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.

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.

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.

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.

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).

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.

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

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

3. 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.

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 machine-cut 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.