Isometric projection is a simple way to draw 3D shapes. The meaning of isometric is "equal measure," from the Greek words iso- for equal and metric for measure. So, in an isometric drawing, all three axes, x, y, and z, are scaled equally, giving a clear, undistorted view of an object in three dimensions.

Except that isometric drawings can look a little odd and oversimplified. This is because of the lack of perspective, a visual distortion of 3D shapes we experience in the real world. In a perspective drawing, parallel lines converge in the distance towards a vanishing point, but in an isometric drawing, parallel lines stay parallel, and sizes don't get smaller in the distance.

The lack of perspective in an isometric view can make it look artificial, but it always looks clear.

I learned isometric drawing when studying engineering. Armed with a stack of isometric paper with a printed isometric grid, we had to reel off exercises involving drawing isometric views of 3D objects. And isometric projection is really handy for this. It can take a long time to build the skills to sketch a realistic 3D-looking object, perspective and all, but with isometric paper, you can quite quickly produce something that communicates to you or others what's in your head or on the workbench.

Isometric projection is handy for boxy shapes—I chose an approximation of the Bauhaus Dessau building by Walter Gropius to show it. If you need curves and angles, just like with perspective drawings, it can help to draw more boxes around these areas and use them to align your curves and meeting points for your lines.

Isometric views and their variations have had somewhat of a resurgence of late in video and board games. It turns out they're pretty helpful in map-based or city-building games such as Zynga's Farmville, Civilisation, or Sim City as the isometric view allows all parts of a scene to be viewed equally—in the distance or up close—while still seeing every detail in, say, a building, wherever it is.

If you want to try some isometric drawings, making your own isometric grid paper is easy. Just draw equally-spaced vertical stripes and then a criss-cross of lines in both directions at 30 degrees from the horizontal. This gives a host of equilateral triangles and an easy base to start drawing your 3D objects. Or just download some templates online. You'll find that building up more complex shapes out of cubes is dead simple if you keep to the lines on the isometric grid.

Just as in the drawing here, sometimes shapes drawn in isometric view lend themselves to curious optical effects. The lack of perspective can make the difference between heights and depths ambiguous. So, you can't always tell if two surfaces are at very different heights or if one is in the distance. The brilliant puzzle game Monument Valley uses this quirk of isometric projection to create mind-bending puzzles that are well worth a try. For instance, rotating a high surface can suddenly make a platform that extends far into the distance 🤯.

Isometric-like projection can also help make impossible shapes, such as the Impossible Staircase, or Penrose stairs. Another type of projection, anamorphosis, creates a drawing that only looks correct from a particular viewpoint. Anamorphosis leads to some remarkable street art.

2.5D objects, including an old video of me drawing a sketchplanation

The Impossible Staircase, or Penrose stairs

When drawn nice and faint, the isometric grid is an example of a ghost grid

Isometric projection is quite the opposite of "draw what you see, not what you think." Foreshortening can be hard to get the hang of.

Isometric projection

Parallax is the change in the apparent position of objects from different viewpoints. For example, from one viewpoint, a nearby house may appear in front of a hill, and from another, it may be in front of a lake. Objects at different distances appear to move by different amounts. As you move between viewpoints, say when driving along a road, nearby objects move past you quickly, while distant objects appear to move by slowly. This difference in motion from near to far objects helps us determine how far objects are away.

I remember learning parallax from video games, like playing Sonic the Hedgehog on the old Sega Mega Drive. As the character moves in the foreground, elements at different distances in the background move progressively slower, creating a sense of depth. Saturation and contrast change at with distance also, known as atmospheric perspective.

I also enjoy observing parallax while looking out of a train window; nearby hedges and trees race by, buildings in the middle distance move more slowly, and distant hills or mountains barely seem to change. It's fascinating how our brains interpret this relative movement to judge distances.

One of the more intriguing applications of parallax is stellar parallax in astronomy. The basic geometry of parallax allows us to measure the distance of (relatively) nearby stars by observing relative shifts against the background of distant stars. Here's how it works: we observe the stars from different points in our orbit around the Sun. As a result, the stars appear to move relative to each other. By measuring this apparent shift, we can calculate the distance of the stars.

Parallax

The impossible staircase, also known as the Penrose stairs, is an optical illusion of never-ending stairs.

Named after its inventor, the mathematician Roger Penrose, who first introduced this concept in the 1950s, the illusion uses multiple, conflicting lines of perspective to trick your eye into seeing the stairs continually rise.

I imagined this is what would happen if you visited M.C. Escher's house. Escher made the staircase famous in his drawings Ascending Descending, and Waterfall, after being introduced to it by Roger Penrose, who Escher had inspired to create some impossible shapes.

The mindbending Penrose steps also appear in the movie Inception.

It took quite a long time to get the perspective right. Ultimately, I used the handy tutorial on drawing the Penrose staircase from the excellent Circle Line Art School.

Also see: the ring-segment illusion, the frequency illusion, the moon illusion, and the Hermann Grid, necker cube, and blivet

Impossible staircase

A ghost grid is a guide for organising thoughts, information and sketches, that doesn't compete with content.

Content itself can also be the ghost grid to highlight changes and help draw comparisons — as when you might sketch options for extending a house or designing a garden.

A grid is useful for structure and creation but needs to fade back from content or disappear when no longer needed. Like freeing data from its data prison, a ghost grid emphasises content and information without non-data-ink taking attention.

I learned the term ghost grid from Edward Tufte's Seeing with Fresh Eyes: Meaning, Space, Data, Truth.

I rarely buy other notebooks for work than a dot grid, preferably in a funky colour. Some of my favourites: Leuchtterm dot grid hardcover, Moleskine dot grid softcover, Moo soft cover dotted journals

Ghost grid

Ma is the negative space — the space that makes the whole. Formed by the rather beautiful Chinese characters of 'Door' and 'Sun', like the sun gleaming through a doorway, it represents what isn't there and how that helps form what is.

Ma is present in art, including beautiful minimalistic ink brush drawings and music where the silence and quiet that surround the notes help make a piece what it is.

Some vintage-related sketches: figure and ground, use white space with care, John Cage

SP 795 - Ma - smaller.png

When I look back at the LEGO sets of my youth compared to the LEGO sets of today, a few things are striking. Today’s is much cooler: the colours are better, the pieces are more interesting, and the sets are more clever (they also have a lot more weapons*). And the sets have their own characters: they’re not just nameless people in characterless towns—every set is full of people with names, expressions, backstories, personalities and goals. My observation, ahem, through our children, is that this makes it way more interesting to play with. It’s the characters and the story that make them so good now. A good part of that I think is also the shift in quality of expressions on the faces.

I am kind of in awe of LEGO faces. The number and variety and subtlety of expressions it’s possible to make with just a few small changes to a few small lines on a face I find truly astounding. This sketchplanation shows just a tiny bit of the variety from the LEGO Movies. Respect to the artists.

*5% of Lego boxes sold in 2001 contained Lego weapons. In 2014 that was 30% according to Bartneck C, Min Ser Q, Moltchanova E, Smithies J, Harrington E (2016) Have LEGO Products Become More Violent? PLoS ONE 11(5): e0155401.

LEGO faces

Anamorphosis is a type of projection that looks distorted when viewed from a standard vantage point or means but can reveal itself spectacularly from the right point or using the right tool.

This is the technique responsible for making 3D-looking ads on rugby fields that players can run over as if they weren’t there, or how they create those amazing street art holes, or how S L O W painted on a road may look just right when driving towards it but weird and long when seen from the side; or how Hans Holbein the younger tucked a skull into his painting The Ambassadors in the National Gallery. However, others may require viewing with a mirror or a circular viewer to reveal themselves as intended.

Anamorphic art is referred to as intimate art, as even in an art gallery, the true picture may only reveal itself to one person viewing it in just the right way.

P.S. You’ll have to tilt your screen or move to quite an angle to see Tilt Me look like normal letters in the sketch.

Also see: one-point perspective, two-point perspective, 3-point perspective, draw what you see, not what you think, atmospheric perspective.

Anamorphosis

The effect you may have noticed where things further in the distance lose their intensity and colour until they fade into the sky. Most often noticeable with hills or mountains, but also in a misty forest as mist, dust, fog or things like pollution increase the effect.

