Normally I do critiques twice a week (Tuesdays/Thursdays) and on those days I only handle the submissions that came in by midnight that morning. As such, yours is a few hours past the cut-off, but I decided to tackle it today anyway for two reasons:

• I didn't really want to leave you waiting 5 days for feedback if you didn't need to, and more importantly

• You've done a really good job, so this critique shouldn't be too time consuming to tackle.

Jumping in with your form intersections, your work here is coming along quite well. That's not to say it's perfect, but this exercise is one that represents the core challenges we explore throughout this course as a whole, so it also happens to be one that is expected to evolve and improve for students as they face the different kind of spatial reasoning problems this course introduces throughout its length. All that is to simply say that we expect students to have improved upon what they were able to do back in Lesson 2, but that this exercise will come up again in Lesson 7, so we don't expect students to handle this perfectly (although we technically don't expect that at Lesson 7 either).

What's normal to see here is that students are solidly comfortable with intersections involving flat surfaces, but might still struggle with those involving curving surfaces, especially those involving multiple curved surfaces. I would put your work at being far enough along so as to demonstrate a level of comfort that is beyond what I would expect at this stage, but there are a few intersections where things can be improved, as shown here.

There are a few points to keep in mind:

• Intersections can be thought of kind of like multiplication, in that multiplying any number by 1 just gives you the same number. We can think of a flat surface as being like 1, whereas a curved surface is like a number greater than 1. Multiply two flat surfaces together, and you still get a straight line (like 1 x 1 = 1). Multiply a flat surface and a curved surface together, and you get the curvature of the curved surface (1 x n = n). Multiply two curved surfaces together and you get a much more complex value (3 x 4 = 12), which for our purposes here can be thought of as the difference between a simple C curve, and a more complex S-curve.

• A single surface can be curved in one direction, and flat/straight in another. We can see this in cylinders for instance, for which the lengthwise surface curves in one direction, but is actually composed of straight edges when we look at the dimension going from one end to the other.

• This diagram may help as well - it demonstrates how we identify which "slices" of the forms are relevant to a given construction (like how the planes of the box determine which slices of the sphere we should be looking at to determine its curvature in the orientations of those individual planes), shows how our intersections end up with sharp corners when they have to change trajectory to jump from one surface to another where they meet at an edge, and shows how that sharp corner transitions to a more gradual one when that edge is turned into more of a rounded surface.

Continuing onto your object constructions, you've really knocked this one out of the park. Your work shows a clear adherence and focus on the concept of "precision" which underpins all of the concepts shared 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.

In leveraging the orthographic plans introduced here so fastidiously, and really using them to make concrete decisions that can be applied in precisely the same manner in 3D space as they are laid out in 2D (using subdivisions), you've really done a fantastic job of ensuring that every action is the result of a clear decision made ahead of time. As a result, this is reflected in the extremely solid nature of your 3D object constructions, which also bely the patience and care that was taken in their production.

I am also very pleased to see that you followed and applied the point introduced here regarding building up curves by first starting with chains of straight edges or flat surfaces. It's very common for students to skip over that, or to forget to do it, so seeing it leveraged in your work at multiple points - especially in the guitar - shows how carefully you've gone through the material.

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