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Lesson 6: Applying Construction to Everyday Objects
Overview
Prerequisites
By this point, I expect you've completed up to lesson 5, as well as the following challenges:
What you learn in these challenges will play an enormous role in the work for this lesson, as you'll primarily be manipulating boxes and cylinders, as well as forms that share similar properties to them.
About your tools
Up until lesson 5, I've been very adamant drawing everything freehand, with felt tip pens, and so on. And this has been for a good reason  it's important to maintain a certain degree of the right kinds of challenges to ensure that you guys gain as much as you can from each lesson.
This lesson, however, is going to be a little different. I am allowing, and in fact encouraging the use of the following:

Ballpoint pen for your linework (don't switch pens to do any sort of "cleanup" pass  use the same pen through all your lines, including construction/box subdivision/etc)

Brush pens for filling in large areas with solid black

Rulers/straight edges for drawing precise linework (this lesson is not where you want to be practicing your freehanding skills, so refer to the exercises from earlier in the course for that sort of thing)

Ellipse guides for constructing and aligning your ellipses

French curves for any complex, curving lines
Whenever drawing freehand, I still want you to apply the methodology I've outlined in the past  the ghosting method, drawing through ellipses, and so on. That said, in this case it is inevitable that with all of the necessary construction lines, and the significance placed on precision, it's important for you to be able to use tools that will allow you to focus more on the meat of the lesson, which is really about the manipulation and construction of complex compound forms.
As before, do not use pencil or digital media.
Introduction
Originally, at this point I tackled 'hard surface objects' by diving into vehicles like tanks and locomotives. This time I've decided to add one more lesson to the list  every day objects. The vehicles will come in the next one, so we can work our way up to them.
The last handful of lessons all dealt with fairly organic subject matter. The constructions involved fairly fluid interpretations of geometric forms at most, though usually we'd construct voluminous blobs and then chisel them into planar forms. So, lets look at some basic concepts before we go into the demos.
Form Intersections
If you remember lesson 2's form intersections, this is going to be very similar. The only difference is that instead of arbitrarily dropping in forms and connecting them however you like, we're going to attempt to construct concrete objects. This means keeping an eye on the proportions and the positions of your forms.
Center of a plane
On the left, you'll see an invaluable technique for finding the center of a quadrilateral plane. Finding the intersection point of the two diagonals of your quad will give you its physical center.
This is extremely useful. Due to the basic premise of perspective, we can't simply use a ruler to measure things out.
Subdividing
With the center of the plane found, you can draw lines that converge towards the same vanishing points as each of the other two sets of parallel lines that pass through our center point to subdivide the plane into four quadrants of equal size.
For more information on subdivision as a whole, you can check out this video on taking the exercise from the box challenge further.
Subdividing more
This technique can be used multiple times, as every time you find the center of a quad, you can use it in conjunction with vanishing points (whether explicit or estimated) to divide your quad into four smaller quads. You can then repeat the technique on those quads to further subdivide them.
This can be a great way to create a grid on a surface in perspective, which is a great way to pinpoint the correct proportions, or the accurate positioning of a detail or other intersecting form.
Subdividing thirds
That works great when you want to divide your planes up evenly, but what if you want to split them into thirds? This image explains how to go about it.
Basically you lay out the lines you'd need to subdivide your plane twice evenly, and in doing so, you'll find that your diagonals will also cross at four other points. These mark where your plane can be divided into thirds.
You can find information on how to subdivide your planes into many different fractions from this post on Andreas Aronsson's blog (we previously linked to the website, but it has since been taken down, so this is a PDF saved off the Internet Wayback Machine).
Mirroring
Another technique you'll need for this lesson is to be able to mirror a line across the center of a plane, from one side to the other. For example, say you have a line some distance in from the right side of a plane. This technique will allow you to draw another line the same distance away from the left side of the plane.

First, we find the center of the plane using the technique above.

Next, we draw a diagonal from the ends of the line we want to mirror, through the center of the plane.

Finally, we note the points where the diagonals intersect the edges of the plane and draw a line between these points.
You'll find yourself using this technique pretty frequently, and it comes up in some of the demonstrations as well.
Orthographic plans
In the computer mouse demo, specifically this step we introduce the concept of using orthographic plans to help lay out our object.
As I've taught this concept and critiqued this lesson's homework over the years, I've come to realize how valuable this concept is towards the specific focus of this lesson  and have taken it much, much farther than originally explained.
Eventually, when the gradual overhaul of the lesson demos reaches this lesson this approach will be leveraged throughout the material, but in the meantime, I wanted to provide a detailed explanation on how this works. You will find a demonstration on how to approach orthographic plans here. Try to apply this throughout all of your object constructions for this lesson, as well as those in Lesson 7.
There are two key points in this demo to keep in mind:

Every single action I've demonstrated there for this orthographic, two dimensional analysis of the object, can be reproduced in three dimensions. It relies either on subdivision, mirroring, or leveraging the points at which diagonals cross established horizontals or verticals. We can follow the exact same steps on a plane in 3D space, allowing us to transfer this information into 3D space... as long as we're patient about it.

We are not finding the accurate locations for each landmark. Rather, we are deciding where they will go. The reference image is a source of information, but how we ultimately use it is up to us to decide, so we do have the freedom to say "I'm going to go with 2/5ths instead of 19/50ths". Of course the more of this we use, the further we may drift from the actual reference, but for our purposes in this course that is fine. What matters is that the plan we create here, and the construction we ultimately create in 3D space match up and follow the same process.
Curves
One important point to keep in mind here is the nature of curves. Curves are inherently vague  they capture the essence of several different configurations of straight lines, and in doing so, can very easily be used to fudge a construction. Given what we're dealing with here is often machinecut with precision, the last thing we want is for our constructions to carry an air of approximation.
As such, we need to ensure that every single decision we make with our construction and linework is a clear and singular one.
As such, I want you to hold off on curves for as long as you can. Stick through most of your construction to squared edges. Then, as you come to the end, you can tightly round off corners as needed. This adherence to a specific configuration of straight lines until the final step will help imbue your drawing with a sense of clear intent.
You will also find a demonstration of this approach within a construction in how the handle was constructed on this mug. Be sure to employ this approach in your constructions, whenever dealing with any kinds of curves or rounded surfaces that don't conform to a basic primitive (like a sphere or a cylinder).
Homework and exercises
Before starting the homework, be sure to go through all of the demonstrations included in this lesson. I strongly recommend drawing along with them as well and following them closely when doing so.
Also, remember that this homework must be drawn from reference. When looking for reference, I recommend that you specifically look for those of a higher resolution. Google's image search tools allows you to limit your search to large images, and I recommend you take advantage of this. You frankly should also be working a great deal from life for this lesson, as you ought to be surrounded by fantastic subject matter, given that it's all about everyday objects.
The homework assignment for this section is as follows:

3 pages of form intersections, just like from lesson 2.

8 pages of everyday objects. Vary your subject matter and the nature of their construction  choose some that are largely cylindrical, some that are boxier, etc.
All the assigned work for this section should be done in ink. You may however use ballpoint pens, rulers, ellipse guides and french curves as needed. In this lesson we are no longer focusing on freehanding our lines, rather on our use of the kinds of marks we draw.
Proko's Drawing Basics
Drawabox isn't the beall, endall of drawing fundamental education. Our approach prioritizes certain concepts over others, and while we believe it do so for good reasons, ultimately it doesn't appeal to everyone. If Drawabox simply doesn't work for you, give Proko's Drawing Basics course a try  at the very least, you'll probably find it to be a hell of a lot more fun.