If it’s a blue sky day, the distance will take on a bluer tone like the colour of the sky.

This scene painted from our ascent of Mt Rainier in the Pacific Northwest. And here’s a sunset version.

Atmospheric perspective

The 60-30-10 color rule is a handy and memorable technique for a great start in simple branding. 

Think of a suit where about 60% of the colour you see is the suit, 30% the shirt and 10% accent or highlight with the tie. Classic.

Also see: The basic colour wheel other drawing sketchplanations

60-30-10 Colour rule

With primary colours - red, blue and yellow - secondary colours, made by mixing the primaries - orange, purple and green - and complementary colours - from the opposites on the colour wheel - red and green, blue and orange, yellow and purple.

It’s fair to say there’s a lot more to colour than this basic wheel. I will try to get back to it.

The basic colour wheel

…by using the natural geometry of your joints. It took me a while to figure out that it’s easy to draw lines in some directions and hard in others. And most of the time it’s simply down to respecting the pivots of the elbow and the wrist. And also why we tend to angle our notebooks so much to the desk, and why, if you want to draw a smooth line at another angle, you’re really best-off just turning the paper.

As a corollary, I figured out that by looking at angle of most of Leonardo Da Vinci’s cross-hatching you can see that he was drawing left-handed.

Draw smooth lines

Orthographic projection is a handy technique for communicating much of what you need about something. In an orthographic drawing, you draw a face-on, side-on, and top-down view of an object, allowing you to see the same shape from different perspectives in a single drawing.

The neat thing I found about an orthographic drawing is how, when laid out as in the sketch, the dimensions of one view can be extended into the adjacent views, helping to keep the drawing accurate. I definitely felt some satisfaction and enjoyment working on an orthographic projection drawing on a large drawing board with a built-in ruler.

While orthographic projections can be helpful for accurately representing an object, they struggle a bit with hollows and some other features that can make them start to look a bit fiddly.

Perhaps combine an orthographic view with an isometric projection.

Orthographic projection

The proportions of the golden ratio pop up in all sorts of places. They are a handy shortcut to make something we seem to innately find pleasingly proportioned.

In nature, the golden spiral abounds in the shell of the nautilus, the spiral of strawberry seeds, the spikes of cacti, and hurricanes.

It’s found in the pyramids, the Parthenon, the Mona Lisa, violins, photography and, very deliberately, in corporate logos. No wonder it’s sometimes called the golden ratio of beauty.

There’s a pleasing simplicity to the equation too, where the ratio of the long over the short dimension is the same as both added together over the long dimension.

Check out some golden ratio examples. Even Trump.

This sketch features in my book Big Ideas Little Pictures along with 136 other fun and fascinating concepts.

The golden ratio

A 2.5D shape is three-dimensional, but the use of the third dimension, usually height, is limited to simple top-down operations. I learned about 2.5D, or two and a half dimensions, from my engineering days.

It turns out it’s really quite common to make 2.5D things because, for example, it’s easy to drill or mill down into something, and it's a pain to turn something on its side and drill from the other side. Or, as with vacuum forming, it’s easy to suck plastic onto a mold but a pain to get it off if you’ve got any overhangs as you can’t lift it straight up again. Hence, the plastic sandpit in our garden is a 2.5D object rather than true 3D.

As we become more sophisticated at making things, more objects will be true 3D rather than 2.5D. But the simple two-and-a-half-dimensional option is still generally cheaper and easier and will not disappear soon.

Civilization, in general, looks rather 2.5D from the air as we tend to build upwards, but we don’t find overhangs that easy or practical, thanks also to gravity, e.g., the Pyramids.

I recorded a video of the drawing of this sketch. Watch making a sketchplanation—2.5D

2.5D

Basics to consider for your photo and drawing composition. It has a long history.

Compose with the rule of thirds

Scribbling on a post-it doesn’t give your ideas they respect they deserve. Change the way you and others consider them by using a simple format that makes people think twice before dismissing and does more to get your idea across.

Treat your ideas with respect

Not my invention. Most recently spotted via the excellent Eva-lotta Lamm.

