Starting with your form intersections, one important point I would recommend is that, as shown in the demonstration for the exercise, you generally only draw the portion of the intersection that is visible to the viewer. While drawing through our forms in general can be quite beneficial, here with the intersection lines going full x-ray vision can actually become a lot more visually confusing and make it harder for us to keep track of where we're defining our intersections. The only case where I'd still draw all the way through is if the intersection itself is a primitive shape (like an ellipse) where drawing all the way around helps us maintain the appropriate curvature.

Overall, your intersections themselves are coming along well - they're not perfect, but they do demonstrate by and large that your understanding of how these forms relate to one another in 3D space is progressing well. It's normal to still have some hiccups, and we do assign this exercise one last time in Lesson 7 - but I did want to point out a couple issues I noticed to keep you moving in the right direction:

• Firstly, remember that every single mark we freehand must be executed using the ghosting method - that includes each and every line we draw to construct our forms, as well as the intersection lines themselves. I've noticed based on your linework that you may not be adhering as closely to the specific steps of the ghosting method (as explained here) as you could be - mainly when it comes to the planning and preparation phases (for example, I'm not seeing any signs of you marking out the start/end points of your straight lines with dots). When constructing your forms, you're generally quite confident, so your marks are smooth, but when you draw your intersection lines you have a far greater tendency to hesitate, resulting in a lot of wobbling.

• Secondly, I'm definitely noticing some issues with intersections that involve curved surfaces, as I've noted here on one of your pages. It's pretty normal for students at this stage to be reasonably comfortable with intersections between flat surfaces, but to still struggle with those either between flat and curved surfaces, or between two curved surfaces. The key here is to always regard your intersections not as being between two forms (for example, thinking about an intersection between a sphere and a cylinder as an intersection between two rounded forms would be incorrect), but rather to look at the individual pairings of surfaces that intersect over the course of the whole intersection.

If we look at the intersection I focused most on, towards the bottom right (the sphere and cylinder), you'll notice that there are two pairings of surfaces. There's the sphere's single curved surface with the lengthwise direction of the cylinder's length, and there's the sphere's single curved surface with the flat end of the cylinder. Of these, the cylinder's end being flat is pretty clear, but what one might not always consider is that the length of the cylinder is curved in one direction (as we wrap around the shaft of the cylinder), and straight/flat in the other (lengthwise).

It simply isn't enough to memorize what kind of intersections occur between different forms - we have to look at the nature of the intersection, and all of the individual pairings that make it up. This may seem daunting, but this diagram may help you better understand how to think through these kinds of spatial problems. It explains how we might decide which surfaces are relevant to a given section, and how that changes if we were to take an edge of one form and make it more of a rounded transition.

Alrighty! Moving onto the object constructions, in principle you're moving in the right direction, but there are a lot of cases I can see where mistakes were made that could have been avoided by giving yourself more time to execute the work to the best of your ability. The most significant of these comes down to how you're deciding to orient your lines as you draw. This manifests in a few different ways.

• This water jug is a pretty good example of a case where on one axis, the bounding box you started off with was pretty heavily skewed. If we extend the lines as shown here, we can see that the top plane of the box has far more dramatic foreshortening applied to it than the bottom plane, resulting in the edges of the top plane converging very rapidly, while the bottom ones barely converge at all. These kinds of things definitely happen, and the main solution (aside from what I'm going to explain about using rulers momentarily) is to ensure that you have been keeping up with your box challenge type exercises as part of your warmups (with the line extensions included). Of course, once it's happened, all we can really do is push forwards and work within the box we have, but it certainly does have a negative impact (as we can see here with the subdivision lines that result from this, and we need to do all we can to avoid it - especially putting in the extra time to consider how our lines behave as they extend off into the distance.

• I'm putting this as a separate point for clarity - I wanted to quickly explain how we can actually leverage our rulers to help us when deciding the orientation of our lines. While it's always necessary to put the time into considering how our lines are oriented in order to achieve consistent convergences, when we are allowed to use a ruler this can be made considerably easier. While the edge we wish to draw may not be more than a few inches, rulers are generally a great deal longer than that. As a result, they give us the opportunity to see, by following the edge of the ruler, the direction in which that line will continue if extended, giving us something to compare more visually against the other lines that are already present in our construction, all without ever having to commit to making a stroke. If we are conscious of this, we can use the ruler to help us avoid really egregious misalignments and keep our margins of error relatively low.

• As shown here on this stool there appears to be quite a few elements that were largely approximated/eyeballed, resulting from structural steps being skipped. Drawing through our forms and ensuring that each stage of construction builds directly off the last one (adding intermediate steps as needed to help make those decisions) is an important part of what we're doing here. Remember - the goal is to go through the process in order to rewire our brains and develop our internal spatial reasoning skills, not to simply do whatever is necessary to achieve a given result. Each step, which we take purposefully and intentionally, contributes directly to what we get out of the exercise.

• For the cylindrical structure in the bottom half of this construction, it would certainly have been beneficial to build it up as a box first, as this can be oriented in 3D space, and in relation to the structure to which it was attaching, more effectively than a minor axis line alone. I can also see a number of points that were approximated - for example, the vertical positioning of both the lock and the doorknob.

Ultimately this lesson leans heavily into the concept of precision. 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, and other such intermediary steps. 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 explained here and by extension here as well (in the context of drawing curved structures), these intermediary steps and orthographic plans allow us to make clear and intentional decisions about the object we're constructing. Having those decisions made prior to actually executing them in our 3D construction allows us to focus entirely on execution when that time comes.

Now, while I feel that you could certainly have produced better results had you given yourself more time to go through all the steps, I am going to be marking this lesson as complete. I will warn you however - it's extremely important that you address the points I raised here, especially when it comes to avoiding skipping steps, making sure each step builds directly onto the one before it, and focusing on making your decisions separately from their executions, as Lesson 7 is more of the same, but vastly more difficult. The constructions we do in that lesson can easily take several hours, so be ready when you get there to really give them your all, as is required of all our students (as explained in Lesson 0).