Fields

Overview

Any single point in the 3D world is filled with an infinite number of measurable quantities, such as temperature, pressure, humidity, luminous flux, magnetic flux, and so on. Fields are essentially a function with spatial and/or temporal support that is continuously defined across all points in that support. This is a broad definition and in fact, fields or field-like structures are used across many disciplines, such as meteorology, electrical engineering, and so on. Even audio is a type of field since it is defined over a temporal domain.

Mathematics of fields

The backbone of a field is the plenoptic function. Plenoptic stems from the Latin word plenus, meaning complete or full, and optic, meaning relating to vision. The plenoptic function defines a mapping between locations defined in space or time and some output value.

We will define this more concretely using an example that will be useful for representing 3D scenes: light transport. Imagine if we had an instrument that could allow us to record the flow of light through any point in 3D space and convert that to an RGB color. Such a function might take the following form: