switch to the Part Workbench, and begin with the first foot:
You should obtain two high boxes, one 8mm apart from the other:
Observe that the newly created object, called "Cut", still contains the two cubes we used as operands. In fact, the two cubes are still there in the document, they have merely been hidden and grouped under the Cut object in the tree view. You can still select them by expanding the arrow next to the Cut object, and, if you wish, turn them visible again by right-clicking them or change any of their properties.
You might have been thinking that, instead of duplicating the base cube six times, we could have duplicated the complete foot three times. This is totally true, as always in FreeCAD, there are many ways to achieve a same result. This is a precious thing to remember, because, as we will advance into more complex objects, some operations might not give the correct result and we often need to try other ways.
You will notice that the cylinders are a bit longer than needed. This is because, as in all solid-based 3D applications, boolean operations in FreeCAD are sometimes oversensitive to face-on-face situations and might fail. By doing this, we put ourselves on the safe side.
As you can see, each foot has become a quite long series of operations. All this stays parametric, and you can go change any parameter of any of the older operations anytime. In FreeCAD, we often refer to this pile as "modeling history", since it in fact carries all the history of the operations you did.
Another particularity of FreeCAD is that the concept of 3D object and the concept of 3D operation tend to blend into one same thing. The Cut is at the same time an operation, and the 3D object resulting from this operation. In FreeCAD this is called a "feature", rather than object or operation.
Notice that, although the legs are 8mm thick, we placed it 10mm away, leaving 2mm between them. This is not necessary, of course, it won't happen with the real table, but it is a common thing to do in that kind of "assembled" models, it helps people who look at the model to understand that these are independent parts, that will need to be attached together manually later.
Now that our five pieces are complete, it is a good time to give them more proper names than "Cut015". By right-clicking the objects in the tree view (or pressing F2), you can rename them to something more meaningful to yourself or to another person who would open your file later. It is often said that simply giving proper names to your objects is much more important than the way you model them.
The internal structure of Part objects
As we saw above, it is possible in FreeCAD to select not only whole objects, but parts of them, such as the circular border of our screw hole. This is a good time to have a quick look at how Part objects are constructed internally. Every workbench that produces Part geometry will be based on these:
In the 3D view, you can select individual vertices, edges or faces. Selecting one of these also selects the whole object.
A note about shared design
You might look at the table above, and think its design is not good. The tightening of the feet with the tabletop is probably too weak. You might want to add reinforcing pieces, or simply you have other ideas to make it better. This is where sharing becomes interesting. You can download the file made during this exercise from the link below, and modify it to make it better. Then, if you share that improved file, others might be able to make it even better, or use your well-designed table in their projects. Your design might then give other ideas to other people, and maybe you will have helped a tiny bit to make a better world...