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Colour.rst

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Colour

Curv provides operations for constructing colour values, displaying colours on the screen, and applying colours to geometric shapes.

For example:

  • red is a colour value.
  • show_colour red displays the colour red in the graphics window.
  • cube >> colour red is a red cube.

Colour Spaces

A colour space maps a set of coordinates (usually called R, G and B) onto a set of absolute, colorimetrically quantified colours. Each Curv colour value is constructed using a specific colour space, and denotes an absolute colour.

The gamut of a colour space is the set of absolute colours it contains. The gamut of most popular colour spaces is smaller than the set of colours that can be perceived by the human visual system.

The sRGB colour space has been the industry standard for the computer graphics industry for many years. It's the colour space of most older monitors. It's the default colour space for images and for the world wide web.

Newer displays support larger colour spaces with wider gamuts than sRGB. Newer Apple products support the DCI-P3 colour space, and the Rec.2020 colour space in the UHDTV standard is even larger.

For now, Curv only supports sRGB. However, support for other colour spaces is planned, both to fully support modern display hardware, and to accurately describe and display coloured shapes intended for 3D printing, since colour 3D printers have very different gamuts and colour spaces than display hardware.

Colour spaces are represented by Curv values. For now, we just have one such value, called sRGB.

Constructors

High level operations for constructing colour values.

sRGB [r,g,b]
Construct a colour value using red, green and blue coordinates in the sRGB colour space. Each colour component is in the range 0 to 1.
webRGB [r,g,b]
Another way to specify sRGB colours, where the colour components are in the range 0 to 255. A web colour like PeachPuff (#FFDAB9 or rgb(255,218,185)) can be transcribed in Curv like this: webRGB[0xFF,0xDA,0xB9] or webRGB[255,218,185].
sRGB.hue h

A hue is a pure colour with no white or black mixed in. sRGB.hue is a colour map that can construct any of the hues in the sRGB colour space. h is a number between 0 and 1:

0 red -- the red primary of the sRGB colour space
1/12 orange
1/6 yellow
1/4 chartreuse
1/3 green -- the green primary of the sRGB colour space
5/12 spring green
1/2 cyan
7/12 azure
2/3 blue -- the blue primary of the sRGB colour space
3/4 violet
5/6 magenta
11/12 rose
1 red
sRGB.grey i
A greyscale colour map containing all of the neutral colours in the sRGB colour space. i is between 0 and 1, where 0 is black and 1 is white.
sRGB.HSV [hue,saturation,brightness]

HSV (also known as HSB) is a popular colour model supported by many graphics languages. sRGB.HSV is a more user-friendly way to specify sRGB colours. The three arguments are:

hue
A number between 0 and 1, specifying a hue (a pure colour). See sRGB.hue.
saturation

Saturation is the distance from a neutral colour (white/grey/black), in the range 0 to 1. Turning down the saturation leaches out the hue and brings the colour closer to neutral.

  • A saturation of 0 constructs a neutral greyscale colour based on the brightness, ignoring the hue. So sRGB.HSV[h,0,b] is white if b==1, medium grey if b==0.5, and black if b==0.
  • A saturation of 1 constructs a "shade" (a mixture of a pure colour and black), where hue is the pure colour, and brightness is the distance from black.
brightness

Brightness (aka "value") is the distance from black, from 0 to 1. Turning down the brightness makes the colour dimmer and closer to black.

  • If the brightness is 0, then the resulting colour is black, ignoring the hue and saturation.
  • A brightness of 1 constructs a "tint" (a mixture of a pure colour and white), where hue is the pure colour, and saturation is the distance from white.

For convenience, there is a limited set of predefined sRGB colour names:

  • red
  • yellow
  • green
  • cyan
  • blue
  • magenta
  • white
  • black

Applying Colours to Shapes

show_colour colour
Display colour in the graphics window.
colour colour shape
Apply a colour to a shape.

Internal Representation (Linear RGB)

A colour value is an [R,G,B] triple, where:

  • The R, G and B components represent the linear intensity of red, green and blue light in the colour. This is different from sRGB, which uses a non-linear encoding.
  • Each component is a number between 0 and 1 inclusive.

This representation (called linear RGB) is a low-level representation that is useful internally, for mixing colours and performing computations within the 3D lighting model.

The actual colour space that gives meaning to these coordinates is defined by the rendering environment. You should use high level operations to construct colour values, and not try to create linear R,G,B triples by hand.

Future Work

  • Add the LAB and HCL colour spaces. These are perceptually uniform colour spaces, useful for interpolation and generating colour sequences.
  • Add sRGB.HWB colour space. It's the best RGB based colour space for colour picking by artists.