Strict definition

A colormap^[4] is a function which associate a real value r with point c in color space ${\displaystyle C}$

${\displaystyle f:[r_{min},r_{max}]\subset \mathbf {R} \to C}$

which is defined by:

• a colorspace C
• an increasing sequence of sampling points ${\displaystyle r_{0}<...<r_{m}\in [r_{min},r_{max}]}$
• a series of values in the colorspace ${\displaystyle c_{0},...,c_{m}\in C}$
• the mapping ${\displaystyle f(r_{i})=c_{i},i=0,...,m}$
• a rule for interpolating the intermediate values ${\displaystyle r_{i-1}<r<r_{i}\in [r_{min},r_{max}]}$

where:

• r is a real number ${\displaystyle r\in [r_{min},r_{max}]\subset \mathbf {R} }$
• ${\displaystyle \mathbf {R} }$ is a set of real numbers
• c is a color = point in colorspace C

Dimension

• 1D
• 2D:^[7] Multivariate map, bivariate or trivariate
• 3D

Shapes

Axial gradients

An axial color gradient, with a white line segment connecting the two points

An axial color gradient (sometimes also called a linear color gradient) is specified by two points, and a color at each point. The colors along the line through those points are calculated using linear interpolation, then extended perpendicular to that line. In digital imaging systems, colors are typically interpolated in an RGB color space, often using gamma compressed RGB color values, as opposed to linear. CSS and SVG both support linear gradients.^[8][9]

Radial gradients

A radial color gradient

A radial gradient is specified as a circle that has one color at the edge and another at the center. Colors are calculated by linear interpolation based on distance from the center. This can be used to approximate the diffuse reflection of light from a point source by a sphere. Both CSS and SVG support radial gradients.^[10][11]

Conic gradients

conic gradient

Conic or conical gradients are gradients with color transitions rotated around a center point (rather than radiating from the center). Example conic gradients include pie charts and color wheels.^[12] Conic gradients are sometimes called "sweep gradients" (for example in the OpenType specification) or angular gradients.

Color space

• 
  LCH
• 
  HSV

HSV rainbow

• HSV rainbow
• 
  RGB 2D profiles
• 
  HSV 2D profiles
• 
  3D RGB profile