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

It’s pretty hard to get to grips with the scale of the solar system. It's really, really, really big.

To help process the vast distances within our system, astronomers use Astronomical Units where 1 AU is the distance of Earth from the Sun. If you see Venus in the night sky, our closest neighbour just 0.7 AU from the sun, it looks impossibly far away. But the further out you go, the more the distances multiply.

Earth and Venus are practically on top of each other compared to Uranus and Neptune. Neptune is a full 30 times the distance between Earth and the Sun.

Now think about the fact that our little solar system is over 250,000 AUs from our nearest star, which is, in turn, just one of many tucked away in a small corner of the Milky Way, which is only one of many galaxies that make up the known universe.

James O'Donoghue has made some brilliant videos about the solar system that explain this and more.

This sketch, and plenty more in the Starry-eyed Surprises section, features in my book Big Ideas Little Pictures

Solar system planets — distances to scale

Astronauts returning from space have repeatedly shared experiences like this:

“You develop an instant global consciousness, a people orientation, an intense dissatisfaction with the state of the world, and a compulsion to do something about it. From out there on the moon, international politics look so petty.”— Edgar Mitchell, Apollo 14 astronaut

“When we look down at the earth from space, we see this amazing, indescribably beautiful planet. It looks like a living, breathing organism. But it also, at the same time, looks extremely fragile … Anybody else who’s ever gone to space says the same thing because it really is striking and it’s really sobering to see this paper-thin layer and to realize that that little paper-thin layer is all that protects every living thing on Earth from death, basically. From the harshness of space.”— Shuttle/ISS astronaut Ron Garan

The overview effect, coined by Frank White, is kind of the mother of seeing the forest for the trees. It’s the realisation that we live on a fragile planet, we are all connected, and this is all we’ve got.

The sketch is based on the image of earth from the moon taken on the Apollo 11 mission.

The overview effect

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 Rashomon effect is the name given to situations where people give mutually contradictory versions of the same event. 

Named after the 1950’s Japanese film Rashomon—widely seen as a masterpiece—which hinges on four conflicting descriptions of the same incident.

Also commonly seen on the football field by coaches after the game.

The Rashomon effect

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

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

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

Sometimes see the good in what you have come to resent.

Perspective sketches