What is a LUT?
A LUT, or lookup table, describes how to convert a set of values into another set of values. In the case of professional film and video applications, a LUT describes how to convert RGB values into other RGB values. A LUT is applied globally to an image and does not contain information for position-based corrections such as vignettes or local contrast enhancement. Generally a LUT doesn't contain an entry for every possible color value, so software and hardware that support them use various interpolation algorithms to provide a "best guess" for values that aren't explicitly defined in the table.
A 1D LUT is a set of 3 one-dimensional lookup tables. The tables are lookups for the red, green, and blue color channels. Transformations for each color channel are independent of each other. For example, a red color value cannot be transformed based its corresponding green or blue color values (a 3D LUT can do this, however). A 1D LUT cannot perform hue or saturation adjustments of any kind. The RGB curves tool in Photoshop, Lightroom, Resolve, or any other professional image correction application is a good example of the capabilities of a 1D LUT.
1D LUTs are often used for situations where high-precision is needed. Uses include curve adjustments, ASC CDL application (without saturation), white point adjustment, and transforming high dynamic range scene-linear material (usually from an OpenEXR image container) into camera log or display-referred material. Most software and hardware solutions utilize linear interpolation when interpreting 1D LUTs.
A 3D LUT is a three-dimensional lookup table. Transformations for each color channel can be co-dependent. For example, a red color value can be transformed based on its corresponding green or blue color values. Because of this, global and selective hue and saturation adjustments are possible. Any color grading tool in Resolve that doesn't involve position-based transformations (vignettes, power windows, etc.) can be preserved in a 3D LUT.
3D LUTs are used for a mix of technical and creative purposes. Because of their ability to change hue and saturation, many professionals use them for colorspace conversions, film print stock emulation, and communicating color grade looks across platforms. Due to the increased amount of data required in a three-dimensional lookup table, the size of 3D LUTs are generally no higher than 65x65x65. Because of their low precision, they are not very useful for transforming high dynamic range scene-linear material. Most software and hardware solutions utilize trilinear interpolation or tetrahedral interpolation when interpreting 3D LUTs.