Easily draw expressions

One of the best things we did when on a significant traveling trip was to make our journal as a mindmap. There are all sorts of reasons why we found it better and more enjoyable to do at the time and better and more enjoyable once returned. Get a better idea than this sketchplanation by flicking through our mindmap travel journal

Try a mindmap travel journal

The little things like these make all the difference. Comic artists can only draw realistic bulging muscles because they know what muscles are actually where. Thinking through an object carefully, not superficially, makes a huge difference in being able to represent it well.

Think through the whole object

It’s very easy to draw what we think something looks like, rather than what we’re actually seeing. One of the things art classes teach you is to measure what you’re seeing to not let your eyes be fooled by your common sense. An art teacher in a class at Berkeley once, memorably, sat on the classroom floor to illustrate foreshortening like I’ve shown here. It has stuck with me.

Draw what you see, not what you think

In two-point perspective, we draw our vertical lines, vertical. In three-point perspective, our vertical lines are at an angle, converging on our third vanishing point above or below. 

The simplest way to experience third-point perspective is to stand at the corner of a tall building like a church tower and look up. Not only will the sides of the church converge to vanishing points to either side, but the parallel vertical lines of the tower will appear to converge at some point high in the sky—our third vanishing point.

Three-point perspective makes for a more realistic scene but only becomes apparent when there's enough vertical relief, either up to the sky or below, in what we're viewing. As a result, we most commonly see it in views of downtown skyscrapers, perhaps with a caped or swinging superhero.

Three-point perspective

Two-point perspective has lines that converge to two points on a horizon.

Two-point perspective

Perspective can be tricky to get your head around. In drawing and art, using perspective creates the illusion of three-dimensional space on a flat surface. The simplest form to understand is one-point perspective. You will have experienced one-point perspective when standing in a corridor or looking down the center of a street. If you continue the parallel lines of the walls and ground toward the center, they would appear to converge at a central point in front of you at eye level, known as the vanishing point. When real-life features are parallel like this, you can use a central vanishing point as a guide to help capture the scene accurately.

The simplicity of one-point perspective makes it impactful. Leonardo Da Vinci, a personal hero of mine, famously employed one-point perspective in his painting of the Last Supper in the Santa Maria delle Grazie monastery in Milan. The vanishing point, carefully placed behind Jesus' head, draws the viewer's attention to the main subject of the scene.

Turns out Kubrick is pretty handy at one-point perspective.

One-point perspective

Principles from Edward Tufte. Remove chart junk. Erase redundant and non-data-ink. Above all else show the data.

Of course the present infographic trend laughs in the face of these principles in the interests of trying to encourage people to actually look at the data in the first place. But, assuming you actually want people to seriously infer some meaning from the data, these are not bad principles to follow when constructing your data graphics. Some basic Excel templates could do with a clean up for example.

Maximise data-ink

Draw a basic bike

That little bit of extra space you give real edges makes a big difference.

Life is 3D. Give edges thickness

References and a better looking and interactive explanation on cuteify. Inspired by a brilliant little exhibit at the even brillianter Exploratorium in San Francisco. 

Rules of cute

Always handy to be able to draw some quick sensible looking people. Worth practicing.

6 simple sketch people

The Hermann Grid, the Necker cube, and the Blivet

Some optical illusions

Do: Structure and organise information as it’s said

Do: Write big - aim for letters at least 2in high

Most of what I know about visual recording from Jump Associates and The Grove.

When visual recording

Checking that things fit by rehearsing in the air is often a few seconds well spent.

Air-write before inking

Regail/bore people with the subtleties of leading, tracking and kerning.

Be a type geek

Most people I meet think I can draw. But they also don’t know how many times in my life I’ve screwed up a drawing and it didn’t come out like I wanted it to. I really believe that almost anyone can draw. With attention, practice, a thoughtful eye and a tolerance for mistakes we can all get there. No excuses.

Trust your picture

By now I have learned a thing or two. Massive thanks for following along.

Create a sketchplanation

The key is endarkening edges where you can’t see both sides. And maybe a little more on the bottom for solidity. That’s about it.

Draw iconic objects

Draw a grey nurse shark

Use white space with care to make your point

I figured this out while trying to draw one. The epiphany was noticing that the s-line in the centre is uninterrupted but part of two chain links. Neat.

Drawing sketches