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Lesson 1: Lines, Ellipses and Boxes
Organic Perspective
This is the last exercise of lesson 1, and it's a doozy. Like the rotated boxes, what I want most is for you to complete the recommended number of pages to the best of your current ability. No more, no less. We're not looking for you to impress anyone, but rather to face the challenges head on so they can start making you think and consider a new kind of spatial problem.
Draw a path for our boxes to follow
This exercise is going to involve drawing a lot of boxes that flow along a gently swooping path through the depth of our scene. In order to help us keep track of our desired path, we'll start out by drawing it.
Be sure to use your shoulder for this, and draw confidently. Accuracy isn't particularly important here - just let your arm flow naturally to create a swooping stroke that goes back and forth.
Draw a Y for your first box
Using the ghosting method, draw a Y as shown here. The lengths of the various arms is up to you, but do make sure that the angles between them are of at least 90 degrees - when the angles get smaller than that, things tend to get a little... weird.
This Y gives us 3 edges of our box, radiating out from the corner (the center of the Y) which is closest to the viewer. This is very much 3 point perspective - meaning that we're dealing with 3 concrete vanishing points, and we're going to have convergence for all three sets of parallel edges. That suits this exercise just fine, as we'll be drawing boxes that are rotated randomly, rather than aligned in any particular fashion to the direction the viewer is looking.
This is the first step of the "Y Method", something we'll be using extensively throughout this course.
The Y Method
The Y method is extremely useful - not only as a tool for drawing our boxes, but as an exercise to help us keep our focus on the convergence of our parallel edges. The main challenge that faces us when constructing boxes like this is that we ideally want all of the edges of a given set to converge to exactly the same point. That means judging the angle of their trajectory to nail a point that could be quite far off - it's not easy to do.
This approach starts out with 3 edges, one from each set, pointing to its own vanishing point. As we add more edges one at a time, we solidify where each vanishing point will be (the first line points at it, and the second line points at where along the first's trajectory the VP is located specifically), and then the rest of the edges simply have to match up with the first two.
Well, I say "simply". It's not so simple, but this technique allows us to target this specific skill of estimating convergences and develop it efficiently. We'll be doing a lot more of this after Lesson 1, in the 250 box challenge, but the organic perspective exercise allows us to introduce it to you.
Negotiating a corner
The Y method hinges on drawing a Y, but it doesn't necessarily dictate what order in which you should be drawing your other edges. What we can do however is combine it with the tools given to us by the ghosting method - specifically the points we use to mark out where a line should start and end - to consider a variety of sources of information before deciding on and committing to a particular line to represent an edge.
As shown here, I've got a blue arrow, ending in a little dot. The blue arrow isn't something you'll draw on the page, but rather it represents the path we think our edge will need to follow. Since we're at the early stages and only have one edge actually drawn (from the original Y), technically anything we choose here will be correct as long as it converges in the same direction as the existing edge.
As we add more however, we'll have to focus on having those edges converge consistently. To do that, you can ghost in the direction you think the edge should go, and place a little point somewhere along that path (ideally a little beyond where you think that edge should actually end).
The great thing about these points is that they're so small. Mine has been drawn a little bigger than I normally would so it can be visible in the example, but these points can be quite tiny. This also means that unlike a whole drawn line, they don't really carry a lot of weight and are very easy to ignore.
So, using these points, we can consider certain trajectories, mark them out on the page, and then consider other edges to see if our idea is going to work out.
Negotiating a corner, continued
A corner is where multiple edges meet - but if we only consider an edge coming from one direction to decide where a corner should be, we've only got part of the information. So, let's consider a different edge.
Here, just like before, I've got an arrow in red representing the trajectory I think this edge will need to follow. Rather than drawing it, I've ghosted through its path, and like before, placed a dot at its end.
A compromise
We've got two points, but a single corner must exist in a single location. There are a few ways we can decide where this corner should be, given the information we've got. We can either choose to pick one of the two we've already drawn, or we can create a third point based on the other two - a sort of "average".
It doesn't specifically have to be perfectly in between the two - at the end of the day, you're making that call based on the information you have.
I ended up adding a third point, somewhere in between the two others.
Repeat the process
We can do the same thing for our other three visible corners. As noted in the video at the top of the page, when you're first doing this exercise as part of your Lesson 1 homework, you won't need to draw "through" the boxes as though you have x-ray vision, so each corner's going to be the result of 2 edges.
When doing this exercise in your warmups, and when doing the 250 box challenge, you'll be drawing through your boxes, meaning that there will be a third edge coming in from the opposite side of the box, adding yet more information to help you make an informed decision.
Similarly, as we consider the other corners of this box, we should also be thinking about more than just the two edges at play - because each edge also has to consistently converge with the others in its set. This means you'll be jumping around a lot, considering not only the 2 edges that meet at a given corner, but also the other edges from elsewhere in the box.
This may be a lot for you to worry about all at once, especially this early on, so take it slow. It's okay to limit yourself to focusing on just the two edges for now - as you get used to it, you'll find the number of things you can be considering simultaneously will increase, especially with all the practice we'll be getting through the 250 box challenge.
There's really no reason to rush into things or push yourself beyond your limits here. We're simply introducing the concept, so do what you can. Students who have done their current best to follow the instructions for this exercise (and who despite that still end up with all kinds of issues) do not get assigned revisions.
Fill in the rest of the frame
All that's left is to fill in the rest of the frame. You might have noticed here that the example is entirely different from the last one - I just switched to the example from the video.
Keep in mind that as you draw boxes farther away along your given path, they'll be getting smaller. For the purposes of this exercise, avoid particularly dramatic foreshortening - keep the convergences of your box pretty gradual, so we can avoid ending up with scale that feels inconsistent across the whole set.
The purpose of this exercise
The purpose of this exercise is to throw you into the deep end of the pool without having yet taught you to swim. By diving into this exercise, you're being forced to contend with freely rotating boxes in 3D space without any real grounding of how to deal with them. There's no concrete vanishing points that you're marking out on the page, no neighbouring forms to base things off. It's more guesswork than you'll have dealt with by this point. It's actually been the pattern we've followed - gradually stripping away our rules, forcing you to rely more and more on educated guesses and intuition.
So expect to make a lot of mistakes. The point isn't to be able to nail this, but to get your gears turning as you start thinking about the fact that this is a kind of spatial problem you're facing, likely for the first time. We're exposing you to it because you likely wouldn't have really considered this sort of thing otherwise.
Example homework
So like the last exercise, it doesn't really matter if your work comes out looking like this. What's important is that you strive for it, so you're forced to start thinking about how these forms can be rotated freely in 3D space. You will struggle with it, and you're meant to.
When you're done, that'll mark the completion of this lesson. Don't worry if you had any trouble at all - it's expected, and you'll be diving into the 250 box challenge after this (once you've had your Lesson 1 homework critiqued and marked as complete).
Orconomics by J. Zachary Pike
This is one of my favourite books. It's a fantasy-comedy romp, and the world that J. Zachary Pike has created honestly takes my breath away. There are laughs at every turn, but the story is not without its heart wrenching moments - some for which I have yet to fully forgive the author.
If you're at all curious about the kinds of nonsense I read, or just need something new to sink your teeth into, this is one I can highly recommend. On top of that, being self-published by an indie author, it's the kind of thing where your individual support can go a long way.
P.S: The audiobook, with narration from Doug Tisdale, is especially good, and elevates the story in ways I can't rightly describe.