Hi Simon, and just to clarify:

> I thought that in some way I could create new edges inside the faces of an object (such as a circle
> on the side of a cube) but I can't seem to do this.

Just drawing a circle on the side of a cube does not in itself introduce new edges - you just have a separate circle that happens to be located there. (Some day I may try to make some kind of drawing mode where this could be different though and have drawn curves auto trim things but that does not happen currently)

In order to introduce a new edge you can use the Edit > Trim command to actually cut the surface of the cube by that curve and then you'll have edges there after that.

But again that will have a somewhat limited effect on the topology of the generated mesh because the underlying UV quads will still be the same as before, you will just get new n-gon structures where the quads run into those newly introduced surface trim edges.

In order to have a larger effect on the topology you would need to construct the specific surface using a tool like loft or sweep that generates a simple "untrimmed" surface to start with where the surface's UV flow is matching that specific curve, rather than the curve being a trim curve that is just marking a zone of the surface as a cut away area rather than directly defining the UV structure of the surface itself.

This all comes from the concept in NURBS modeling where you can have "underlying surfaces", where surfaces can be big broad sheets that then have trim curves that live on top of them and mark areas of the surface as the outer boundary or as interior holes.

When you do a boolean or trim operation, all the "underlying surfaces" remain the same as before and only new trim curves are calculated. This is fundamentally why booleans work much better with a NURBS modeler than they do with a polygon modeler though, because surfaces remain simple and accurate underneath things as you do more booleans and cuts in different areas, rather than things fragmenting up into tons of little tinier and tinier bits like happens with polygon booleans.

- Michael