Jumping right in with your form intersections, this is more or less the first point we revisit this exercise after first having assigned it back in Lesson 2. What we expect to see isn't a perfect mastery, as it relies on the same spatial reasoning concepts the course as a whole seeks to strengthen and develop, but it's normal for students to be more comfortable with intersections involving flat surfaces, while still having some difficulty with those involving surfaces that curve.

Overall I think you're progressing fine with the focus of the exercise, although I do think there are some issues with how you're choosing to approach the assignment that may reduce its effectiveness a little. In addition to the issues I noted here, here are some points to keep in mind:

• I noted this on the page, but I wanted to reiterate it here given that we just got out of the cylinder challenge. You should be constructing your cylinders around a minor axis line (which was actually first introduced in one of the steps of the form intersections (specifically the diagram), and then reintroduced in the cylinder challenge. You should also not be drawing your cylinders with edges that are parallel in the page, given that these cylinders are rotated freely in space and not specifically aligned to the viewer, as explained here. I believe I also mentioned this in your cylinder challenge.

• I noticed some spots where the intersection you drew would be on the opposite side of a form - in other words, not actually visible from our viewpoint. While we stress the importance of drawing through our forms in their entirety, when it comes to the intersections, it's best just to draw the part that would be visible as to avoid unnecessary confusion.

• When drawing your intersections, always focus on the surfaces that are actually present. You generally do, but when it comes to curving surfaces you do sometimes get the curvature of the surface reversed when drawing your intersection line - for example here where the box-sphere intersection should actually be curving in the opposite direction, along the surface of the sphere. As shown in this diagram, considering the individual surfaces that are intersecting can help you identify in more complex situations, like spheres that curve in many different directions, which direction to focus on.

• In general, there's a lot of space left on the page that could be used for more forms, so you may want to reflect on why you're deciding to stop where you do. Remember that the purpose of homework is not to get it done and out of the way - it's to learn from it. We already have structures in place to keep students from grinding needlessly (as long as they follow the instructions, only do the number of assigned pages, etc), so you really shouldn't be actively making choices to reduce that further.

Continuing onto your object constructions, while admittedly your orthographic plans look a little rough and haphazard at first glance, looking more closely I can see that you are indeed applying the concepts to them quite well in most cases, and that you are holding to the core principle of precision that we push throughout this lesson.

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.

One of the biggest tools we have to achieve that is the combination of the various subdivision/mirroring techniques, and the orthographic plans in which we figure all of those steps out before reconstructing it all in 3D space in a repetition of the same steps we performed in two dimensions.

There are two quick points to keep in mind though - looking at these orthographic plans of a mug, the top-down view probably isn't really necessary (in that it doesn't actually provide additional information so you don't really need to draw it), and for the side view, you seem to have gotten a little confused and tried to place ellipses/curves on the top and bottom edges. Since we're looking at it straight on from the side, the top and bottom edges of the mug would be completely straight, no curve or ellipse visible, because here we are using orthographic projection, rather than the usual perspective projection employed to make something appear three dimensional. You can read more about this here, and in the video at the top of that page.

Actually - in terms of the top view not being necessary, there may be more value in it if we included not just the outer circumference of the circular cup, but also the inner wall to create a ring with thickness. In your construction you left that inner wall out (so the cup reads as being paper thin) - not the worst thing in the world, but it probably should have been something you included in the construction.

Aside from that, you've done a great job with the object constructions. So, I'll go ahead and mark this lesson as complete. The form intersections will also be assigned as part of Lesson 7, so be sure to continue practicing them in your warmups to apply what I've shared here.