Starting with your form intersections, you're making good progress here, but I do have some suggestions on how your work here can be improved.

• Firstly, a minor point - just as when you're constructing your cylinders around a minor axis, cones can benefit from the same use of the minor axis in order to position the tip correctly.

• For the intersections themselves, there are still areas that can be improved upon, though that's still normal. Most students at this stage will be more comfortable with the flat-on-flat intersections (which you appear to be as well), but still struggling with those that involve curved surfaces. I've noted some corrections here, with the most notable one being the intersection between that cone on the top, and the cylinder. Since the cylinder's surface is curving, then the intersection line would also follow this curving surface, while continuing to run along the base of the cone.

While I don't share this earlier on, as students prior to this stage are really meant to use the form intersections exercise to experiment and plant seeds, which are then nurtured through the several constructional drawing lessons which have us consider the relationships between our forms in a less strict fashion, once students hit this lesson they've generally developed enough spatial reasoning skill to be able to make use of more direct explanations. So, take a look at this diagram.

It demonstrates how the intersections themselves require us to first determine which surfaces are relevant to the intersection, and thus which surfaces the intersection line must run along simultaneously. In the diagram, the intersection between the box and sphere run first along both purple elements - the side face of the box and the cross-sectional slice of the sphere that aligns to that side face - then jumps to following orange elements - the top face of the box and the corresponding slice of the sphere.

When we get to the last part of the diagram, where we replace one of the edges with a more gradual, rounded transition, we can see how the intersection gets more complicated when we deal with multiple rounded surfaces. This puts us in a more similar situation to the intersection between the lower cone and the cylinder (in the corrections from above). The correction I made there was very subtle, but basically as we lead into the intersection, we're still following along the curve of the cylinder, so we have these slightly curving ends on either end of the intersection.

You can think of each of these as being their own separate curve - along the outside, the curve of the cylinder is primarily what we're following, because we're following along the relatively straight length of the cone. Then we transition to following the curve of the cone, but the straight length of the cylinder, and then back to the cone again as shown here. Were there sharp edges between these transitions (as there are on the sphere-box diagram, where the box's own edges create sharp jumps from one face to another, leading to sharp corners in the intersection itself), we'd just jump from one curve to the other. But since we're actually dealing with two rounded surfaces, we actually have to gradually transition from one to the next, resulting in more of an S-like curve, rather than a series of distinct C curves.

Now, don't worry too much if not all of this makes sense right off the bat. Revisit this explanation periodically, and we'll have another opportunity to talk about the form intersections in lesson 7.

Continuing on, as a whole your object constructions are very well done. You've demonstrated a lot of investment of time and patience, and have as a result, worked through these constructions with a great deal of focus on the idea of precision. Up until this point, especially Lessons 3-5, we primarily work in a reactionary fashion. Put down a form, might be bigger or smaller than you intended, but that's fine - we keep building upon it, with the construction changing in small ways from our intent based on where our marks are a little off here and there. This lesson however is the first major shift towards an approach that focuses on pre-planning, on establishing our intent first.

Precision is often conflated with accuracy, but they're actually two different things (at least insofar as I use the terms here). Where accuracy speaks to how close you were to executing the mark you intended to, precision actually has nothing to do with putting the mark down on the page. It's about the steps you take beforehand to declare those intentions.

So for example, if we look at the ghosting method, when going through the planning phase of a straight line, we can place a start/end point down. This increases the precision of our drawing, by declaring what we intend to do. From there the mark may miss those points, or it may nail them, it may overshoot, or whatever else - but prior to any of that, we have declared our intent, explaining our thought process, and in so doing, ensuring that we ourselves are acting on that clearly defined intent, rather than just putting marks down and then figuring things out as we go.

In our constructions here, we build up precision primarily through the use of the subdivisions. These allow us to meaningfully study the proportions of our intended object in two dimensions with an orthographic study, then apply those same proportions to the object in three dimensions.

As you have done very well, I have only two things to call out, both of them being quite minor:

• I have seen other situations where you generally would start your structures out with straight lines and flat surfaces, then round them out. With this soap dispenser nozzle however you did start with a simple box but then you largely ended up redrawing the majority of that structure right on top, resulting in a much weaker relationship with the previous stage. This can undermine the solidity of our results, as we rely on the solidity to transfer forward from the earlier, simpler stages, as we build up more complexity. Instead, this nozzle would have been better off being approached as shown here, which more directly implements the concepts explained in these notes. It is certainly a lot more tedious, but it's also a lot more precise.

• The other point is more of a recommendation going forward. Here you opted to use fineliners - when you hit Lesson 7, I would encourage you to use a ballpoint pen for the entire drawing, simply because the ability to make some of your earlier marks fainter without giving up the confidence of the stroke, is greatly beneficial, especially with the level of complexity we end up dealing with there.

So! All in all, great work. I'll go ahead and mark this lesson as complete.