Perception & Depth

Imagine you are looking at an object through a camera. The image you see doesn't look flat but rather like a 3D object being viewed on a 2D display. That's what a 3D projection is — a technique to display a 3D object on a 2D surface. Camera in this context refers to the point of view.

There are two main types of projection — parallel and perspective. The parallel projection is formed by extending parallel lines from each vertex of an object until these lines intersect the plane of the screen. In the parallel projection, we specify a direction of projection instead of the center, which allows preserving scale and shape. For example, if you project a cube, its parallel sides appear as parallel.

In turn, there are various types of parallel projections. In the orthographic projection, the direction of the projection is perpendicular to one of the coordinate planes. The three types of orthographic projections are the front, the top, and the side projections, which give us 3 respective primary views, allowing us to see one face of an object at a time.^[1]

The isometric projection is another type of parallel projection. With its help, we can see three planes of an object at once. The projection plane intersects each coordinate axis in the model coordinate system at an equal distance. In this projection, the parallelism of lines — not angles — is preserved. The isometric projections are particularly useful for displaying conceptual design features on paper and communicating those features to others.

In the real world, parallel lines converge as they get farther from the viewer, like a road going to the horizon. To replicate that, we use perspective projection, where the distance and angles are not preserved, and parallel lines do not remain parallel — instead, they converge at the center of the projection. The perspective projection depends on the relative position of the eye and the view plane. This projection includes one-point, 2-point, and 3-point perspective projection types, each defined by the number of vanishing points.^[2]

A vanishing point, or direction point, is a point on the image plane where parallel lines in 3D space appear to converge. If you have ever stood on train tracks and looked along them, you may have noticed that they seem to meet at the horizon.

In graphic editing and video games, the vanishing point perspective is used to render 3D shapes like buildings and objects, add depth to background scenes (such as roads or train tracks), and create realistic shadow effects.

In the real world, when you focus a camera on a subject in the middle distance, the background and foreground go out of focus. This effect is called the depth of field or DOF, which makes 3D scenes look more realistic. Also, changing the depth of field allows you to divert the audience's attention to a different subject without even moving your camera.

Another way to add depth is stereoscopy. It works by presenting a slightly different 2D image to each eye, and two images are then combined in the brain to give the perception of depth. However, it has its downsides as the focus is not duplicated, and the image separation is not always perfect, so it doesn't look completely natural for the human eye.^[3]

Anaglyph is a type of stereoscopy that uses filters of different colors, typically red and cyan, to encode distinct images for each eye. The viewer needs glasses with lenses in the same colors to filter out the unwanted image. As a result, the brain sees two different pictures through each eye and interprets them as a three-dimensional scene.^[4]

Motion in film and video games is an optical illusion. It's created by composing a series of still images into a complete moving picture seen from a fixed camera, creating the perception of movement. A frame is one of the many still images that make up the complete moving picture.^[5]

So, how fast do the frames need to change to create the illusion of motion? The science says that 16 FPS (frames per second) is enough. Use fewer, and the brain will perceive them as a series of discrete images displayed one after the other. More frames, the better the illusion works.

For example, the standard frame rate is 24 FPS for cinema and 30 FPS for television. It can go over 100 FPS for games, depending on the graphics engine, as they often need to display objects moving at high speed.^[6]