After the implementation
of the 2d sketcher I decided to come up with a proof of concept of designing
things in 3d where one can:

- pick a face and then draw a sketch on a that face
- Convert the 2d sketch to 3d by either extruding or revolving it
- Perform a Boolean operation: either union or subtract

My first
implementation of 3D sub-system was based on csg.js library https://evanw.github.io/csg.js/.
It’s a great library and allowed me to put 2d and 3d sub-systems together and
come up with the first prof of concept. This library gave me the most important
piece I didn't have is to perform the 3d operations on 3d objects(union, intersect and subtract).

CSG.js uses the mesh
representation which means I had to tessellate the faces to triangles in order
to perform a boolean operation loosing the information about a face boundary such as kind of line(circle,
arc, line…) and its parameters. This fact means that it's not really possible
to draw a sketch applying constraints to the face boundary.

The second big
limitation of the csg approach was unable to perform any operations on edges
like facets or fillet. Neither on vertices. Because all this information gets
lost after the tessellation.

Recovering the
boundaries information wasn't really
possible and I hade few failed attempts to solve this problem.

So taking into
account that such implementation of 3d was a just proof of concept it was a
time to move on and coming up with a better engine for the 3d part.

The industrial
standard for 3d CADs is BREP - boundary
representation. Unlike mesh-based data structures which is just a big set of
triangles(or maybe convex polygons) the BREP is a collection of connected
surfaces where each surface can be for example a plane or a conical surface or
a NURBS. A surface is trimmed by a set of edges. A trimmed surface is connected to other trimmed surfaces
through those edges.

Another big
advantage of BREP is that after applying boolean operation the boundary
information(edges and vertices etc.) doesn't get lost. No tessellation is
required for the boolean operations. Tessellation is only needed for
visualizing the BREP.

My plan was to
define the BREP data-structures and try to implement the boolean algorithm on
them. I started only with supporting planes as a surface. And then after awhile
I was able to perform see first real results of my BREP boolean algorithm: