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Lesson 1: Lines, Ellipses and Boxes

Boxes: The Basics of Perspective and Projection

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The purpose behind the rules

On this page, as well as in the next few, we're going to be discussing perspective. This is a concept that is taught in many other courses and books, although it's primarily through listing out a series of rules, then introducing specific techniques (like creating a 1 point, 2 point, or 3 point perspective grid).

The way I wish to tackle it is a bit different, and admittedly a lot longer. The reason is that I've found that by merely memorizing rules and techniques, you're left tied to them, rather than being able to use them as tools to achieve your goals. Having been subjected to this approach as a student myself, I found it led to more confusion in the long run than understanding.

Instead, while we are going to talk about those rules, we're going to be delving into the logic those rules are meant to encapsulate. It will be confusing and complex (especially in the next few pages), but don't let that scare you. Understanding the theory is not the goal here. It merely serves to lay down some context - some of which you may grasp, and some of which may seem baffling.

The true understanding will be developed through the exercises that follow, and even that understanding will develop gradually over time. So don't let yourself feel discouraged by the complexity of the topic. Don't get hung up on the theory, as the worst thing you can do is let it derail you from even reaching the exercises themselves.

Boxes and perspective

Finally, we've reached this course's namesake - boxes, and by extension, perspective.

Perspective, which serves to help us depict 3D spaces on a flat page, is inextricably tied to boxes, for a very simple reason: where 3D space consists of three dimensions, boxes provide us with three distinct sets of edges, each of which flow in the direction of one dimension, and perpendicularly to the other two.

By focusing on boxes, we're able to use the principles of perspective as a starting point, and extract the core element we really want to focus on: an understanding of 3D space, and how we can go about capturing it on a flat page.

Not a perspective course

Firstly, it's important that you all understand what Drawabox is, and what it isn't. Drawabox is NOT a perspective course. Linear perspective is above all else a series of rules and techniques with extremely specific steps and considerations. Study the rules, remember the rules, and painstakingly follow the rules - and you'll be able to construct scenes that look and feel three dimensional. But that's not what we're doing here.

Drawabox is, as discussed in Lesson 0, all about developing students' spatial reasoning skills. This is something we are working to develop on an instinctual level. Everything we do throughout this course - even the constructional drawings we embark upon in Lessons 3-7 - are exercises. The goal is not to create pretty drawings, but rather to follow a process, follow a set of steps, that actively rewire the way in which your brain perceives and approaches 3D space.

The difference is that while most perspective courses will arm you with a ton of things to keep in mind as you're working through a drawing, with the purpose of consciously applying those concepts, what we're doing here is training and shaping your instincts, so that when you do draw your own things, you can focus not on how to execute a particular mark, or how to construct a given form, but rather what it is you actually want to draw. The rest will have been practiced to such an extent that it will be second nature, freeing your brain's mental resources to focus on deciding what it is you actually wish to depict, how to go about designing it, and so on. Not the nitty-gritty of how a particular line gets from point A to point B.

That doesn't mean Drawabox is better at teaching perspective - it's simply got a different goal. There's a lot of value in exploring Linear Perspective in its entirety, especially for when you encounter spatial problems that need to be nailed perfectly. This isn't something you'll encounter often, but having an understanding of the rules, and what rules and techniques actually exist, will ensure that when you run into those situations, you know what to go searching for in order to solve those problems.

Here are a couple courses from our sponsor, New Masters Academy, which can help provide a solid overview of Linear Perspective:

  • Linear Perspective Master Course with Erik Olson

  • This is one of the most comprehensive breakdowns of perspective you can find. Many courses don't go much farther than looking at 1/2/3 point perspective, but one of the things I love about Erik's course is that he dedicates an entire lesson to the idea that scenes and objects are not restricted to a maximum of 3 vanishing points - a concept that is often overlooked, or left to the student to figure out on their own.

  • Stress-Free Perspective Sketching with Sheldon Borenstein

  • This course focuses on the essential principles of perspective without getting lost in the technical stuff - it's great for going out and drawing scenes and buildings from observation, and a great way to learn to have fun and relax with your art.

Sign up to New Masters Academy with the coupon code DRAWABOX — you'll get a full 25% off your first billing cycle (applicable to the Library and Library+ plans).

2D vs 3D

Drawing has always been a matter of taking things that exist in three dimensions - the human figure, the objects around us, animals, and every combination of those we can cook up in our imaginations - and figuring out how to capture them on a two-dimensional flat page. It's about going beyond seeing our drawings as a series of marks upon the page, but rather seeing the page itself as a window, looking out upon a three dimensional world that extends off in every direction to infinity.

This can very quickly become confusing, especially when pinning down exactly what the words we use when describing the problems we face really mean. So, in the interest of consistency, let's try to set out some guidelines on what certain common terms mean, and organize them into terms that refer to 3D elements, versus terms that refer to 2D elements.

2D

  • Shape. For our purposes throughout this course, whenever we use the word "shape", we're going to be referring to the flat shapes like squares, rectangles, circles, and triangles - that is, things that exist only in two dimensions.

  • Line. This describes a path or stroke drawn on a flat surface. It only moves across the page itself as we're drawing.

  • Point. This describes a dot placed on the page - like those we use to define the start and end points of our lines when employing the ghosting method. They exist exclusively in the two dimensions of the flat page.

3D

  • Form. This denotes a three dimensional structure - like a box, a sphere, a pyramid, a cone, a cylinder, as well as more complex or organic structures. While we may draw a representation of a form on a flat page, we're still thinking about it as though it exists in 3D space.

  • Edge. This refers to the hard separation between two distinct faces of a given 3D form. When drawn on a flat page, they're represented using lines, but we still need to consider how the edge being represented exists in three dimensions, and how it relates in three dimensions to the edges and forms around it.

  • Vertex. The "corners" at which different edges meet in 3D space.

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Projection

The act itself of taking something that exists in a 3 dimensional space, and capturing on a 2D surface - or taking anything that exists in some kind of "higher order" of dimensions and having it represented on a lower order of dimensions - is known as projection. In a manner of speaking, if you stand outside on a bright and sunny day and find yourself casting a shadow on the flat surface of the ground, you're effectively projecting yourself - a 3D object - onto a flat surface with no depth.

Perspective is one approach for projecting 3D space onto a 2D surface, but it's not the only one. In fact, it is only functionally useful if your desire is to replicate human binocular vision - that is, capturing how things look when seen from two eyes arranged on a face. There are other approaches that have their own goals, advantages, and disadvantages.

  • Orthographic Projection. This is an approach that uses multiple drawings of an object in order to capture and define how that object exists in space, but only ever depicting two dimensions at a time. So for example, you might be provided with a drawing of the top view, one of the side view, and one of the front view of an object, and using all of these images together we can understand the object in full.

  • Axonometric/Isometric Projection. This is an approach that attempts to combine all of the information of a 3D object in a single drawing, by ensuring that every set of edges that are parallel in 3D space are also drawn as parallel to one another in 2D space. This is quite handy in video games, as things do not get smaller as they move farther away from the viewer - they remain the same size. This allows game artists to create tile sets that can continue in infinitely in any direction, without needing to change in scale.

<<< Ellipses
Boxes: Foreshortening and Vanishing Points >>>
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Getting Your Work Critiqued

Critiques on reddit.com Critiques on our discord chat server

Having your work reviewed by others is critical, as those who are just starting out aren't in a position to properly judge their own work, and won't be for quite some time. Don't be afraid to show your struggles - it's by analyzing your mistakes that we can help you grow. Perfect homework is not what we're looking for; we just need it to be complete.

There are currently two places you can get your work critiqued by the community - Reddit and our Discord Chat Server.

Both of these are completely free.

Private Patreon Critiques

Critiques on reddit.com

If you are interested in receiving extra help, I critique the work of those who support Drawabox on Patreon.

All of these private critiques are done through reddit, in specific threads where students post their work as a comment, including a link to their work (often hosted on Imgur, though most image hosts are okay).

My requirements are more strict than the free community critiques:

  • You must complete the lessons in order, in their entirety, starting from lesson 1
  • All work for the lesson must be completed - that means all exercises in the lesson, not just those in a given section
  • You may only move onto the next lesson once the previous has been marked complete
  • The work must be done in the tools recommended in the lesson

The minimum pledge for this lesson is $5.00/month. The orange button above will take you to the reddit thread for this lesson, you can post a link to your work there and I'll be notified. Once I catch the submission, I'll add it to this backlog spreadsheet.

Pledges are collected at the beginning of the following month, but you may start submitting your work immediately. If you're a new patron, I'll be reaching out to your shortly to collect your reddit username.

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